Superconductivity

Superconductivity

If mercury is cooled below 4.1 K, it loses all electric resistance. This discovery of

superconductivity by H. Kammerlingh Onnes in 1911 was followed by the observation of

other metals which exhibit zero resistivity below a certain critical temperature. The fact that

the resistance is zero has been demonstrated by sustaining currents in superconducting lead

rings for many years with no measurable reduction. An induced current in an ordinary metal

ring would decay rapidly from the dissipation of ordinary resistance, but superconducting

rings had exhibited a decay constant of over a billion years! One of the properties of a

superconductor is that it will exclude magnetic fields, a phenomenon called the Meissner

effect.The disappearance of electrical resistivity was modeled in terms of electron pairing in

the crystal lattice by John Bardeen, Leon Cooper, and Robert Schrieffer in what is commonly

called the BCS theory. A new era in the study of superconductivity began in 1986 with the

discovery of high critical temperature superconductors.

History of Superconductivity

Before you hear Bob Schrieffer tell about some of the highlights

of the work he did with John Bardeen and Leon Cooper - work

that led to an explanation of superconductivity — I want to tell

you a bit about superconductivity and why their achievement was

one of the major scientific events of the 20th century.

First of all: what is superconductivity? It's an absolutely

remarkable phenomenon discovered in 1911 by a student working

with the famous Dutch scientist, Kamerlingh-Onnes. Kamerlingh-

Onnes pioneered work at very low temperatures — temperatures

just a few degrees above the absolute zero of temperature. He

succeeded in reaching temperatures much colder than anyone

before him, and thus opened a new frontier for science — a field

of science previously unexplored, the field of low temperature physics.

He and his students set to work to study what happened to various properties of materials

when they were that cold. One of his students was studying the electrical resistance of wires.

He found that as he cooled mercury wire the electrical resistance of the wire took a

precipitous drop when he got to about 3.6 degrees above absolute zero. The drop was

enormous - the resistance became at least twenty thousand times smaller. The drop took place

over a temperature interval too small for them to measure. As far as they could tell, the

electrical resistance completely vanished.

Charlie Slichter

To test for the complete vanishing of the electrical resistance,

Kamerlingh-Onnes devised an ingenious experiment. He took a

closed circle of mercury wire and caused a current to flow around

the circle. With his experimental arrangement one would expect

ordinarily that resistance would cause the current to die out

quickly, much as friction and air resistance cause a bicycle

coasting on a level road to come to a stop. He found that for a

loop of mercury wire the current, once started, would persist for

as long as the wire was kept cold. The persistence of the electrical

current in the circuit is a kind of perpetual motion — it's a totally

startling phenomenon for physicists.

Physicists understand quite well why an ordinary metal resisted

the flow of electric current — why, so to speak, the electrons experienced friction in flowing

through a conductor — yet something must go wrong with those ideas when the metal

becomes superconducting, in order to allow the persistent seemingly-frictionless flow of

current in the superconductor.

The general picture scientists had was that the resistance arises because moving electrons —

which are what produce the electric current — from time to time bump into the atoms of the

metal and are deflected. Thus, though they may be given an initial motion through the crystal,

that motion does not persist. It's like trying to throw a baseball through a grove of trees. It

bounces off the trees and comes to rest. The vanishing of electrical resistance seems

analogous to requiring that the grove of trees vanish — and explaining superconductivity is

like explaining why the grove appears to vanish. Remember, it's not fair for physicists to take

magic as a reason! The fact is that below a certain temperature many metals enter into a new

state of matter: the superconducting state. Just suppose you knew water only as a liquid - how

curious you'd be when you discovered its transition into a new state of matter: ice.

You can well imagine that the explanation of this phenomenon of persistent current

challenged the very best theoretical minds. Yet superconductivity remained an enigma for

decades. Many of the world's greatest scientists tried to solve the mystery of the perpetual

motion, but without success - at least five Nobel Prize winners. John Bardeen tried

unsuccessfully shortly after finishing graduate school. [Bardeen talks about this here.] Even

while working on semiconductors - and sharing in the discovery of the transistor - the

challenge of superconductivity kept nagging at him in the back of his mind.

There was really no chance for any of the theorists to solve this problem at the time of

discovery because before one could explain it, one had to have the quantum theory in the

form that Schrödinger and Heisenberg developed, which didn't take place until the 1920's.

For a long time the phenomenon of superconductivity was characterized by the statement that

the electrical resistance vanished completely.

H. Kamerlingh-Onnes

However, in 1933 Meissner and Ochsenfeld discovered another

property of superconductors, which is in fact believed by many to be

an even more basic characterization. This phenomenon, which is

popularly called the Meissner effect, has to do with the magnetism

of a superconductor. You're no doubt familiar with the fact that iron

has remarkable magnetic properties. Iron tends to draw to it the lines

of magnetic force of a magnet. That's why iron is often used to make

electromagnets. It helps to guide the magnetic lines of force around

in space where you wish to have them. The superconductor is just

the opposite. It's what is called a perfect diamagnet. A

superconductor excludes the lines of magnetic force. If you bring a

small bar magnet up to a superconductor, the superconductor bends

the lines of force away from it and doesn't allow them to penetrate.

Around 1935 another important theoretical advance in understanding superconductivity was

made by Fritz London and his brother Heinz. In an ordinary metal we describe the

phenomenon of electrical resistance by the famous Ohm's law. What the London brothers did

was to show that there was another mathematical relationship which should be used in place

of Ohm's law to describe superconductors. From this other relationship which they

developed, they were able to explain both the Meissner-Ochsenfeld experiment as well as the

persistent current of Kamerlingh-Onnes as two manifestations of the same thing.

I suppose in some ways the single most important experiment which directly played a role in

guiding the way to an explanation of superconductivity was the experiment on the "isotope

effect." This occurred in 1950 and, as so often happens in science, papers from two

laboratories simultaneously revealed the same results. One paper told of the work of

Reynolds, Serin, Wright and Nesbitt at Rutgers [University]. The other was by Maxwell

working at the [National] Bureau of Standards.

You know that the same chemical element may come with different nuclear masses - so-

called isotopes. What these workers did was to prepare samples of material - in this case

mercury - with their isotopic masses varying by a few percent between different samples.

They found that the critical temperature for the superconducting transition was lower in the

sample which had the higher isotopic mass. In fact the critical temperature was inversely

proportional to the square root of the average isotopic mass of the substance. Well, this tells

you that the mass of the nuclei was playing some role in the phenomenon of

superconductivity.

Physicists are quite familiar with expressions which involve the square root of a mass.

Suppose you think of a spring with a mass attached to it. If you give the mass a little push it

will vibrate and the frequency of that vibration goes inversely with the square root of the

mass. You may wonder what a mass and a spring has to do with superconductivity. Well, the

connection is simple. If you want to have a simple picture of a solid you might think of it as a

regular array of atoms - for example, think of a jungle gym and think of the intersections of

the points on the jungle gym as representing the positions of the atom. In a jungle gym the

joining points of course are rigidly spaced apart by the rods of the jungle gym, but in a solid

it's probably a better approximation to think that the atoms which are joined together are not

rigidly attached, and in fact the distance between them can be varied a little bit if you squeeze

on the solid or pull on it. It's probably a good approximation to think of the solid as consisting

of a bunch of masses - the masses of the atom - joined together by a set of springs. If you

Walther Meissner

think of the solid in this manner then you realize that if you gave the solid a little poke you

would set all those masses jiggling and all the springs vibrating. In any ordinary solid, this

kind of jiggling phenomenon is always present unless you are at absolute zero. It goes by the

name of the lattice vibrations.

So what the isotopic experiments we've just talked about showed was that although the

electrical conductivity was known to arise because of the motion of the electrons, there's

some role of these lattice vibrations. They enable the electrons suddenly to move through the

lattice, evidently without hindrance, when the sample is cooled to the critical superconducting

temperature.

The next big experimental discovery was done by two groups: Goodman, who was making

thermal conductivity experiments, and Brown, Zemansky and Boorse, who were making

specific heat measurements. They discovered what is called the energy gap. I must confess

that I find explaining the energy gap the most difficult part of the explanation of

superconductivity. You have to be patient with me while I back up a bit to get us all together

in our concepts.

You're all familiar with the way in which one builds up the periodic table by adding electrons

to an atom. As one does this, one thinks of orbits of an atom which one fills with electrons.

The unique chemical properties are associated with the extent to which an orbit is full or

empty. Here the electrons can go only into certain orbits and only one electron can go into

any given orbit. This exclusive property of electrons was first noted by Wolfgang Pauli, after

whom the phenomenon is named: the Pauli Exclusion Principle. It's of great importance

throughout all of physics and it plays an important

role in understanding superconductors.

Now, when we talk about a metal and we think of

putting the electrons in it, we can get a pretty good

picture if we think of those electrons as bouncing

around inside the metal - the metal being, so to

speak, like a box. We can think of the electrons

very much as we think of the atoms of a gas which

are bouncing around inside whatever container the

gas is in. In an ordinary classical view of the world

- the way people thought before the quantum

theory was discovered - we would say that if we

got the metal very cold, the electrons would be

moving around rather slowly, and in fact they'd

come to rest when one got to absolute zero. That

would be a proper description of things were it not for the Pauli exclusion principal. The fact

is that when electrons are in a metal, they can possess certain orbits in much the same way as

electrons in an atom can possess only certain orbits. One way of thinking about these orbits is

that some electrons move slowly, some move somewhat faster and some move even faster.

The orbits which are possible can be specified by the speed and the direction in which the

electrons are allowed to move. If we then start putting electrons into a metal to achieve the

situation at absolute zero, the first electron we would put in would go into the lowest energy

orbit, the next would go into a somewhat higher energy orbit, and so on until we had put in

the proper number of electrons. Those last ones we put in have a good deal more energy than

Wolfgang Pauli

the first ones. The energy which they have relative to the first one is commonly called the

"Fermi energy," after Enrico Fermi who first calculated its value.

Now, suppose we think about what happens in this metal if we were to heat it a bit above the

absolute zero. When you heat something, you give a little more energy to all its parts. The

electrons are no exception. Think of one of those electrons which initially has a rather low

amount of energy. Of course, if you try to give it more energy it has a problem, because the

orbits of somewhat higher energy are already occupied by other electrons, and the Pauli

Principle does not let this electron switch over into an orbit which is already occupied. This

same argument applies to most of the electrons. But now let's talk about those electrons

which have the Fermi energy - that is to say, they were the last ones to get added into the

energy states and the ones therefore which are moving around most rapidly. Those electrons

have nearby energy orbits which are not occupied by electrons. So if you heat the metal, they

are free to speed up a little bit and thus go into an orbit which is just a bit above the orbit in

which they used to be. There is in fact a continuous set of energies available to those

electrons at the Fermi energy, so they can gradually add energy as the metal is warmed.

This brings us to the point of the energy gap. Suppose instead of having the situation I've just

described in which one could give those electrons of the Fermi energy just a little bit more

energy, suppose they had to pay, so to speak, an entrance fee to gain energy. Suppose there

weren't any states which were available close by. Suppose you had to give them a really large

chunk of energy before their motion could change. Then one has described what is called a

gap in the spectrum of the possible energy states. This is the situation which exists in

superconductors. This energy gap was discovered in the experiments of Goodman on thermal

conductivity and Brown, Zemansky and Boorse on specific heat. The experimental evidence

was clear.

It was in the early 1950's when John Bardeen decided to work again on the problem of

superconductivity. By then some more clues had been found, but I won't explain them since it

would take too long. But, although scientists had accumulated a number of facts about the

new state of matter, no one had been able to put it all together and provide a theoretical

explanation for it.

Now, let's go back a bit to the discovery of the

isotope effect in 1950. When John Bardeen heard

about it, he was stimulated to work again on the

problem of superconductivity. He had in fact

worked on it at various earlier times and always

kept it in the back of his mind. Meanwhile, the

British physicist Fröhlich was very interested in

superconductivity. He'd not known about the

isotope effect, but he guessed that lattice vibrations

might play a similar role. At the same time,

Bardeen and Fröhlich independently put forward

theories of superconductivity which later on turned

out to be incorrect. However, both of them said

they thought an essential portion of the problem

had to do with what happened to the electrons whose energy was equal to the Fermi energy.

Bardeen is such a great physicist that even when he's wrong, to some extent, he is still right

for the most part. That's what we mean when we say a physicist has great physical intuition.

John Bardeen

After these theories proved to be unsuccessful, Bardeen went back to work on further aspects

of superconductivity to try to take the problem apart more thoroughly. At this point Bardeen

had come to the University of Illinois from Bell Laboratories, where he, William Shockley

and Walter Brattain had invented the transistor. By the way, these three men won the Nobel

Prize for that invention in 1956, and in Bob Schrieffer's tape you'll notice the reference to

Bardeen going off to Stockholm to receive the Prize. Bardeen was jointly a professor of

physics and a professor of electrical engineering at the University of Illinois at Urbana.

There, with David Pines, he studied the details of the interactions of the electrons with the

lattice vibrations and with one another.

At this point Bardeen proved a tremendously important theorem. He said: suppose we

consider that a superconductor is nothing but a normal metal in which we have introduced an

energy gap. That is to say - instead of having some states which we know are present in a

normal metal, slightly higher in energy than the energy of the electron with the Fermi energy,

one would simply omit those orbits from the calculations and proceed from there. Bardeen

then analyzed what happened to that metal when a magnetic field was applied to it. He

succeeded in showing that he was able to derive an equation very similar to the London

equation, describing the exclusion of a magnetic field by a superconductor. Bardeen made the

statement at that time that if one could find the reason for the energy gap, one would very

likely have the explanation of superconductivity. It's clear when one considers the papers

Bardeen was writing and the thinking he was doing at that time that he was very close to the

solution of the problem of superconductivity.

He had a very deep and intuitive feeling for exactly what was taking place. He knew it

involved an energy gap. He knew it involved the interactions of the electrons with the lattice.

There was one other thing which he knew as well, and that is that superconductivity is a

phase transition of a very special kind, a type which is called a condensation in velocity or

momentum space.

So now I want to explain just what we mean by such a condensation. I can't help but thinking,

however, that you are sitting there scratching your head and feeling, oh boy, there sure are a

lot of explanations involved in superconductivity! The fact is that this is a tough subject and

you're beginning to get a feel for why it is that people like Niels Bohr, Felix Bloch, Richard

Feynman, Werner Heisenberg, Lev Landau, the Londons, and others who are just brilliant

physicists worked on this problem all those years and in fact didn't succeed in cracking the

problem. Well, it's difficult, and that's why we find that even an effort at an elementary

description of what happened is a pretty tough thing to listen to as well.

Phase transitions are something that we're all familiar with. I suppose the most common ones

we all know are the melting of snow or ice or the vaporizing of water into steam. Now,

usually when we think about phase transitions, we think about condensation in real space. To

illustrate that - in the summertime we've all had the experience that if you have a drink with

ice in it, water condenses on the outside of the glass. That's why people use coasters. What's

involved is simply that the water vapor which is always present in the air is no longer

permitted to remain there when it's in contact with something that is as cold as the surface of

the glass, and the water molecules prefer to gather together to form the droplets of liquid on

the cold surface of the glass. That's an example of a condensation - condensation in real space

- that is to say, the molecules physically come together to form little droplets of water.

Almost all the time when physicists think about condensation, they naturally revert to

condensations in real space.

But the kind of condensation which is important for superconductivity is the condensation in

another sort of space; it is the condensation in what one could call "velocity space." This is a

slightly abstract idea, but there are very concrete ways to illustrate it. What is meant by a

condensation in velocity space is that a whole bunch of objects assume nearly the same

velocities. Contrast that with a condensation in real space where they assume nearly the same

positions. To visualize a condensation of velocities think for example of a playground with a

whole bunch of children playing in all different portions of it, running back and forth and

scattered around on the playground. Suppose the bell rings signifying that recess is over.

Then all the children suddenly start running towards the doorway from all over the

playground. What happens is that, although their positions are scattered, suddenly they're all

running in the same direction. They have nearly the same velocity. Note that you can

condense their velocities without condensing their positions. Think of another example -

think of the cars driving along a superhighway, which by and large they do at the speed limit.

All up and down the superhighway there are automobiles miles apart all going the same

direction at the same speed, and as different cars enter the superhighway from the entrance

ramps, they pick up speed until they're driving at the speed limit. And thus we see a

condensation of velocity even though the positions are widely separated. When you think

about an east-west highway you might say that the velocity of the cars are condensed at two

particular points in velocity space, namely the speed limit going east and the speed limit

going west. That is the kind of condensation that takes place in superconductivity. The

electrons condense in velocity space. The fact that this condensation takes place in velocity

space was first recognized by Fritz London, who pointed out that this was almost surely

involved in superconductivity.

That then represented the situation in the knowledge of superconductivity when Bardeen,

Cooper and Schrieffer got together at the University of Illinois. There were three critical

elements — 1: there was a condensation in velocity space; 2: there was an energy gap; and 3:

the interactions of the conduction. electrons with the lattice vibrations were evidently critical

in making the phenomenon occur.

I have to count it as one of the luckiest things in my life that I happened to be working as an

experimenter in the field of superconductivity here at the University of Illinois back in 1955

to '57, just at the time that Bardeen, Cooper, and Schrieffer were working on the explanation

of superconductivity. Bardeen's theoretical work in the early 1950's had stimulated my

student Chuck Hebel and me to undertake a new kind of experiment on superconductivity.

Our results were surprising, and we'd been to John to talk about them. And then, one day

early in 1957, John Bardeen stopped me in the hall of the physics building. And it was clear

he wanted to talk. He seemed to stand there almost for hours before he spoke. He's a quiet

and a modest man. And then he said, "Well, I think we've finally figured out

superconductivity." This was one of the great scientific announcements of the century. I may

have been the first person apart from the three of them to know they'd actually solved it. You

can imagine how excited I was!

I'd like to tell you just a few things about this trio that

cracked the problem of superconductivity. John

Bardeen came to Illinois in the early 1950's from Bell

Laboratories where he, Walter Brattain, and William

Shockley invented the transistor. Leon Cooper had

recently completed his PhD, in a totally different area

of physics, and in the process he'd learned a set of

mathematical techniques for what is called quantum

field theory. He'd become quite expert in this and was

viewed as one of the best young men in that general

area. Bardeen felt it might be important to know these

techniques in order to tackle the problem of

superconductivity. So he invited Cooper to come to

Urbana from the Institute for Advanced Study in

Princeton. You could say Bardeen called in a quantum

mechanic from the East.

Now, the first major breakthrough this trio made in

superconductivity came from Leon Cooper. Scientists

often crack a tough problem by judiciously unraveling one part of the mystery at a time.

Here's where the role of judgment and physical intuition is paramount. You've got to decide

which piece to tackle. Experiments on thermal conductivity and heat capacity had shown that

superconductors had what is known as an energy gap. Bardeen's own work had shown that if

one could understand why there was an energy gap, one would most likely be close to the

heart of the explanation of superconductivity. Cooper set about trying to explain the existence

of the energy gap.

Meanwhile, Bob Schrieffer was at the University of Illinois

as a graduate student. He had completed his undergraduate

studies at MIT, working in a group of solid state physicists.

When he reached graduation time, he decided that the man

he'd most like to do his graduate work with was John

Bardeen. Schrieffer began to work with Bardeen. As a

warm-up, Bardeen suggested some work on

semiconductors. When it came time for a thesis, Schrieffer

chose to work on superconductivity. Bardeen suggested he

familiarize himself with the theoretical work Keith

Brueckner had recently done on the nuclei of atoms. Nuclei,

like metals, consist of many particles close together

interacting strongly, so Bardeen hoped that theoretical

methods helpful to nuclear physicists might help on the

problem of superconductivity. Actually this tack did not

lead Schrieffer to anything useful.

Leon Cooper was making an effort to find out why there

was an energy gap. Now, I should point out to you that if you start with a system which

represents a normal metal, and you introduce some sort of interaction which is going to cause

the transition to a superconductor, it's not easy to find a situation in which a gap of energy

occurs. So Cooper studied the general theories of quantum mechanics to see under what

circumstances gaps arose. He decided to pick a highly simplified physical model of the

Leon Cooper

J. Robert Schrieffer

system, because a real metal has many electrons in it, and the fact there are so many particles

interacting presents overwhelming complexities. He found a very clever way of simplifying

this problem. He said: let's just consider the interactions of two electrons. Now all the other

electrons are present in the problem and we have to take account of them, but he said the

most important thing which they did was to occupy all the low energy states - that is to say

the states which were filled up to the Fermi energy. Since those electrons are occupying those

states, those states were not available in any way for the two electrons whose interactions he

wished to study.

He then examined what happened to these two electrons, taking into account two aspects

which Pines and Bardeen had delineated. The first was that the electrons repelled one

another, because they're particles of the same charge. The second thing was that the electrons

are moving through this lattice, which contained the positive nuclei with their masses kept

apart by their springs. As we mentioned previously, it's not proper to think of the lattice as

being totally rigid. Instead, when you bring an electron in between two of the positive ions,

these ions are attracted to the electron and thus pull somewhat closer together than they

would be if the electrons were not there. When one electron was there and the ions pulled

together, it made that point in space somewhat more favorable for a second electron to be

there also. Since the pulling together was due to one electron, one could say that in this way

one had an interaction of one electron with another by means of the lattice, and that the

interaction was energetically favorable - that is to say, it was an attraction.

Cooper succeeded in solving the problem of the electrons interacting in the two ways I've

described. He found that there was a delicate balance between repulsion of the electrons

because they are of the same electrical charge, and the attraction brought about by the lattice

distortions we've just described, and that when the lattice distortion term was somewhat

larger, the two electrons had a net attraction and an energy gap was formed. Thus he was led

to the conclusion that superconductivity arose when the attractive interaction of one electron

for the other, through the lattice, was larger than the direct repulsion. This then became a

criterion for superconductivity. This paper was published in 1956 and is one of the famous

papers in the history of superconductivity. The interacting pairs of electrons have since been

known as "Cooper pairs" after their discoverer.

Important as the step was which Cooper made, one must understand that a large amount of

the problem yet remained unsolved, because he had considered the interaction of only a

single pair of electrons, whereas in a real metal there are many interacting electrons -

something like 1023

.

At this point Bardeen, Cooper and Schrieffer set about trying to generalize Cooper's results to

the problem of many interacting electrons. That is - to make a many-body theory out of it.

Now, the trouble was that when they tried to put together solutions, they would find that

although they could make two electrons interact favorably with one another, quite typically

what that did was to make them interact with a third or fourth electron unfavorably. The

problem is somewhat analogous to one of those complicated three-dimensional puzzles which

one attempts to assemble. When you try to put the puzzle together you may find you may

have a couple of pieces that fit, but then when you try to get the third piece in, it won't fit, and

the two pieces you already have interfere with adding it. What you have to do is find how to

fit those pieces together in just such a way that they all simultaneously go together in a

favorable manner. That was exactly the problem that was posed to Bardeen, Cooper and

Schrieffer.

The break came when Bob Schrieffer succeeded in guessing, in essence, the nature of the

solution at absolute zero. The form of the solution which he found turned out to be especially

simple when expressed in a highly ingenious mathematical form. You can well imagine the

feverish activity which then followed as the three attempted to generalize the solution to the

higher temperatures, and to show that in fact they could account for all of the facts of

superconductivity. Schrieffer in his description tells about their work carrying through to the

final solution. The theory was published in the spring of 1957. This theory accounted for

essentially all of the known experimental facts of superconductivity.

The trio then felt they were hot on the trail. But they still had lots to do. It's like assembling

one of those three-dimensional puzzles. They knew how to handle any two electrons — but a

metal has many more than just two. But within one year they were successful. They

understood that a single Cooper pair was unstable. That is, the other electrons in the

neighborhood would want to pair off, too. At the critical temperature — in their full

explanation — the other electrons all do so. And that constitutes the phase transition from a

normal metal into a superconductor.

How was it greeted? Experimenters greeted the theory with great acclaim, because it had

such success in explaining their experimental results. The theory created a great flurry among

the theorists as well. It's interesting however, and I think it illustrates the true nature of

science, that many of the theorists felt a surge of disappointment that someone else solved

this exciting problem. I remember, in fact, riding in an automobile from New Hampshire to

Boston, returning from a conference on solid state physics. In the car with us was one of the

truly great physicists of the time who'd worked on the problem, and he told of the enormous

disappointment he felt when he found that someone else solved the problem. That led to a

conversation in the car in which various people recollected their reactions. One member of

the group told about a confession made to him by another truly great scientist, who said that

when he first saw the account that Bardeen, Cooper and Schrieffer published saying they had

solved the problem, he looked at it just closely enough to be able to see that it looked right,

but couldn't bring himself to read the paper. He had to wait until one day when he himself

had solved a particularly tough problem, and felt in a real mood of elation, to be able to bring

himself to the point where he could sit down and really seriously study the Bardeen, Cooper,

Schrieffer solution.

But the resistance to the theory was not solely because people were disappointed in not

having solved the problem. When the theory first came out, it had some aspects which people

questioned. But in a short period of time theorists were able to straighten those matters out

and become satisfied that indeed the theory was correct. There's a marvelous quote which

illustrates this, when David Schonberg remarked at the Cambridge [England] conference on

superconductivity in 1959, "Let us see to what extent the experiments fit the theoretical

facts."

One might have supposed that a theory which was as successful as this one would have

closed the field and allowed physics to move on to other things. That was not the case. In fact

the original work of Bardeen, Cooper and Schrieffer has been an enormous stimulus to work

on superconductivity.

In 1972 John Bardeen, Leon Cooper and Bob Schrieffer got the Nobel Prize in physics for

their theory of superconductivity.

Bardeen, Cooper & Schrieffer receiving

honorary

degrees from the University of Illinois, 1974

Superconductivity: So simple, yet so hard to explain!

For half a century the world’s most

brilliant physics theorists tried

scribbling equations, only to crumple

the paper and hurl it at a wastebasket.

Bend a metal wire into a circle, make

it as cold as you possibly can, and set

an electric current moving around it.

The current can persist. Put the circle

of wire above a magnet, and it will

float there until the end of the world.

In the decades after this strange

discovery, physicists figured out the

laws of relativity and quantum

mechanics. They worked out

equations to calculate all the colors

and chemistry of the natural world, they cracked open the atomic nucleus, they uncovered the

forces that light the stars... and still nobody had explained that little floating wire.

This exhibit tells how three extraordinary minds worked together to finally solve the puzzle.

You will see that getting to a new theory may take not just one "Moment of Discovery" but a

string of dozens of such moments among many people. For a personal account, listen to Bob

Schrieffer, the youngest of the team, tell what happened in his own words. To get the full

background, you can read or listen to how a noted physicist saw the story from an outside

perspective. You can also read a detailed account by a historian of physics, and explore other

supplementary materials.

Conductors lose all of their electrical resistance when cooled to super-low temperatures (near

absolute zero, about -273o Celsius). It must be understood that superconductivity is not

merely an extrapolation of most conductors' tendency to gradually lose resistance with

decreasing temperature; rather, it is a sudden, quantum leap in resistivity from finite to

nothing. A superconducting material has absolutely zero electrical resistance, not just some

small amount.

Superconductivity was first discovered by H. Kamerlingh Onnes at the University of Leiden,

Netherlands in 1911. Just three years earlier, in 1908, Onnes had developed a method of

liquefying helium gas, which provided a medium with which to supercool experimental

objects to just a few degrees above absolute zero. Deciding to investigate changes in

electrical resistance of mercury when cooled to this low of a temperature, he discovered that

its resistance dropped to nothing just below the boiling point of helium.

There is some debate over exactly how and why superconducting materials superconduct.

One theory holds that electrons group together and travel in pairs (called Cooper pairs)

within a superconductor rather than travel independently, and that has something to do with

their frictionless flow. Interestingly enough, another phenomenon of super-cold temperatures,

superfluidity, happens with certain liquids (especially liquid helium), resulting in frictionless

flow of molecules.

Superconductivity promises extraordinary capabilities for electric circuits. If conductor

resistance could be eliminated entirely, there would be no power losses or inefficiencies in

electric power systems due to stray resistances. Electric motors could be made almost

perfectly (100%) efficient. Components such as capacitors and inductors, whose ideal

characteristics are normally spoiled by inherent wire resistances, could be made ideal in a

practical sense. Already, some practical superconducting conductors, motors, and capacitors

have been developed, but their use at this present time is limited due to the practical problems

intrinsic to maintaining super-cold temperatures.

The threshold temperature for a superconductor to switch from normal conduction to

superconductivity is called the transition temperature. Transition temperatures for "classic"

superconductors are in the cryogenic range (near absolute zero), but much progress has been

made in developing "high-temperature" superconductors which superconduct at warmer

temperatures. One type is a ceramic mixture of yttrium, barium, copper, and oxygen which

transitions at a relatively balmy -160o Celsius. Ideally, a superconductor should be able to

operate within the range of ambient temperatures, or at least within the range of inexpensive

refrigeration equipment.

The critical temperatures for a few common substances are shown here in this table.

Temperatures are given in kelvins, which has the same incremental span as degrees Celsius

(an increase or decrease of 1 kelvin is the same amount of temperature change as 1o Celsius),

only offset so that 0 K is absolute zero. This way, we don't have to deal with a lot of negative

figures.

Material Element/Alloy Critical temp.(K)

==========================================================

Aluminum -------- Element --------------- 1.20

Cadmium --------- Element --------------- 0.56

Lead ------------ Element --------------- 7.2

Mercury --------- Element --------------- 4.16

Niobium --------- Element --------------- 8.70

Thorium --------- Element --------------- 1.37

Tin ------------- Element --------------- 3.72

Titanium -------- Element --------------- 0.39

Uranium --------- Element --------------- 1.0

Zinc ------------ Element --------------- 0.91

Niobium/Tin ------ Alloy ---------------- 18.1

Cupric sulphide - Compound -------------- 1.6

Superconducting materials also interact in interesting ways with magnetic fields. While in the

superconducting state, a superconducting material will tend to exclude all magnetic fields, a

phenomenon known as the Meissner effect. However, if the magnetic field strength intensifies

beyond a critical level, the superconducting material will be rendered non-superconductive.

In other words, superconducting materials will lose their superconductivity (no matter how

cold you make them) if exposed to too strong of a magnetic field. In fact, the presence of any

magnetic field tends to lower the critical temperature of any superconducting material: the

more magnetic field present, the colder you have to make the material before it will

superconduct.

This is another practical limitation to superconductors in circuit design, since electric current

through any conductor produces a magnetic field. Even though a superconducting wire would

have zero resistance to oppose current, there will still be a limit of how much current could

practically go through that wire due to its critical magnetic field limit.

There are already a few industrial applications of superconductors, especially since the recent

(1987) advent of the yttrium-barium-copper-oxygen ceramic, which only requires liquid

nitrogen to cool, as opposed to liquid helium. It is even possible to order superconductivity

kits from educational suppliers which can be operated in high school labs (liquid nitrogen not

included). Typically, these kits exhibit superconductivity by the Meissner effect, suspending

a tiny magnet in mid-air over a superconducting disk cooled by a bath of liquid nitrogen.

The zero resistance offered by superconducting circuits leads to unique consequences. In a

superconducting short-circuit, it is possible to maintain large currents indefinitely with zero

applied voltage!

Rings of superconducting material have been experimentally proven to sustain continuous

current for years with no applied voltage. So far as anyone knows, there is no theoretical time

limit to how long an unaided current could be sustained in a superconducting circuit. If you're

thinking this appears to be a form of perpetual motion, you're correct! Contrary to popular

belief, there is no law of physics prohibiting perpetual motion; rather, the prohibition stands

against any machine or system generating more energy than it consumes (what would be

referred to as an over-unity device). At best, all a perpetual motion machine (like the

superconducting ring) would be good for is to store energy, not generate it freely!

Superconductors also offer some strange possibilities having nothing to do with Ohm's Law.

One such possibility is the construction of a device called a Josephson Junction, which acts as

a relay of sorts, controlling one current with another current (with no moving parts, of

course). The small size and fast switching time of Josephson Junctions may lead to new

computer circuit designs: an alternative to using semiconductor transistors.

Superconductors

Superconductors, materials that have no resistance to the flow of electricity, are one of

the last great frontiers of scientific discovery. Not only have the limits of

superconductivity not yet been reached, but the theories that explain superconductor

behavior seem to be constantly under review. In 1911 superconductivity was first

observed in mercury by Dutch physicist Heike Kamerlingh Onnes of Leiden University

(shown above). When he cooled it to the temperature of liquid helium, 4 degrees Kelvin

(-452F, -269C), its resistance suddenly disappeared. The Kelvin scale represents an

"absolute" scale of temperature. Thus, it was necessary for Onnes to come within 4

degrees of the coldest temperature that is theoretically attainable to witness the

phenomenon of superconductivity. Later, in 1913, he won a Nobel Prize in physics for

his research in this area.

The next great milestone in understanding how matter behaves at extreme cold

temperatures occurred in 1933. German researchers Walther Meissner (above left) and

Robert Ochsenfeld (above right) discovered that a superconducting material will repel a

magnetic field (below graphic). A magnet moving by a conductor induces currents in

the conductor. This is the principle on which the electric generator operates. But, in a

superconductor the induced currents exactly mirror the field that would have otherwise

penetrated the superconducting material - causing the magnet to be repulsed. This

phenomenon is known as strong diamagnetism and is today often referred to as the

"Meissner effect" (an eponym). The Meissner effect is so strong that a magnet can

actually be levitated over a superconductive material.

In subsequent decades other superconducting metals, alloys and compounds were

discovered. In 1941 niobium-nitride was found to superconduct at 16 K. In 1953

vanadium-silicon displayed superconductive properties at 17.5 K. And, in 1962

scientists at Westinghouse developed the first commercial superconducting wire, an

alloy of niobium and titanium (NbTi). High-energy, particle-accelerator electromagnets

made of copper-clad niobium-titanium were then developed in the 1960s at the

Rutherford-Appleton Laboratory in the UK, and were first employed in a

superconducting accelerator at the Fermilab Tevatron in the US in 1987.

The first widely-accepted theoretical understanding of superconductivity was

advanced in 1957 by American physicists John Bardeen, Leon Cooper, and John

Schrieffer (above). Their Theories of Superconductivity became know as the BCS theory

- derived from the first letter of each man's last name - and won them a Nobel prize in

1972. The mathematically-complex BCS theory explained superconductivity at

temperatures close to absolute zero for elements and simple alloys. However, at higher

temperatures and with different superconductor systems, the BCS theory has

subsequently become inadequate to fully explain how superconductivity is occurring.

Another significant theoretical advancement came in 1962 when Brian D. Josephson

(above), a graduate student at Cambridge University, predicted that electrical current

would flow between 2 superconducting materials - even when they are separated by a

non-superconductor or insulator. His prediction was later confirmed and won him a

share of the 1973 Nobel Prize in Physics. This tunneling phenomenon is today known as

the "Josephson effect" and has been applied to electronic devices such as the SQUID, an

instrument capabable of detecting even the weakest magnetic fields. (Below SQUID

graphic courtesy Quantum Design.)

The 1980's were a decade of unrivaled discovery in the field of superconductivity. In

1964 Bill Little of Stanford University had suggested the possibility of organic (carbon-

based) superconductors. The first of these theoretical superconductors was successfully

synthesized in 1980 by Danish researcher Klaus Bechgaard of the University of

Copenhagen and 3 French team members. (TMTSF)2PF6 had to be cooled to an

incredibly cold 1.2K transition temperature (known as Tc) and subjected to high

pressure to superconduct. But, its mere existence proved the possibility of "designer"

molecules - molecules fashioned to perform in a predictable way.

Then, in 1986, a truly breakthrough discovery was made in the field of

superconductivity. Alex Müller and Georg Bednorz (above), researchers at the IBM

Research Laboratory in Rüschlikon, Switzerland, created a brittle ceramic compound

that superconducted at the highest temperature then known: 30 K. What made this

discovery so remarkable was that ceramics are normally insulators. They don't conduct

electricity well at all. So, researchers had not considered them as possible high-

temperature superconductor candidates. The Lanthanum, Barium, Copper and Oxygen

compound that Müller and Bednorz synthesized, behaved in a not-as-yet-understood

way. (Original article printed in Zeitschrift für Physik Condensed Matter, April 1986.)

The discovery of this first of the superconducting copper-oxides (cuprates) won the 2

men a Nobel Prize the following year. It was later found that tiny amounts of this

material were actually superconducting at 58 K, due to a small amount of lead having

been added as a calibration standard - making the discovery even more noteworthy.

Müller and Bednorz' discovery triggered a flurry of activity in the field of

superconductivity. Researchers around the world began "cooking" up ceramics of

every imaginable combination in a quest for higher and higher Tc's. In January of 1987

a research team at the University of Alabama-Huntsville substituted Yttrium for

Lanthanum in the Müller and Bednorz molecule and achieved an incredible 92 K Tc.

For the first time a material (today referred to as YBCO) had been found that would

superconduct at temperatures warmer than liquid nitrogen - a commonly available

coolant. Additional milestones have since been achieved using exotic - and often toxic -

elements in the base perovskite ceramic. The current class (or "system") of ceramic

superconductors with the highest transition temperatures are the mercuric-cuprates.

The first synthesis of one of these compounds was achieved in 1993 at the University of

Colorado and by the team of A. Schilling, M. Cantoni, J. D. Guo, and H. R. Ott of

Zurich, Switzerland. The world record Tc of 138 K is now held by a thallium-doped,

mercuric-cuprate comprised of the elements Mercury, Thallium, Barium, Calcium,

Copper and Oxygen. The Tc of this ceramic superconductor was confirmed by Dr. Ron

Goldfarb at the National Institute of Standards and Technology-Colorado in February

of 1994. Under extreme pressure its Tc can be coaxed up even higher - approximately 25

to 30 degrees more at 300,000 atmospheres.

In recent years, many discoveries regarding the novel nature of superconductivity have

been made. In 1997 researchers found that at a temperature very near absolute zero an

alloy of gold and indium was both a superconductor and a natural magnet.

Conventional wisdom held that a material with such properties could not exist! Since

then, over a half-dozen such compounds have been found. Recent years have also seen

the discovery of the first high-temperature superconductor that does NOT contain any

copper (2000), and the first all-metal perovskite superconductor (2001).

Also in 2001 a material that had been sitting on laboratory shelves for decades was

found to be an extraordinary new superconductor. Japanese researchers measured the

transition temperature of magnesium diboride at 39 Kelvin - far above the highest Tc of

any of the elemental or binary alloy superconductors. While 39 K is still well below the

Tc's of the "warm" ceramic superconductors, subsequent refinements in the way MgB2

is fabricated have paved the way for its use in industrial applications. Laboratory

testing has found MgB2 will outperform NbTi and Nb3Sn wires in high magnetic field

applications like MRI.

Though a theory to explain high-temperature superconductivity still eludes modern

science, clues occasionally appear that contribute to our understanding of the exotic

nature of this phenomenon. In 2005, for example, Superconductors.ORG discovered

that increasing the weight ratios of alternating planes within the layered perovskites can

often increase Tc significantly. This has led to the discovery of more than 50 new high-

temperature superconductors, including a candidate for a new world record.

The most recent "family" of superconductors to be discovered is the "pnictides".

These iron-based superconductors were first observed by a group of Japanese

researchers in 2006. Like the high-Tc copper-oxides, the exact mechanism that

facilitates superconductivity in them is a mystery. However, with Tc's over 50K, a great

deal of excitement has resulted from their discovery.

Researchers do agree on one thing: discovery in the field of superconductivity is as

much serendipity as it is science. Stay tuned!

Types I and II Superconductors

There are thirty pure metals which exhibit zero resistivity at low temperatures and have the

property of excluding magnetic fields from the interior of the superconductor (Meissner

effect). They are called Type I superconductors. The superconductivity exists only below

their critical temperatures and below a critical magnetic field strength. Type I

superconductors are well described by the BCS theory.

Starting in 1930 with lead-bismuth alloys, a number of alloys were found which exhibited

superconductivity; they are called Type II superconductors. They were found to have much

higher critical fields and therefore could carry much higher current densities while remaining

in the superconducting state.

The variations on barium-copper-oxide ceramics which achieved the superconducting state at

much higher temperatures are often just referred to as high temperature superconductors and

form a class of their own.

Type 1 Superconductors

The Type 1 category of superconductors is mainly comprised of metals and metalloids

that show some conductivity at room temperature. They require incredible cold to slow

down molecular vibrations sufficiently to facilitate unimpeded electron flow in

accordance with what is known as BCS theory. BCS theory suggests that electrons team

up in "Cooper pairs" in order to help each other overcome molecular obstacles - much

like race cars on a track drafting each other in order to go faster. Scientists call this

process phonon-mediated coupling because of the sound packets generated by the

flexing of the crystal lattice.

Type 1 superconductors - characterized as the "soft" superconductors - were

discovered first and require the coldest temperatures to become superconductive. They

exhibit a very sharp transition to a superconducting state (see above graph) and

"perfect" diamagnetism - the ability to repel a magnetic field completely. Below is a list

of known Type 1 superconductors along with the critical transition temperature (known

as Tc) below which each superconducts. The 3rd column gives the lattice structure of

the solid that produced the noted Tc. Surprisingly, copper, silver and gold, three of the

best metallic conductors, do not rank among the superconductive elements. Why is this

?

Lead (Pb)

Lanthanum (La)

Tantalum (Ta)

Mercury (Hg)

Tin (Sn)

Indium (In)

Palladium (Pd)*

Chromium (Cr)*

Thallium (Tl)

7.196 K

4.88 K

4.47 K

4.15 K

3.72 K

3.41 K

3.3 K

3 K

2.38 K

FCC

HEX

BCC

RHL

TET

TET

(see note 1)

(see note 1)

HEX

Rhenium (Re)

Protactinium (Pa)

Thorium (Th)

Aluminum (Al)

Gallium (Ga)

Molybdenum (Mo)

Zinc (Zn)

Osmium (Os)

Zirconium (Zr)

Americium (Am)

Cadmium (Cd)

Ruthenium (Ru)

Titanium (Ti)

Uranium (U)

Hafnium (Hf)

Iridium (Ir)

Beryllium (Be)

Tungsten (W)

Platinum (Pt)*

Lithium (Li)

Rhodium (Rh)

1.697 K

1.40 K

1.38 K

1.175 K

1.083 K

0.915 K

0.85 K

0.66 K

0.61 K

0.60 K

0.517 K

0.49 K

0.40 K

0.20 K

0.128 K

0.1125 K

0.023 K (SRM 768)

0.0154 K

0.0019 K

0.0004 K

0.000325 K

HEX

TET

FCC

FCC

ORC

BCC

HEX

HEX

HEX

HEX

HEX

HEX

HEX

ORC

HEX

FCC

HEX

BCC

(see note 1)

BCC

FCC

*Note 1: Tc's given are for bulk (alpha form), except for Palladium, which has been

irradiated with

He+ ions, Chromium as a thin film, and Platinum as a compacted powder.

Many additional elements can be coaxed into a superconductive state with the

application of high pressure. For example, phosphorus appears to be the Type 1 element

with the highest Tc. But, it requires compression pressures of 2.5 Mbar to reach a Tc of

14-22 K. The above list is for elements at normal (ambient) atmospheric pressure. See

the periodic table below for all known elemental superconductors (including Niobium,

Technetium and Vanadium which are technically Type 2).

**Note 2: Normally bulk carbon (amorphous, diamond, graphite, white) will not

superconduct at any temperature. However, a Tc of 15K has been reported for elemental

carbon when the atoms are configured as highly-aligned, single-walled nanotubes. And

non-aligned, multi-walled nanotubes have shown superconductivity near 12K. Since the

penetration depth is much larger than the coherence length, nanotubes would be

characterized as "Type 2" superconductors.

Type 2 Superconductors

A Type 2 Layered Cuprate

Except for the elements vanadium, technetium and niobium, the Type 2 category of

superconductors is comprised of metallic compounds and alloys. The recently-

discovered superconducting "perovskites" (metal-oxide ceramics that normally have a

ratio of 2 metal atoms to every 3 oxygen atoms) belong to this Type 2 group. They

achieve higher Tc's than Type 1 superconductors by a mechanism that is still not

completely understood. Conventional wisdom holds that it relates to the planar layering

within the crystalline structure (see above graphic). Although, other recent research

suggests the holes of hypocharged oxygen in the charge reservoirs are responsible.

(Holes are positively-charged vacancies within the lattice.) The superconducting

cuprates (copper-oxides) have achieved astonishingly high Tc's when you consider that

by 1985 known Tc's had only reached 23 Kelvin. To date, the highest Tc attained at

ambient pressure for a material that will form stoichiometrically (by formula) has been

138 K. And the highest Tc overall is 28 C for a material which does not form

stoichiometrically (see below list). One theory predicts an upper limit for the layered

cuprates (Vladimir Kresin, Phys. Reports 288, 347 - 1997). Others assert there is no

limit. Either way, it is almost certain that other, more-synergistic compounds still await

discovery among the high-temperature superconductors.

The first superconducting Type 2 compound, an alloy of lead and bismuth, was

fabricated in 1930 by W. de Haas and J. Voogd. But, was not recognized as such until

later, after the Meissner effect had been discovered. This new category of

superconductors was identified by L.V. Shubnikov at the Kharkov Institute of Science

and Technology in the Ukraine in 1936(1)

when he found two distinct critical magnetic

fields (known as Hc1 and Hc2) in PbTl2. The first of the oxide superconductors was

created in 1973 by DuPont researcher Art Sleight when Ba(Pb,Bi)O3 was found to have

a Tc of 13K. The superconducting oxocuprates followed in 1986.

Type 2 superconductors - also known as the "hard" superconductors - differ from

Type 1 in that their transition from a normal to a superconducting state is gradual

across a region of "mixed state" behavior. Since a Type 2 will allow some penetration by

an external magnetic field into its surface, this creates some rather novel mesoscopic

phenomena like superconducting "stripes" and "flux-lattice vortices". While there are

far too many to list in totality, some of the more interesting Type 2 superconductors are

listed below by similarity and with descending Tc's. Where available, the lattice

structure of the system is also noted.

(Tl5Pb2)Ba2Mg2Cu9O17+

(As a D223 structure)

(Tl5Pb2)Ba2MgCu10O17+

(As a D223 structure)

(Tl4Pb)Ba2MgCu8O13+

(As a 9223 structure)

(Tl4Ba)Ba2MgCu8O13+

(As a 9223 structure)

(Tl4Ba)Ba2Mg2Cu7O13+

+28 C

+18 C

+3 C

~265 K

~258 K

(As a 9223 structure)

(Tl4Ba)Ba2Ca2Cu7O13+

(As a 9223 structure)

(Tl4Ba)Ba4Ca2Cu10Oy

(As a 9212/2212C intergrowth.)

Tl5Ba4Ca2Cu10Oy

(As a 9212/2212C intergrowth.)

(Sn5In)Ba4Ca2Cu11Oy

(As a B212/2212C intergrowth.)

(Sn5In)Ba4Ca2Cu10Oy

(As a B212/1212C intergrowth.)

Sn6Ba4Ca2Cu10Oy

(As a B212/1212C intergrowth.)

(Sn1.0Pb0.5In0.5)Ba4Tm6Cu8O22+

(As a 1256/1212 intergrowth.)

(Sn1.0Pb0.5In0.5)Ba4Tm5Cu7O20+

(As a 1245/1212 intergrowth.)

(Sn1.0Pb0.5In0.5)Ba4Tm4Cu6O18+

(As a 1234/1212 intergrowth)

Sn3Ba4Ca2Cu7Oy

(As a 5212/1212C intergrowth.)

~254 K

~242 K

~233 K

~218 K

~212 K

~200 K

~195 K

~185 K

~163 K

~160 K

(Hg0.8Tl0.2)Ba2Ca2Cu3O8.33

HgBa2Ca2Cu3O8

HgBa2Ca3Cu4O10+

HgBa2(Ca1-xSrx)Cu2O6+

HgBa2CuO4+

138 K*

133-135 K

125-126 K

123-125 K

94-98 K

Lattice: TET

* Note: As a result of a topological "defect", Hg will also go into the Cu atomic sites. Thus,

the volume fraction of the intended structure type is typically just 15 - 30% of the bulk.

Tl2Ba2Ca2Cu3O10

127-128 K

(Tl1.6Hg0.4)Ba2Ca2Cu3O10+

TlBa2Ca2Cu3O9+

(TlSn)Ba4TmCaCu4O14+

(Tl0.5Pb0.5)Sr2Ca2Cu3O9

Tl2Ba2CaCu2O6

TlBa2Ca3Cu4O11

(SnTl0.5Pb0.5)Ba4Tm3Cu5O16+

TlBa2CaCu2O7+

Tl2Ba2CuO6

TlSnBa4Y2Cu4Ox

126 K

123 K

~121 K (Superconductors.ORG - 2005)

118-120 K

118 K

112 K

105 K (Superconductors.ORG - 2011)

103 K

95 K

86 K (Superconductors.ORG - 2007)

Lattice: TET

Sn4Ba4(Tm2Ca)Cu7Ox

Sn2Ba2(Tm0.5Ca0.5)Cu3O8+

SnInBa4Tm3Cu5Ox

Sn3Ba4Tm3Cu6Ox

Sn3Ba8Ca4Cu11Ox

SnBa4Y2Cu5Ox

Sn4Ba4Tm2YCu7Ox

Sn4Ba4TmCaCu4Ox

Sn4Ba4Tm3Cu7Ox

Sn2Ba2(Y0.5Tm0.5)Cu3O8+

Sn3Ba4Y2Cu5Ox

SnInBa4Tm4Cu6Ox

Sn2Ba2(Sr0.5Y0.5)Cu3O8

Sn4Ba4Y3Cu7Ox

~127 K (TmTm-Ca structure only) ~115 K (Superconductors.ORG - 2005)

~113 K (Superconductors.ORG - 2005)

109 K (Superconductors.ORG - 2007)

109 K (One-of-a-Kind Resonant - 2006)

107 K (Superconductors.ORG - 2007)

~104 K (First Hi-Tc Reentrant - 2007)

~100 K (Superconductors.ORG - 2007)

~98 K (Superconductors.ORG - 2006)

~96 K (Superconductors.ORG - 2007)

~91 K (Superconductors.ORG - 2006)

87 K (Superconductors.ORG - 2005)

86 K (Aleksandrov, et al - 1989)

~80 K (Superconductors.ORG - 2005)

Bi1.6Pb0.6Sr2Ca2Sb0.1Cu3Oy

Bi2Sr2Ca2Cu3O10***

Bi2Sr2CaCu2O9***

Bi2Sr2(Ca0.8Y0.2)Cu2O8

Bi2Sr2CaCu2O8

115 K (thick film on MgO substrate)

110 K

110 K

95-96K

91-92K

Lattice: ORTH

*** Though not always listed as a component, a small amount of Lead (x=.2-.26) is often

used with Bismuth compounds to help facilitate a higher-Tc crystalline phase.

CaSrCu2O4 110 K

YSrCa2Cu4O8+

(Ba,Sr)CuO2

BaSr2CaCu4O8+

(La,Sr)CuO2

101 K (Superconductors.ORG - 2007)

90 K

90 K (Superconductors.ORG - 2007)

42 K

*** The above 5 compounds are all "infinite layer".

Pb3Sr4Ca3Cu6Ox

Pb3Sr4Ca2Cu5O15+

(Pb1.5Sn1.5)Sr4Ca2Cu5O15+

Pb2Sr2(Ca, Y)Cu3O8

106 K (Superconductors.ORG - 2007)

101 K (Superconductors.ORG - 2005)

~95 K (Superconductors.ORG - 2006)

70 K (Cava, et al - 1989)

AuBa2Ca3Cu4O11

AuBa2(Y, Ca)Cu2O7

AuBa2Ca2Cu3O9

99 K (Kopnin, et al - 2001)

82 K

30 K

Lattice: ORTH

YBa3Cu4Ox (9223C

structure)

YCaBa3Cu5O11+

(Y0.5Lu0.5)Ba2Cu3O7

(Y0.5Tm0.5)Ba2Cu3O7

Y3Ba5Cu8Ox

Y3CaBa4Cu8O18+

(Y0.5Gd0.5)Ba2Cu3O7

177 K (Superconductors.ORG - 2009)

107 K (Superconductors.ORG - 2010)

106 K (Superconductors.ORG - 2005)

104 K (Superconductors.ORG - 2005)

104 K (Superconductors.ORG - 2008)

99 K (Superconductors.ORG - 2010)

97 K (Superconductors.ORG - 2005)

96 K (Superconductors.ORG - 2006)

Y2CaBa4Cu7O16

Y3Ba4Cu7O16

Y2Ba5Cu7Ox

NdBa2Cu3O7

Y2Ba4Cu7O15

GdBa2Cu3O7

YBa2Cu3O7

TmBa2Cu3O7

YbBa2Cu3O7

YSr2Cu3O7

Lattice: TET

96 K (Superconductors.ORG - 2005)

96 K (Superconductors.ORG - 2008)

96 K

95 K

94 K

92 K (See above graphic)

90 K

89 K

62 K

Comment: "1-2-3" superconductors actually have the 1212C structure. Thus, the formula

for YBCO could be written CuBa2YCu2O7.

GaSr2(Ca0.5Tm0.5)Cu2O7

Ga2Sr4Y2CaCu5Ox

Ga2Sr4Tm2CaCu5Ox

La2Ba2CaCu5O9+

(Sr,Ca)5Cu4O10

GaSr2(Ca, Y)Cu2O7

(In0.3Pb0.7)Sr2(Ca0.8Y0.2)Cu2Ox

(La,Sr,Ca)3Cu2O6

La2CaCu2O6+

(Eu,Ce)2(Ba,Eu)2Cu3O10+

(La1.85Sr0.15)CuO4

SrNdCuO****

(La,Ba)2CuO4

(Nd,Sr,Ce)2CuO4

Pb2(Sr,La)2Cu2O6

(La1.85Ba.15)CuO4

99 K (Superconductors.ORG - 2006)

85 K (Superconductors.ORG - 2006)

81 K (Superconductors.ORG - 2006)

79 K (Saurashtra Univ., Rajkot, India - 2002)

70 K

70 K

60 K

58 K

45 K

43 K

40 K

40 K

35-38 K

35 K

32 K

30 K (First HTS ceramic SC discovered - 1986)

**** First ceramic superconductor discovered without a non-superconducting oxide layer.

Comment: All of the above are copper perovskites, even though their metal-to-oxygen

ratios are not exactly 2-to-3. The best performers are those compounds that contain one or

more of the electron-emitters BaO, SrO or CaO, along with a Period 6 heavy metal like

Mercury, Thallium, Lead, Bismuth, or Gold.

GdFeAsO1-x (Ca,Sr,Ba)Fe2As2

LiFeAs

53.5 K (Highest Tc iron-based compound)

38 K

18 K

Comment: The above are members of the newly discovered iron pnictide family.

MgB2

Ba0.6K0.4BiO3

39 K (Highest Tc Non-Fullerene Alloy)

30 K (First 4th order phase compound)

Nb3Ge

Nb3Si

Nb3Sn

Nb3Al

V3Si

Ta3Pb

V3Ga

Nb3Ga

V3In

23.2 K

19 K

18.1 K

18 K

17.1 K

17 K

16.8 K

14.5 K

13.9 K

Lattice: A15

Comment: Among the binary alloys, these are some of the best performers; combining

Group 5B metals in a ratio of 3-to-1 with 4A or 3A elements.

PuCoGa5 18.5 K (First SC transuranic compound)

NbN 16.1 K

Comment: After NbTi (below) NbN is the most widely used low-temperature

superconductor.

Nb0.6Ti0.4

MgCNi3

9.8 K (First superconductive wire)

7-8 K (First all-metal perovskite superconductor)

C

Nb

Tc

15 K (as highly-aligned, single-walled nanotubes)

9.25 K

7.80 K

V 5.40 K

Lattice: C=Fullerene, Nb=BCC, Tc=HEX, V=BCC

Comment: These four are the only elemental Type 2 superconductors.

RuSr2(Gd,Eu,Sm)Cu2O8

ErNi2B2C

YbPd2Sn

UGe2

URhGe2

AuIn3

Tc ~58 K (Ruthenium-oxocuprate)

Tc 10.5 K (Nickel-Borocarbide)

Tc ~2.5 K (Heusler compound)

Tc ~1K (Heavy fermion)

Tc ~1K ( " )

Tc 50 uK

Comment: The above 6 compounds are all rare ferromagnetic superconductors.

Sr.08WO3

Tl.30WO3

Rb.27-.29WO3

2-4 K (Tungsten-bronze)

2.0-2.14 K (")

1.98 K (")

Lattice: TET

SrTiO3 0.35 K

Comment: This is the first oxide insulator found to be superconductive.

Critical Temperature for Superconductors

The critical temperature for superconductors is the temperature at

which the electrical resistivity of a metal drops to zero. The transition

is so sudden and complete that it appears to be a transition to a

different phase of matter; this superconducting phase is described by

the BCS theory. Several materials exhibit superconducting phase

transitions at low temperatures. The highest critical temperature was

about 23 K until the discovery in 1986 of some high temperature

superconductors.

Materials with critical temperatures in the range 120 K have received a

Material Tc

Gallium 1.1K

Aluminum 1.2

K

Indium 3.4

K

Tin 3.7

K

great deal of attention because they can be maintained in the

superconducting state with liquid nitrogen (77 K). Mercury 4.2

Lead 7.2

K

Niobium 9.3

K

La-Ba-Cu-

oxide

17.9

K

Y-Ba-Cu-

oxide 92 K

Tl-Ba-Cu-

oxide

125

K

Elementary properties of superconductors

Most of the physical properties of superconductors vary from material to material, such as the

heat capacity and the critical temperature, critical field, and critical current density at which

superconductivity is destroyed.

On the other hand, there is a class of properties that are independent of the underlying

material. For instance, all superconductors have exactly zero resistivity to low applied

currents when there is no magnetic field present or if the applied field does not exceed a

critical value. The existence of these "universal" properties implies that superconductivity is a

thermodynamic phase, and thus possesses certain distinguishing properties which are largely

independent of microscopic details.

Zero electrical DC resistance

Electric cables for accelerators at CERN. Both the massive and slim cables are rated for 12,500 A.

Top: conventional cables for LEP; bottom: superconductor-based cables for the LHC

The simplest method to measure the electrical resistance of a sample of some material is to

place it in an electrical circuit in series with a current source I and measure the resulting

voltage V across the sample. The resistance of the sample is given by Ohm's law as R = V/I.

If the voltage is zero, this means that the resistance is zero.

Superconductors are also able to maintain a current with no applied voltage whatsoever, a

property exploited in superconducting electromagnets such as those found in MRI machines.

Experiments have demonstrated that currents in superconducting coils can persist for years

without any measurable degradation. Experimental evidence points to a current lifetime of at

least 100,000 years. Theoretical estimates for the lifetime of a persistent current can exceed

the estimated lifetime of the universe, depending on the wire geometry and the temperature.[1]

In a normal conductor, an electric current may be visualized as a fluid of electrons moving

across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice,

and during each collision some of the energy carried by the current is absorbed by the lattice

and converted into heat, which is essentially the vibrational kinetic energy of the lattice ions.

As a result, the energy carried by the current is constantly being dissipated. This is the

phenomenon of electrical resistance.

The situation is different in a superconductor. In a conventional superconductor, the

electronic fluid cannot be resolved into individual electrons. Instead, it consists of bound

pairs of electrons known as Cooper pairs. This pairing is caused by an attractive force

between electrons from the exchange of phonons. Due to quantum mechanics, the energy

spectrum of this Cooper pair fluid possesses an energy gap, meaning there is a minimum

amount of energy ΔE that must be supplied in order to excite the fluid. Therefore, if ΔE is

larger than the thermal energy of the lattice, given by kT, where k is Boltzmann's constant and

T is the temperature, the fluid will not be scattered by the lattice. The Cooper pair fluid is thus

a superfluid, meaning it can flow without energy dissipation.

In a class of superconductors known as type II superconductors, including all known high-

temperature superconductors, an extremely small amount of resistivity appears at

temperatures not too far below the nominal superconducting transition when an electric

current is applied in conjunction with a strong magnetic field, which may be caused by the

electric current. This is due to the motion of vortices in the electronic superfluid, which

dissipates some of the energy carried by the current. If the current is sufficiently small, the

vortices are stationary, and the resistivity vanishes. The resistance due to this effect is tiny

compared with that of non-superconducting materials, but must be taken into account in

sensitive experiments. However, as the temperature decreases far enough below the nominal

superconducting transition, these vortices can become frozen into a disordered but stationary

phase known as a "vortex glass". Below this vortex glass transition temperature, the

resistance of the material becomes truly zero.

Superconducting phase transition

Behavior of heat capacity (cv, blue) and resistivity (ρ, green) at the superconducting phase transition

In superconducting materials, the characteristics of superconductivity appear when the

temperature T is lowered below a critical temperature Tc. The value of this critical

temperature varies from material to material. Conventional superconductors usually have

critical temperatures ranging from around 20 K to less than 1 K. Solid mercury, for example,

has a critical temperature of 4.2 K. As of 2009, the highest critical temperature found for a

conventional superconductor is 39 K for magnesium diboride (MgB2),[4][5]

although this

material displays enough exotic properties that there is some doubt about classifying it as a

"conventional" superconductor.[6]

Cuprate superconductors can have much higher critical

temperatures: YBa2Cu3O7, one of the first cuprate superconductors to be discovered, has a

critical temperature of 92 K, and mercury-based cuprates have been found with critical

temperatures in excess of 130 K. The explanation for these high critical temperatures remains

unknown. Electron pairing due to phonon exchanges explains superconductivity in

conventional superconductors, but it does not explain superconductivity in the newer

superconductors that have a very high critical temperature.

Similarly, at a fixed temperature below the critical temperature, superconducting materials

cease to superconduct when an external magnetic field is applied which is greater than the

critical magnetic field. This is because the Gibbs free energy of the superconducting phase

increases quadratically with the magnetic field while the free energy of the normal phase is

roughly independent of the magnetic field. If the material superconducts in the absence of a

field, then the superconducting phase free energy is lower than that of the normal phase and

so for some finite value of the magnetic field (proportional to the square root of the difference

of the free energies at zero magnetic field) the two free energies will be equal and a phase

transition to the normal phase will occur. More generally, a higher temperature and a stronger

magnetic field lead to a smaller fraction of the electrons in the superconducting band and

consequently a longer London penetration depth of external magnetic fields and currents. The

penetration depth becomes infinite at the phase transition.

The onset of superconductivity is accompanied by abrupt changes in various physical

properties, which is the hallmark of a phase transition. For example, the electronic heat

capacity is proportional to the temperature in the normal (non-superconducting) regime. At

the superconducting transition, it suffers a discontinuous jump and thereafter ceases to be

linear. At low temperatures, it varies instead as e−α /T

for some constant, α. This exponential

behavior is one of the pieces of evidence for the existence of the energy gap.

The order of the superconducting phase transition was long a matter of debate. Experiments

indicate that the transition is second-order, meaning there is no latent heat. However in the

presence of an external magnetic field there is latent heat, because the superconducting phase

has a lower entropy below the critical temperature than the normal phase. It has been

experimentally demonstrated[7]

that, as a consequence, when the magnetic field is increased

beyond the critical field, the resulting phase transition leads to a decrease in the temperature

of the superconducting material.

Calculations in the 1970s suggested that it may actually be weakly first-order due to the

effect of long-range fluctuations in the electromagnetic field. In the 1980s it was shown

theoretically with the help of a disorder field theory, in which the vortex lines of the

superconductor play a major role, that the transition is of second order within the type II

regime and of first order (i.e., latent heat) within the type I regime, and that the two regions

are separated by a tricritical point.[8]

The results were strongly supported by Monte Carlo

computer simulations.[9]

Meissner effect

When a superconductor is placed in a weak external magnetic field H, and cooled below its

transition temperature, the magnetic field is ejected. The Meissner effect does not cause the

field to be completely ejected but instead the field penetrates the superconductor but only to a

very small distance, characterized by a parameter λ, called the London penetration depth,

decaying exponentially to zero within the bulk of the material. The Meissner effect is a

defining characteristic of superconductivity. For most superconductors, the London

penetration depth is on the order of 100 nm.

The Meissner effect is sometimes confused with the kind of diamagnetism one would expect

in a perfect electrical conductor: according to Lenz's law, when a changing magnetic field is

applied to a conductor, it will induce an electric current in the conductor that creates an

opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced,

and the resulting magnetic field exactly cancels the applied field.

The Meissner effect is distinct from this—it is the spontaneous expulsion which occurs

during transition to superconductivity. Suppose we have a material in its normal state,

containing a constant internal magnetic field. When the material is cooled below the critical

temperature, we would observe the abrupt expulsion of the internal magnetic field, which we

would not expect based on Lenz's law.

The Meissner effect was given a phenomenological explanation by the brothers Fritz and

Heinz London, who showed that the electromagnetic free energy in a superconductor is

minimized provided

where H is the magnetic field and λ is the London penetration depth.

This equation, which is known as the London equation, predicts that the magnetic field in a

superconductor decays exponentially from whatever value it possesses at the surface.

A superconductor with little or no magnetic field within it is said to be in the Meissner state.

The Meissner state breaks down when the applied magnetic field is too large.

Superconductors can be divided into two classes according to how this breakdown occurs. In

Type I superconductors, superconductivity is abruptly destroyed when the strength of the

applied field rises above a critical value Hc. Depending on the geometry of the sample, one

may obtain an intermediate state[10]

consisting of a baroque pattern[11]

of regions of normal

material carrying a magnetic field mixed with regions of superconducting material containing

no field. In Type II superconductors, raising the applied field past a critical value Hc1 leads to

a mixed state (also known as the vortex state) in which an increasing amount of magnetic flux

penetrates the material, but there remains no resistance to the flow of electric current as long

as the current is not too large. At a second critical field strength Hc2, superconductivity is

destroyed. The mixed state is actually caused by vortices in the electronic superfluid,

sometimes called fluxons because the flux carried by these vortices is quantized. Most pure

elemental superconductors, except niobium, technetium, vanadium and carbon nanotubes, are

Type I, while almost all impure and compound superconductors are Type II.

London moment

Conversely, a spinning superconductor generates a magnetic field, precisely aligned with the

spin axis. The effect, the London moment, was put to good use in Gravity Probe B. This

experiment measured the magnetic fields of four superconducting gyroscopes to determine

their spin axes. This was critical to the experiment since it is one of the few ways to

accurately determine the spin axis of an otherwise featureless sphere.

Theories of superconductivity

Since the discovery of superconductivity, great efforts have been devoted to finding out how

and why it works. During the 1950s, theoretical condensed matter physicists arrived at a solid

understanding of "conventional" superconductivity, through a pair of remarkable and

important theories: the phenomenological Ginzburg-Landau theory (1950) and the

microscopic BCS theory (1957).[12][13]

Generalizations of these theories form the basis for

understanding the closely related phenomenon of superfluidity, because they fall into the

Lambda transition universality class, but the extent to which similar generalizations can be

applied to unconventional superconductors as well is still controversial. The four-dimensional

extension of the Ginzburg-Landau theory, the Coleman-Weinberg model, is important in

quantum field theory and cosmology. Superfluidity of helium and superconductivity both are

macroscopic quantum phenomena.

London theory

The first phenomenological theory of superconductivity was London theory. It was put

forward by the brothers Fritz and Heinz London in 1935, shortly after the discovery that

magnetic fields are expelled from superconductors. A major triumph of the equations of this

theory is their ability to explain the Meissner effect,[14]

wherein a material exponentially

expels all internal magnetic fields as it crosses the superconducting threshold. By using the

London equation, one can obtain the dependence of the magnetic field inside the

superconductor on the distance to the surface.[15]

There are two London equations:

The first equation follows from the Newton's second law for superconducting electrons.

High-temperature superconductivity

Timeline of superconducting materials

Main article: High-temperature superconductivity

Until 1986, physicists had believed that BCS theory forbade superconductivity at

temperatures above about 30 K. In that year, Bednorz and Müller discovered

superconductivity in a lanthanum-based cuprate perovskite material, which had a transition

temperature of 35 K (Nobel Prize in Physics, 1987).[2]

It was soon found that replacing the

lanthanum with yttrium (i.e., making YBCO) raised the critical temperature to 92 K, which

was important because liquid nitrogen could then be used as a refrigerant (the boiling point of

nitrogen is 77 K at atmospheric pressure).[29]

This is important commercially because liquid

nitrogen can be produced cheaply on-site from air, and is not prone to some of the problems

(for instance solid air plugs) of helium in piping. Many other cuprate superconductors have

since been discovered, and the theory of superconductivity in these materials is one of the

major outstanding challenges of theoretical condensed matter physics.[30]

From about 1993, the highest temperature superconductor was a ceramic material consisting

of thallium, mercury, copper, barium, calcium and oxygen (HgBa2Ca2Cu3O8+δ) with Tc = 138

K.[31]

In February 2008, an iron-based family of high-temperature superconductors was

discovered.[32][33]

Hideo Hosono, of the Tokyo Institute of Technology, and colleagues found

lanthanum oxygen fluorine iron arsenide (LaO1-xFxFeAs), an oxypnictide that superconducts

below 26 K. Replacing the lanthanum in LaO1−xFxFeAs with samarium leads to

superconductors that work at 55 K.[34]

Crystal structure of high-temperature ceramic superconductors

The structure of a high-Tc superconductor is closely related to perovskite structure, and the

structure of these compounds has been described as a distorted, oxygen deficient multi-

layered perovskite structure. One of the properties of the crystal structure of oxide

superconductors is an alternating multi-layer of CuO2 planes with superconductivity taking

place between these layers. The more layers of CuO2 the higher Tc. This structure causes a

large anisotropy in normal conducting and superconducting properties, since electrical

currents are carried by holes induced in the oxygen sites of the CuO2 sheets. The electrical

conduction is highly anisotropic, with a much higher conductivity parallel to the CuO2 plane

than in the perpendicular direction. Generally, Critical temperatures depend on the chemical

compositions, cations substitutions and oxygen content. They can be classified as

superstripes; i.e., particular realizations of superlattices at atomic limit made of

superconducting atomic layers, wires, dots separated by spacer layers, that gives multiband

and multigap superconductivity.

YBaCuO superconductors

YBCO unit cell

The first superconductor found with Tc > 77 K (liquid nitrogen boiling point) is yttrium

barium copper oxide (YBa2Cu3O7-x), the proportions of the 3 different metals in the

YBa2Cu3O7 superconductor are in the mole ratio of 1 to 2 to 3 for yttrium to barium to copper

respectively. Thus, this particular superconductor is often referred to as the 123

superconductor.

The unit cell of YBa2Cu3O7 consists of three pseudocubic elementary perovskite unit cells.

Each perovskite unit cell contains a Y or Ba atom at the center: Ba in the bottom unit cell, Y

in the middle one, and Ba in the top unit cell. Thus, Y and Ba are stacked in the sequence

[Ba–Y–Ba] along the c-axis. All corner sites of the unit cell are occupied by Cu, which has

two different coordinations, Cu(1) and Cu(2), with respect to oxygen. There are four possible

crystallographic sites for oxygen: O(1), O(2), O(3) and O(4).[35]

The coordination polyhedra

of Y and Ba with respect to oxygen are different. The tripling of the perovskite unit cell leads

to nine oxygen atoms, whereas YBa2Cu3O7 has seven oxygen atoms and, therefore, is

referred to as an oxygen-deficient perovskite structure. The structure has a stacking of

different layers: (CuO)(BaO)(CuO2)(Y)(CuO2)(BaO)(CuO). One of the key feature of the

unit cell of YBa2Cu3O7-x (YBCO) is the presence of two layers of CuO2. The role of the Y

plane is to serve as a spacer between two CuO2 planes. In YBCO, the Cu–O chains are

known to play an important role for superconductivity. Tc is maximal near 92 K when x ≈

0.15 and the structure is orthorhombic. Superconductivity disappears at x ≈ 0.6, where the

structural transformation of YBCO occurs from orthorhombic to tetragonal.[36]

Bi-, Tl- and Hg-based high-Tc superconductors

The crystal structure of Bi-, Tl- and Hg-based high-Tc superconductors are very similar. Like

YBCO, the perovskite-type feature and the presence of CuO2 layers also exist in these

superconductors. However, unlike YBCO, Cu–O chains are not present in these

superconductors. The YBCO superconductor has an orthorhombic structure, whereas the

other high-Tc superconductors have a tetragonal structure.

The Bi–Sr–Ca–Cu–O system has three superconducting phases forming a homologous series

as Bi2Sr2Can−1CunO4+2n+x (n = 1, 2 and 3). These three phases are Bi-2201, Bi-2212 and Bi-

2223, having transition temperatures of 20, 85 and 110 K, respectively, where the numbering

system represent number of atoms for Bi, Sr, Ca and Cu respectively.[37]

The two phases have

a tetragonal structure which consists of two sheared crystallographic unit cells. The unit cell

of these phases has double Bi–O planes which are stacked in a way that the Bi atom of one

plane sits below the oxygen atom of the next consecutive plane. The Ca atom forms a layer

within the interior of the CuO2 layers in both Bi-2212 and Bi-2223; there is no Ca layer in the

Bi-2201 phase. The three phases differ with each other in the number of CuO2 planes; Bi-

2201, Bi-2212 and Bi-2223 phases have one, two and three CuO2 planes, respectively. The c

axis of these phases increases with the number of CuO2 planes (see table below). The

coordination of the Cu atom is different in the three phases. The Cu atom forms an octahedral

coordination with respect to oxygen atoms in the 2201 phase, whereas in 2212, the Cu atom

is surrounded by five oxygen atoms in a pyramidal arrangement. In the 2223 structure, Cu

has two coordinations with respect to oxygen: one Cu atom is bonded with four oxygen

atoms in square planar configuration and another Cu atom is coordinated with five oxygen

atoms in a pyramidal arrangement.[38]

Tl–Ba–Ca–Cu–O superconductor: The first series of the Tl-based superconductor

containing one Tl–O layer has the general formula TlBa2Can-1CunO2n+3,[39]

whereas the

second series containing two Tl–O layers has a formula of Tl2Ba2Can-1CunO2n+4 with n = 1, 2

and 3. In the structure of Tl2Ba2CuO6 (Tl-2201), there is one CuO2 layer with the stacking

sequence (Tl–O) (Tl–O) (Ba–O) (Cu–O) (Ba–O) (Tl–O) (Tl–O). In Tl2Ba2CaCu2O8 (Tl-

2212), there are two Cu–O layers with a Ca layer in between. Similar to the Tl2Ba2CuO6

structure, Tl–O layers are present outside the Ba–O layers. In Tl2Ba2Ca2Cu3O10 (Tl-2223),

there are three CuO2 layers enclosing Ca layers between each of these. In Tl-based

superconductors, Tc is found to increase with the increase in CuO2 layers. However, the value

of Tc decreases after four CuO2 layers in TlBa2Can-1CunO2n+3, and in the Tl2Ba2Can-1CunO2n+4

compound, it decreases after three CuO2 layers.[40]

Hg–Ba–Ca–Cu–O superconductor: The crystal structure of HgBa2CuO4 (Hg-1201),[41]

HgBa2CaCu2O6 (Hg-1212) and HgBa2Ca2Cu3O8 (Hg-1223) is similar to that of Tl-1201, Tl-

1212 and Tl-1223, with Hg in place of Tl. It is noteworthy that the Tc of the Hg compound

(Hg-1201) containing one CuO2 layer is much larger as compared to the one-CuO2-layer

compound of thallium (Tl-1201). In the Hg-based superconductor, Tc is also found to increase

as the CuO2 layer increases. For Hg-1201, Hg-1212 and Hg-1223, the values of Tc are 94,

128 and 134 K respectively, as shown in table below. The observation that the Tc of Hg-1223

increases to 153 K under high pressure indicates that the Tc of this compound is very

sensitive to the structure of the compound.[42]

Critical temperature (Tc), crystal structure and lattice constants of some high-Tc superconductors

Formula Notation Tc (K) No. of Cu-O planes

in unit cell Crystal structure

YBa2Cu3O7 123 92 2 Orthorhombic

Bi2Sr2CuO6 Bi-2201 20 1 Tetragonal

Bi2Sr2CaCu2O8 Bi-2212 85 2 Tetragonal

Bi2Sr2Ca2Cu3O6 Bi-2223 110 3 Tetragonal

Tl2Ba2CuO6 Tl-2201 80 1 Tetragonal

Tl2Ba2CaCu2O8 Tl-2212 108 2 Tetragonal

Tl2Ba2Ca2Cu3O10 Tl-2223 125 3 Tetragonal

TlBa2Ca3Cu4O11 Tl-1234 122 4 Tetragonal

HgBa2CuO4 Hg-1201 94 1 Tetragonal

HgBa2CaCu2O6 Hg-1212 128 2 Tetragonal

HgBa2Ca2Cu3O8 Hg-1223 134 3 Tetragonal

Preparation of high-Tc superconductors

The simplest method for preparing high-Tc superconductors is a solid-state thermochemical

reaction involving mixing, calcination and sintering. The appropriate amounts of precursor

powders, usually oxides and carbonates, are mixed thoroughly using a ball mill. Solution

chemistry processes such as coprecipitation, freeze-drying and sol-gel methods are alternative

ways for preparing a homogenous mixture. These powders are calcined in the temperature

range from 800 °C to 950 °C for several hours. The powders are cooled, reground and

calcined again. This process is repeated several times to get homogenous material. The

powders are subsequently compacted to pellets and sintered. The sintering environment such

as temperature, annealing time, atmosphere and cooling rate play a very important role in

getting good high-Tc superconducting materials. The YBa2Cu3O7-x compound is prepared by

calcination and sintering of a homogenous mixture of Y2O3, BaCO3 and CuO in the

appropriate atomic ratio. Calcination is done at 900–950 °C, whereas sintering is done at

950 °C in an oxygen atmosphere. The oxygen stoichiometry in this material is very crucial

for obtaining a superconducting YBa2Cu3O7−x compound. At the time of sintering, the

semiconducting tetragonal YBa2Cu3O6 compound is formed, which, on slow cooling in

oxygen atmosphere, turns into superconducting YBa2Cu3O7−x. The uptake and loss of oxygen

are reversible in YBa2Cu3O7−x. A fully oxidized orthorhombic YBa2Cu3O7−x sample can be

transformed into tetragonal YBa2Cu3O6 by heating in a vacuum at temperature above

700 °C.[36]

The preparation of Bi-, Tl- and Hg-based high-Tc superconductors is difficult compared to

YBCO. Problems in these superconductors arise because of the existence of three or more

phases having a similar layered structure. Thus, syntactic intergrowth and defects such as

stacking faults occur during synthesis and it becomes difficult to isolate a single

superconducting phase. For Bi–Sr–Ca–Cu–O, it is relatively simple to prepare the Bi-2212

(Tc ≈ 85 K) phase, whereas it is very difficult to prepare a single phase of Bi-2223 (Tc ≈

110 K). The Bi-2212 phase appears only after few hours of sintering at 860–870 °C, but the

larger fraction of the Bi-2223 phase is formed after a long reaction time of more than a week

at 870 °C.[38]

Although the substitution of Pb in the Bi–Sr–Ca–Cu–O compound has been

found to promote the growth of the high-Tc phase,[43]

a long sintering time is still required.

Possible superconductivity of the vacuum

Maxim Chernodub of the French National Centre for Scientific Research has postulated that

the vacuum can be used as a source of superconduction in the presence of immensely strong

magnetic fields of 1016

Tesla or more,[44]

and at temperatures of at least a billion,[45]

perhaps

billions of degrees, with rho mesons being drawn from the virtual vacuum that permeates

space to give rise to superconduction.[46]

Applications

Superconducting magnets are some of the most powerful electromagnets known. They are

used in MRI/NMR machines, mass spectrometers, and the beam-steering magnets used in

particle accelerators. They can also be used for magnetic separation, where weakly magnetic

particles are extracted from a background of less or non-magnetic particles, as in the pigment

industries.

In the 1950s and 1960s, superconductors were used to build experimental digital computers

using cryotron switches. More recently, superconductors have been used to make digital

circuits based on rapid single flux quantum technology and RF and microwave filters for

mobile phone base stations.

Superconductors are used to build Josephson junctions which are the building blocks of

SQUIDs (superconducting quantum interference devices), the most sensitive magnetometers

known. SQUIDs are used in scanning SQUID microscopes and magnetoencephalography.

Series of Josephson devices are used to realize the SI volt. Depending on the particular mode

of operation, a superconductor-insulator-superconductor Josephson junction can be used as a

photon detector or as a mixer. The large resistance change at the transition from the normal-

to the superconducting state is used to build thermometers in cryogenic micro-calorimeter

photon detectors. The same effect is used in ultrasensitive bolometers made from

superconducting materials.

Other early markets are arising where the relative efficiency, size and weight advantages of

devices based on high-temperature superconductivity outweigh the additional costs involved.

Promising future applications include high-performance smart grid, electric power

transmission, transformers, power storage devices, electric motors (e.g. for vehicle

propulsion, as in vactrains or maglev trains), magnetic levitation devices, fault current

limiters, nanoscopic materials such as buckyballs, nanotubes, composite materials and

superconducting magnetic refrigeration. However, superconductivity is sensitive to moving

magnetic fields so applications that use alternating current (e.g. transformers) will be more

difficult to develop than those that rely upon direct current.

The Yamanashi MLX01 MagLev train.

Magnetic-levitation is an application where superconductors perform extremely well. Transport vehicles such as trains can be made to "float" on strong superconducting magnets, virtually eliminating friction between the train and its tracks. Not only would conventional electromagnets waste much of the electrical energy as heat, they would have to be physically much larger than superconducting magnets. A landmark for the commercial use of MAGLEV technology occurred in 1990 when it gained the status of a nationally-funded project in Japan. The Minister of Transport authorized construction of the Yamanashi Maglev Test Line which opened on April 3, 1997. In December 2003, the MLX01 test vehicle (shown above) attained an incredible speed of 361 mph (581 kph).

Although the technology has now been proven, the wider use of MAGLEV vehicles has been constrained by political and environmental concerns (strong magnetic fields can create a bio-hazard). The world's first MAGLEV train to be adopted into commercial service, a shuttle in Birmingham, England, shut down in 1997 after operating for 11 years. A Sino-German maglev is currently operating over a 30-km course at Pudong International Airport in Shanghai, China. The U.S. plans to put its first (non-superconducting) Maglev train into operation on a Virginia college campus. Click this link for a website that lists other uses for MAGLEV.

MRI of a human skull.

An area where superconductors can perform a life-saving function is in the field of biomagnetism. Doctors need a non-invasive means of determining what's going on inside the human body. By impinging a strong superconductor-derived magnetic field into the body, hydrogen atoms that exist in the body's water and fat molecules are forced to accept energy from the magnetic field. They then release this energy at a frequency that can be detected and displayed graphically by a computer. Magnetic Resonance Imaging (MRI) was actually discovered in the mid 1940's. But, the first MRI exam on a human being was not performed until July 3, 1977. And, it took almost five hours to produce one image! Today's faster computers process the data in much less time. A tutorial is available on MRI at this link. Or read the latest MRI news at this link.

The Korean Superconductivity Group within KRISS has carried biomagnetic technology a step further with the development of a double-relaxation oscillation SQUID (Superconducting QUantum Interference Device) for use in Magnetoencephalography. SQUID's are capable of sensing a change in a magnetic field over a billion times weaker than the force that moves the needle on a compass (compass: 5e-5T, SQUID: e-14T.). With this technology, the body can be probed to certain depths without the need for the strong magnetic fields associated with MRI's.

Probably the one event, more than any other, that has been responsible for putting "superconductors" into the American lexicon was the Superconducting Super-Collider project planned for construction in Ellis county, Texas. Though Congress cancelled the multi-billion dollar effort in 1993, the concept of such a large, high-energy collider would never have been viable without superconductors. High-energy particle research hinges on being able to accelerate sub-atomic particles to nearly the speed of light. Superconductor magnets make this possible. CERN, a consortium of several European nations, is doing something similar with its Large Hadron Collider (LHC) recently inaugurated along the Franco-Swiss border.

Other related web sites worth visiting include the proton-antiproton collider page at Fermilab. This was the first facility to use superconducting magnets. Get information on the electron-proton collider HERA at the German lab pages of DESY (with English text). And Brookhaven National Laboratory features a page dedicated to its RHIC heavy-ion collider.

Electric generators made with superconducting wire are far more efficient than conventional generators wound with copper wire. In fact, their efficiency is above 99% and their size about half that of conventional generators. These facts make them very lucrative ventures for power utilities. General Electric has estimated the potential worldwide market for superconducting generators in the next decade at around $20-30 billion dollars. Late in 2002 GE Power Systems received $12.3 million in funding from the U.S. Department of Energy to move high-temperature superconducting generator technology toward full commercialization. To read the latest news on superconducting generators click Here.

Other commercial power projects in the works that employ superconductor technology include energy storage to enhance power stability. American Superconductor Corp. received an order from Alliant Energy in late March 2000 to install a Distributed Superconducting Magnetic Energy Storage System (D-SMES) in Wisconsin. Just one of these 6 D-SMES units has a power reserve of over 3 million watts, which can be retrieved whenever there is a need to stabilize line voltage during a disturbance in the power grid. AMSC has also installed more than 22 of its D-VAR systems to provide instantaneous reactive power support.

The General Atomics/Intermagnetics General superconducting

Fault Current Controller, employing HTS superconductors.

Recently, power utilities have also begun to use superconductor-based transformers and "fault limiters". The Swiss-Swedish company ABB was the first to connect a superconducting transformer to a utility power network in March of 1997. ABB also recently announced the development of a 6.4MVA (mega-volt-ampere) fault current limiter - the most powerful in the world. This new generation of HTS superconducting fault limiters is being called upon due to their ability to respond in just thousandths of a second to limit tens of thousands of amperes of current. Advanced Ceramics Limited is another of several companies that makes BSCCO type fault limiters. Intermagnetics General recently completed tests on its largest (15kv class) power-utility-size fault limiter at a Southern California Edison (SCE) substation near Norwalk, California. And, both the US and Japan have plans to replace underground copper power cables with superconducting BSCCO cable-in-conduit cooled with liquid nitrogen. (See photo below.) By doing this, more current can be routed through existing cable tunnels. In one instance 250 pounds of superconducting wire replaced 18,000 pounds of vintage copper wire, making it over 7000% more space-efficient.

An idealized application for superconductors is to employ them in the transmission of commercial power to cities. However, due to the high cost and impracticality of cooling miles of superconducting wire to cryogenic temperatures, this has only happened with short "test runs". In May of 2001 some 150,000 residents of Copenhagen, Denmark, began receiving their electricity through HTS (high-temperature superconducting) material. That cable was only 30 meters long, but proved adequate for testing purposes. In the summer of 2001 Pirelli completed installation of three 400-foot HTS cables for Detroit Edison at the Frisbie Substation

capable of delivering 100 million watts of power. This marked the first time commercial power has been delivered to customers of a US power utility through superconducting wire. Intermagnetics General has announced that its IGC-SuperPower subsidiary has joined with BOC and Sumitomo Electric in a $26 million project to install an underground, HTS power cable in Albany, New York, in Niagara Mohawk Power Corporation's power grid. Sumitomo Electric's DI-BSCCO cable was employed in the first in-grid power cable demonstration project sponsored by the U.S. Department of Energy and New York Energy Research & Development Authority. After connecting to the grid successfully on July 2006, the DI-BSCCO cable has been supplying the power to approximately 70,000 households without any problems. The long-term test will be completed in the 2007-2008 timeframe.

Hypres Superconducting Microchip,

Incorporating 6000 Josephson Junctions.

The National Science Foundation, along with NASA and DARPA and various universities, are currently researching "petaflop" computers. A petaflop is a thousand-trillion floating point operations per second. Today's fastest computers have only recently reached "petaflop" speeds - quadrillions of operations per second. Currently the fastest is the U.S. Department of Energy "Sequoia" Supercomputer, operating at 16.32 petaflops per second. The fastest single processor is a Lenslet optical DSP running at 8 teraflops. It has been conjectured that devices on the order of 50 nanometers in size along with unconventional switching mechanisms, such as the Josephson junctions associated with superconductors, will be necessary to achieve the next level of processing speeds. TRW researchers (now Northrop Grumman) have quantified this further by predicting that 100 billion Josephson junctions on 4000 microprocessors will be necessary to reach 32 petabits per second. These Josephson junctions are incorporated into field-effect transistors which then become part of the logic circuits within the processors. Recently it was demonstrated at the Weizmann Institute in Israel that the tiny magnetic fields that penetrate Type 2 superconductors can be used for storing and retrieving digital information. It is, however, not a foregone conclusion that computers of the future will be built around superconducting devices. Competing technologies, such as quantum (DELTT) transistors, high-density molecule-scale processors , and DNA-based processing also have the potential to achieve petaflop benchmarks. In the electronics industry, ultra-high-performance filters are now being built. Since superconducting wire has near zero resistance, even at high frequencies, many more filter stages can be employed to achive a desired frequency response. This translates into an ability to pass desired frequencies and block undesirable frequencies in high-congestion rf (radio frequency) applications such as cellular telephone systems. ISCO International and Superconductor Technologies are companies currently offering such filters. Superconductors have also found widespread applications in the military. HTSC SQUIDS are being used by the U.S. NAVY to detect mines and submarines. And, significantly smaller motors are being built for NAVY ships using superconducting wire and "tape". In mid-July, 2001, American Superconductor unveiled a 5000-horsepower motor made with superconducting wire (below). An even larger 36.5MW HTS ship propulsion motor was delivered to the U.S. Navy in late 2006

The newest application for HTS wire is in the degaussing of naval vessels. American Superconductor has announced the development of a superconducting degaussing cable. Degaussing of a ship's hull eliminates residual magnetic fields which might otherwise give away a ship's presence. In addition to reduced power requirements, HTS degaussing cable offers reduced size and weight. The military is also looking at using superconductive tape as a means of reducing the length of very low frequency antennas employed on submarines. Normally, the lower the frequency, the longer an antenna must be. However, inserting a coil of wire ahead of the antenna will make it function as if it were much longer. Unfortunately, this loading coil also increases system losses by adding the resistance in the coil's wire. Using superconductive materials can significantly reduce losses in this coil. The Electronic Materials and Devices Research Group at University of Birmingham (UK) is credited with creating the first superconducting microwave antenna. Applications engineers suggest that superconducting carbon nanotubes might be an ideal nano-antenna for high-gigahertz and terahertz frequencies, once a method of achieving zero "on tube" contact resistance is perfected. The most ignominious military use of superconductors may come with the deployment of "E-bombs". These are devices that make use of strong, superconductor-derived magnetic fields to create a fast, high-intensity electro-magnetic pulse (EMP) to disable an enemy's electronic equipment. Such a device saw its first use in wartime in March 2003 when US Forces attacked an Iraqi broadcast facility.

A photo of Comet 73P/Schwassmann-Wachmann 3, in the act of disintegrating , taken with the European Space Agency S-CAM.

Among emerging technologies are a stabilizing momentum wheel (gyroscope) for earth-orbiting satellites that employs the "flux-pinning" properties of imperfect superconductors to reduce friction to near zero. Superconducting x-ray detectors and ultra-fast, superconducting light detectors are being developed due to their inherent ability to detect extremely weak amounts of energy. Already Scientists at the European Space Agency (ESA) have developed what's being called the S-Cam, an optical camera of phenomenal sensitivity (see above photo). And, superconductors may even play a role in Internet communications soon. In late February, 2000, Irvine Sensors Corporation received a $1 million contract to research and develop a superconducting digital router for high-speed data communications up to 160 Ghz. Since Internet traffic is increasing exponentially, superconductor technology may be called upon to

meet this super need. Irvine Sensors speculates this router may see use in facilitating Internet2.

According to June 2002 estimates by the Conectus consortium, the worldwide market for superconductor products is projected to grow to near US $38 billion by 2020. Low-temperature superconductors are expected to continue to play a dominant role in well-established fields such as MRI and scientific research, with high-temperature superconductors enabling newer applications. The above ISIS graph gives a rough breakdown of the various markets in which superconductors are expected to make a contribution. All of this is, of course, contingent upon a linear growth rate. Should new superconductors with higher transition temperatures be discovered, growth and development in this exciting field could explode virtually overnight.

Another impetus to the wider use of superconductors is political in nature. The reduction of green-house gas (GHG) emissions has becoming a topical issue due to the Kyoto Protocol which requires the European Union (EU) to reduce its emissions by 8% from 1990 levels by 2012. Physicists in Finland have calculated that the EU could reduce carbon dioxide emissions by up to 53 million tons if high-temperature superconductors were used in power plants.

The future melding of superconductors into our daily lives will also depend to a great degree on advancements in the field of cryogenic cooling. New, high-efficiency magnetocaloric-effect compounds such as gadolinium-silicon-germanium are expected to enter the marketplace soon. Such materials should make possible compact, refrigeration units to facilitate additional HTS applications. Stay tuned !

A high-temperature superconductor levitating above a magnet

A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen.

Persistent electric current flows on the surface of the superconductor, acting to exclude the

magnetic field of the magnet (Faraday's law of induction). This current effectively forms an

electromagnet that repels the magnet.

Nobel Prizes for superconductivity

Heike Kamerlingh Onnes (1913), "for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium"

John Bardeen, Leon N. Cooper, and J. Robert Schrieffer (1972), "for their jointly developed theory of superconductivity, usually called the BCS-theory"

Leo Esaki, Ivar Giaever, and Brian D. Josephson (1973), "for their experimental discoveries regarding tunneling phenomena in semiconductors and superconductors, respectively," and "for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects"

Georg Bednorz and Alex K. Müller (1987), "for their important break-through in the discovery of superconductivity in ceramic materials"

Alexei A. Abrikosov, Vitaly L. Ginzburg, and Anthony J. Leggett (2003), "for pioneering contributions to the theory of superconductors and superfluids