Nanostructure studies of strongly correlated materials

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Nanostructure Studies of Strongly Correlated Materials

Jiang Weia and Douglas Natelson

b

Received (in XXX, XXX) Xth XXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX

DOI: 10.1039/b000000x

Strongly correlated materials exhibit an amazing variety of phenomena, including metal-insulator 5

transitions, colossal magnetoresistance, and high temperature superconductivity, as strong electron-

electron and electron-phonon couplings lead to competing correlated ground states. Recently, researchers

have begun to apply nanostructure-based techniques to this class of materials, examining electronic

transport properties on previously inaccessible length scales, and applying perturbations to drive systems

out of equilibrium. We review progress in this area, particularly emphasizing work in transition metal 10

oxides (Fe3O4, VO2), manganites, and high temperature cuprate superconductors. We conclude that such

nanostructure-based studies have strong potential to reveal new information about the rich physics at

work in these materials.

Introduction

Strongly correlated materials (SCMs), in which single-particle 15

band structure is inadequate to describe the electronic and

magnetic structure, remain at the forefront of condensed matter

and materials physics research. Strong electronic correlations and

the interplay between electronic, magnetic, and structural degrees

of freedom lead to an incredibly rich panoply of phenomena.1 20

Metal-insulator transitions, “heavy” charge carriers, colossal

magnetoresistance, and the emergence of high temperature

superconductivity all have their origins in this class of materials.

From the perspective of basic science, these materials are

fascinating precisely because of the richness of emergent 25

phenomena from the collective response of the system. Their low

energy excitations can be exotic, such as having effective masses

much larger than the free electron mass, or having

unconventional properties far from those of electron-like

quasiparticles. Somehow the interactions between electrons (and 30

between electrons and the lattice) give rise to properties vastly

different from those expected from noninteracting band structure.

We are able to understand the electronic structure of a single

copper, iron, phosphorus, or oxygen atom, for example, quite

well using atomic orbitals constructed from the single-electron 35

solution to the Schroedinger equation for the Coulomb potential,

with interaction-based corrections playing a comparatively minor

role (via Hund’s rules, for example). However, magnetite (Fe3O4)

exhibits an electronic structure with a correlated ground state that

has been a topic of controversy for seven decades2, 3 and the 40

copper oxide and iron pnictide superconductors show competition

between magnetic order and superconductivity. Strongly

correlated materials are a laboratory for studying the collective

properties of large numbers of strongly interacting, highly

quantum mechanical particles. 45

These materials are also of considerable technological interest.

Room temperature superconductivity, if it occurred with the right

combination of critical current and field, would be a

transformative technology. Materials with metal-insulator

transitions and large magnetoresistive effects are attractive for 50

possible electronic switching and data storage applications.

A great deal of progress in understanding SCMs has been

made using bulk characterization techniques. These include: x-

ray, electron, and neutron diffraction to determine crystal

structures and long-range order; optical spectroscopies and 55

photoemission to learn about the electronic energetics;

magnetometry and specific heat determination to learn about

magnetic order and phase transitions; and electronic and thermal

transport, often as a function of magnetic field, to find out about

charge carrier dynamics and the mechanisms of energy flow. 60

Likewise, the development of scanned probe microscopies has

given further insights into these systems, providing evidence of

inhomogeneities on the nanoscale4, 5, and other information about

electronic structure6, 7.

Recently, however, there has been a growing realization that 65

making nanodevices based directly on SCMs enables experiments

that give information that is otherwise not readily accessible. This

article is meant to provide an overview of some of the recent

developments in this area. By its nature it is not possible in this

format to provide an exhaustive review of all work in the field. 70

We have done our best to highlight a representative set of results,

and the omission of a reference should be interpreted as an

oversight rather than a critical judgment. We consider systems

confined at the nanoscale in at least one dimension, and when

discussing two-dimensional systems we pay particular attention 75

to those with strong two-dimensional confinement. We will

describe the specific motivations for nanostructure-based SCM

investigations, briefly summarize the various ways of producing

nanostructures that incorporate SCMs, and explain why such

research has been relatively slow, compared with the application 80

of similar techniques to semiconductors and ordinary metals. We

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2 | Journal Name, [year], [vol], 00–00 This journal is © The Royal Society of Chemistry [year]

will then describe recent efforts, broken down by particular

families of materials. We will conclude with some observations

about the state of this approach and its likely future directions.

Nanostructure-based investigations of these materials are

motivated by specific goals directed at better understanding the 5

origins of the rich physics described above:

• Nanostructure experiments can probe SCMs on length

scales of interest. As will be demonstrated below, SCMs can

exhibit inhomogeneities in their properties, particularly

evident in phenomena such as metal-insulator or normal-10

superconductor transitions. These inhomogeneities may

involve percolation or the breakup of the SCM into domains.

Macroscale measurements average over these

inhomogeneities and can therefore obscure single-domain or

single-boundary effects. While scanned probe measurements 15

are extremely useful, there are circumstances where being

able to perform transport through an individual region,

domain, or interface is revelatory.

• Nanostructures allow discrimination between possible

physical mechanisms for phenomena. Fig. 1 shows an 20

example of a dramatic effect in a SCM. In a charge-ordered

complex oxide (praesodymium calcium manganese oxide),

Asamitsu and collaborators observe1 that the application of

hundreds of volts across a mm-scale crystal results in a

transition from the charge-ordered insulating state to a more 25

conducting state. This change is reversible, though hysteretic,

as the voltage is reduced. It is tempting to conclude that this

represents the electric field-induced breakdown of the

correlated state. However, large energies are available to the

charge carriers in this situation, and other explanations are 30

possible. In nanoscale structures, it is possible to achieve

similar magnitudes of applied electric field while using much

lower voltages, thus placing an upper limit on the energy

available per charge carrier.

35

Fig. 1 Application of a large voltage across a ~ 1 mm crystal of a

correlated oxide in a charge-ordered insulating state results in a transition

to a more conducting state. Removal of the voltage leads to

reestablishment of the insulating state. Such large electric fields are

achievable at much lower voltages in nanostructure-based devices. 40

Reprinted by permission from MacMillan Publishers, Ltd.: Asamitsu et

al., Nature 388, 50-52 (1997), copyright 1997

• Nanostructured devices can enable gating/field-effect

experiments. In many SCM the density of charge carriers is a

tuning parameter of critical importance. Very often the carrier 45

density is altered by chemical doping, which carries with it

the necessary evil of simultaneously altering the disorder in

the material. Gating and the field-effect are a means of

altering the carrier density in a nanoscale-thickness channel at

fixed disorder.2 50

• Nanostructured devices are ideal for examining contact

effects and the process of charge injection. Conventionally,

electronic transport measurements employ multiterminal

methods to examine the intrinsic properties of the material

itself, avoiding the effects of contact resistances. In nanoscale 55

devices, contacts necessarily play an amplified role relative to

the bulk. This can be an opportunity rather than a problem. In

many SCMs, the low energy excitations are collective objects

with quantum numbers that differ greatly from those of the

electron-like quasiparticles in ordinary metals. When an 60

electron is injected into such a SCM, there is a ”dressing”

process that must take place, and contact/charge injection

experiments are the natural way to probe this.

• Nanostructured devices are essential for probing the

nonequilibrium physics of SCMs. The nonequilibrium 65

response of SCMs can be dramatic and provides another

probe of the electronic states and their excitations in such

materials. Applying a voltage bias to a SCM drives the local

electronic (and vibrational) distributions out of equilibrium.

Deviations from equilibrium distributions persist on length 70

scales associated with inelastic processes. Any effort to

measure these deviations, through tunneling3, 4, or shot noise5,

must be made using devices that are comparable in scale to

the inelastic scattering length. In SCMs, this distance can

easily be on the nanoscale, requiring electrodes spaced 75

accordingly.

Nanoscale devices may be made from SCMs by a variety of

techniques, many of which are based on approaches developed in

the study and engineering of semiconductors. The simplest is

direct growth of the material into a form useful for nanoscale 80

study. For two-dimensional structures or superlattices, molecular

beam epitaxy and pulsed laser deposition have been invaluable.6, 7

Some SCMs may be grown in even further reduced

dimensionality, as in VO2 nanowires8 produced from the vapor

phase, or nanowires made via templating9, 10. Exfoliation of 85

layered materials is also possible.11

More traditionally, lithographic techniques may be combined

with thin film growth to achieve SCM-based nanostructures.

Electrodes may be fabricated with nanoscale separations directly

on the surfaces of bulk or thin-film SCMs.12, 13 Films of strongly 90

correlated materials may be subtractively patterned into

nanostructures via lithographic definement of features and

chemical etching14-16. Additive patterning via lift-off processing

is also possible under some circumstances17, 18, though that

requires the growth of the SCM in the presence of some material 95

that may be used as a resist.

The patterning required for device fabrication is one reason

why nanostructured studies of SCM are often challenging.

Stoichiometry is often critical to the character of the ground states

exhibited in SCMs, as exemplified in the cuprate 100


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superconductors. The parent compound of the typical cuprate is a

Mott insulator, and depending on the chemical doping (including

alteration of the oxygen content) the ground state of the material

may be an antiferromagnet, a “strange” (non-Fermi liquid) metal,

an unconventional superconductor, or a comparatively normal 5

metal. Preserving stoichiometry in nanostructured materials can

be difficult. In nanostructured form, materials have large surface

to volume ratios, and oxidation or surface reconstruction must be

a concern. Similarly, in nanostructures produced by top-down

patterning of films or bulk materials, exposure of the material to 10

processing conditions (chemical etchants, lithography,

“descumming” techniques) can chemically modify the material

away from the desired composition.

Transition Metal Oxides

Strong correlations are frequently associated with materials 15

containing partially filled orbitals of a comparatively localized

character. Transition metal oxides, with their partially filled d

shells, fit the bill, and can exhibit dramatic deviations from

single-electron band structure expectations. NiO, for example, is

a transparent insulator when conventional band structure would 20

predict metallic conduction19. Here we discuss recent

nanostructure-based experiments on two particular transition

metal oxide systems.

Magnetite

Magnetite, Fe3O4, also known as lodestone, has been known for 25

thousands of years due to its magnetic properties. The oxide

contains two populations of iron atoms, the A-sites (formal

valence +3, tetrahedrally coordinated by oxygens) and the B-sites

(formally mixed valence, split between +2 and +3, octahedrally

coordinated by oxygens). The iron sites order ferrimagnetically at 30

a temperature of 848 K. At room temperature, Fe3O4 is an inverse

spinel with a large, cubic unit cell, and is moderately conductive,

with a resistivity of a few mΩ-cm. Conduction is takes place

through the hopping of charge among the d orbitals of the mixed-

valence B-site irons. As temperature is reduced, the resistivity 35

increases weakly. At a temperature of around 122 K in the bulk,

magnetite undergoes what is now known as the Verwey

transition20, a first-order phase transition to a more resistive state,

with a monoclinic unit cell. A similar transition is also observed

in other inverse spinels, and magnetite is therefore an archetype 40

of this kind of “metal”-insulator transition21. Verwey’s original

hypothesis for this transition, that of simple charge ordering of

the B-site iron valence, has been ruled out via diffraction

experiments22. However, controversy remains concerning the

nature of the Verwey ground state and the relative importance of 45

electronic correlations and the electron-phonon coupling.

One challenge in investigating the Verwey transition through

nanostructures is the sensitivity of the transition to oxygen

content23, 24. A deviation from ideal oxygen stoichiometry by only

a couple of percent completely suppresses the transition 50

temperature, TV, leading instead to a smoothly increasing

resistivity upon cooling. This sensitivity, combined with the

relative stability of other iron oxides, hematite (Fe2O3) and

wustite (FeO), implies that nanoscale magnetite studies may be

hampered by either oxidation or reduction of the material at its 55

surface. Some experiments with magnetite nanoparticles25 report

suppression of the Verwey transition with decreasing particle

size, while others show persistence of the transition even in sub-

10 nm nanoparticles26.

60

Fig. 2 (a) In magnetite nanostructures, the low-temperature, insulating Verwey state is destabilized at large applied voltages, similar to what is seen in Fig.

1. Adapted with permission from MacMillan Publishers, Ltd.: from Lee et al., Nature Mater. 7, 130-133 (2008).

(b) The switching voltage varies linearly with the length of the magnetite channel, consistent with an electric field-driven transition. A. A. Fursina et al.,

unpublished.

Recent studies using nanospaced electrodes with both Fe3O4 65

nanoparticles27 and epitaxially grown, single-crystal thin films12,

27 have revealed the existence of a nonequilibrium transition in

Fe3O4 at temperatures below TV. In the low temperature state, a

sufficiently large dc voltage in a given device drives the material

out of the insulating state and back into a more conducting state, 70

as shown in Fig. 2a. This transition, in which the material returns

to the insulating state as the bias voltage is reduced, is

reminiscent of that shown in Fig. 1, hypothesized to be the result

of field-driven breakdown of a charge-ordered ground state.


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Defining the switching voltage, Vsw(T), as the voltage at which

the device switches to the high-conductance state as the

magnitude of the applied voltage is increased, Fig. 2a shows that

Vsw increases as T is decreased below Vsw, and that the transition

vanishes as T → TV, where TV is determined by the temperature 5

dependence of the zero bias resistance.

In standard non-volatile resistive switching28, 29, sweeping an

applied voltage results in a change in the resistance of a device

that persists when the bias is reduced back to zero (“non-

volatile”). A second voltage sweep is required to recover the 10

original resistance. Note that the transition observed in magnetite

is not nonvolatile, and is not “resistive switching” as described by

the nonvolatile memory community.

In the magnetite case, it is possible to test for the field-driven

character of the transition by examining the geometric scaling of 15

the device characteristics. As shown in Fig. 2b, Vsw varies

approximately linearly with L, the interelectrode separation,

indicating that at any given temperature there is a characteristic

electric field, dVsw/dL, associated with the nonequilibrium

transition. For TV ≈ 110 K, the critical field scale is approximately 20

4 × 106 V/m at 100 K and 8 × 106 V/m at 80 K. Note that the

amount of energy gained by an electron tunneling across one unit

cell in such a field at 80 K would be about 7 meV, comparable to

kBTV. This is consistent with the scenario that the nonequilibrium

transition is a Landau-Zener-like breakdown of the correlated 25

state30, 31.

The hysteresis apparent in Fig. 2a is now known to be a result

of self-heating32. Once the device is switched into the conducting

state, power dissipation due to increased current flow elevates the

local temperature so that Vsw is reduced, leading to hysteresis if 30

the bias voltage is continuously swept. Measurements with 0.5

ms pulses have shown that the hysteresis vanishes, while Vsw(T)

remains essentially unaltered, in the limit of short, well-separated

pulses. High speed pulsed measurements33 indicate that

switching takes place on timescales of tens of nanoseconds. 35

X

Fig. 3 (a) Multiterminal measurements allow the determination of both bulk and contact resistances in magnetite nanostructures. As is clear from inset

(d), the bulk and contact resistances have identical temperature dependences. Reprinted with permission from A. A. Fursina et al., Phys. Rev. B 81,

045123 (2010). Copyright 2010 by the American Physical Society. (b) This trend is true for several different contact metals, and by analogy with similar

observations in organic semiconductor devices, implies that conduction in both the high and low temperature states takes place through a hopping 40

mechanism. This is an example of using contact measurements to infer bulk transport physics. Reprinted with permission from A. A. Fursina et al., Phys.

Rev. B 82, 245112 (2010). Copyright 2010 by the American Physical Society.

Vsw does not extrapolate to zero as L → 0 because some

fraction of the applied voltage is dropped at the injecting and 45

collecting contacts. Using multiterminal measurements, as shown

in Fig. 3a, it has been possible to study the contact resistance in

such structures as well as the bulk resistivity34, 35. Two important

observations came from these measurements. First, at Vsw, the

contact resistances at both the injecting and collecting electrodes 50

drop, as well as the bulk resistance; this is again consistent with a

field-driven breakdown of the correlated state30, 31 Second, the

contact resistance was found to have the same temperature

dependence as the bulk resistance, from room temperature down

to well below TV. This trend is true for multiple contact metals 55

(Cu, Au, Pt), as shown in Fig. 3b.

The apparent proportionality between the bulk resistivity and

the contact resistance over the whole temperature range

demonstrates the power of contact studies to access the bulk

transport mechanism in a SCM. Such a proportionality has been 60

observed previously36, 37 in organic semiconductor structures in

which transport in the bulk is dominated by carrier hopping

between localized states. For charge injection from a metal into a

hopping system, an injected carrier can diffuse away from the

interface via hopping, but at the same time is influenced by its 65

image charge in the metal. This competition leads38 to a contact

resistance that is inversely proportional to the charge mobility,

and hence directly proportional to the resistivity, of the hopping

system. The magnetite contact measurements therefore confirm

that conduction in both the low and high temperature states of 70

magnetite proceeds through hopping39, consistent with observed

temperature dependences, and may permit further studies of the

nature of the mobile charge carriers.

Vanadium Dioxide

VO2 is famous for its dramatic metal-insulator transition with up 75


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to four orders magnitude40 change in conductivity at 67oC - a

convenient temperature for many applications. Below 67oC, VO2

is semiconductor (the M1 phase) featuring a gap about 0.7 eV41, 42

with a monoclinic crystal structure, while above 67oC the lattice

transforms into a bad metal with a rutile structure. The long-term 5

debated mechanism43, 44 of the metal-insulator transition is still

obscure. The lattice structure change suggests a first-order phase

transition where the vanadium chain dimerizes during the

transition, causing the size of the unit cell to double. This

supports a Peierls-like transition from the view of band theory. 10

However, many factors point to a Mott transition, driven by

strong electron-electron interactions. These factors include the

anomalously low conductivity of the metallic state;45-47 the fact

that band structure calculations fail to obtain the insulator band

gap;44, 48 the fact that an intermediate monoclinic “M2” phase, 15

which can be stabilized by stress49 or doping,50 is insulating in

spite of having undimerized vanadium chains;43 and in optical

experiments a dependence of properties on excitation power

which indicates sensitivity to excited carrier density.51-53

Despite the dramatic MIT at a convenient temperature, 20

seemingly easy applications of VO2 in electrical54 and optical55

switching or sensors remain unrealized. The blame for this falls

largely on the large strains associated with the structural

transition. The resulting stresses lead to cracking in bulk VO2

crystals, and the formation of a complicated metal/insulator 25

domain structure (consequently affecting measured resistance) in

films and large particles upon passing through the MIT. The

result is often irreproducibility between samples, broadening and

hysteresis of the characteristics, and mechanical degradation.

X 30

Fig. 4 Discrete switching in the MIT of micro/nanoscale VO2 regions.

Main panel—8 consecutive R-T cycles (R in linear scale) of a 1x 6µm2

VO2 device zoomed in on part of the MIT, as marked in the full

measurement shown in (b) (log scale of R). (a)—Image of 8 devices on

one sample showing VO2 square of side 50 µm, on top of which are 35

V=Au electrodes defining device lengths of 1,2,3, and 4 µm (2 devices of

each) and width of 8 µm for all the devices. Devices with length of 1 and

4 µm are marked. Reprinted with permission from A.Sharoni et al., Phys.

Rev. Lett. 101, 026404 (2008). Copyright 2008 by the American Physical

Society. 40

Thin VO2 films allow strain to relax through the MIT, which

avoids the cracking problem inherent to the bulk VO2. Many

interesting discoveries have been made while investigating the

properties of thin film VO2 samples. Time resolved pump-probe

experiments56, 57 showed that metal-insulator transition can be 45

induced by pumping laser in a time scale less than picosecond,

which exceeds the speed of phonon propagation. In a nano-

clustered film sample, the effective mass inferred in nanometer-

sized metallic puddles exhibits a divergent behavior at the

vicinity of metal-insulator transition, a characteristic sign of the 50

Mott transition58.

Sharoni et al. investigated the transport properties of the

thermally induced metal-insulator transition in VO2 thin film

devices shown in Fig. 4 13. By fabricating two terminal devices

with the separation of the source drain electrodes ranging from 55

microns to nanometers, they showed the overall resistance as a

function of temperature, R(T), resembles the smeared MIT in a

macroscale film. However, within each transition edge there are

small, discrete jumps of resistance which correspond to the sharp

transition from each individual grain. This is a good example of 60

how nanostructured devices can reveal the homogenous behavior

of the material, when device size is approaching the range of

single stable regions going through the MIT.

Fig. 5 Electrically driven MIT in a VO2 thin film device. The delay 65

between the applied voltage pulse and the detected current through a load

resistor is too short to be explained by self-heating, and supports a

transition driven by charge injection. Reprinted from Physica B, Vol 369,

B.-G. Chae et al., “Abrupt metal-insulator transition observed in VO2 thin

films induced by a switching voltage pulse”, 76-80, Copyright 2005, with 70

permission from Elsevier.

Because of the small separation between the electrodes in

nanoscale two terminal devices, the transition can be easily

switched by applying small voltages, reminiscent of the field

driven transition in magnetite discussed above. Studies on simple 75

two-terminal devices with out of plane 59 and in plane geometry 60 (Fig. 5) show a sign of non-equilibrium charge injection

induced metal-insulator transition-based on the observation that

the delay time is two orders magnitude smaller than what would

be expected from just a self-heating electrothermal model. 80

VO2 has a 0.6-0.7 eV band gap in the insulating phase,

resulting in a high carrier density near the transition, up to

2x1018/cm-3 61, and therefore a very short screening length (a few

nanometers). Through field-effect techniques, in principle one

can apply an out-of-plane electric field up to 107 V/m on a VO2 85

film with a modest gate voltage without any significant leakage

through an intervening dielectric layer. However, interdiffusion

between the dielectric layer and VO2 can dramatically degrade the

MIT up to 2 orders magnitude due to large gate leakage. 61 To


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obtain a high enough effective electric field penetrating through

VO2 to achieve field-effect modulation of the MIT remains a

great challenge.

Most recently, single-crystal VO2 nanostructures(wires and

sheets) have been synthesized using physical vapor transport.8 5

Unlike bulk crystals, these nanomaterials display no degradation

going through phase transition due to their small dimension and

high crystallinity. Cao et al. showed62 that a nanowire near the

transition responds to external bending stress by rearrange the

configuration of metallic domain and insulating domains to 10

reduce the total energy. As illustrated in Fig. 6, below the

transition temperature and under no bending stress, the VO2

nanobeam is in a uniform brighter insulating phase. When

temperature is raised toward the transition and with some

bending, the metallic darker phase appears in a triangle pattern. 15

This unique arrange of metallic and insulating domain structure

minimizes the total free energy, which is the sum of both the free

energy of the two phases and the strain energy. More remarkably,

the metallic phase can be stabilized even at room temperature

because of the strain. 20

Fig. 6 Strain engineering domains in a VO2 beam. Before bending, the

beam was purely insulating (bright, top image) at 298 K and purely

metallic (dark, second image) at 343 K. A tungsten needle (denoted by the

arrows) was used to push-bend the beam, which created domain arrays in 25

the strained regions. Scale bar, 10 µm. Adapted with permission from

MacMillan Publishers, Ltd.: from J. Cao et al., Nature Nano. 4, 732-737

(2009).

Such single crystal VO2 nanostructures also provide a model

system for exploring the intrinsic nature of Mott physics. Other 30

than the M1 phase, there is another M2 phase in the bulk stable

only when a uniaxial stress is present or chromium atoms are

partially substituting vanadium atoms in the lattice49, 50. Due to

tight bonding from the substrate, the M2 phase is also observed in

VO2 nanobeams by XRD and Raman measurements63, 64. At the 35

transition temperature, partially formed metallic rutile phase with

a smaller lattice constant causes the development of tension in the

remaining M1 phase. The fact that M1 and M2 have almost the

same free energy and that M2 phase has a longer lattice constant

than M1 makes M2 more favorable to minimize the overall strain 40

energy. Both XRD and micro-Raman data show that the lattice

structure of M1 transformed to M2 on the heating, and vise versa.

Precise resistivity of the M1, M2 and rutile phases were

obtained by electrical transport measurements on single-crystal

suspended VO2 nanobeams42. As shown in Fig. 7a, the suspended 45

nanobeam structure has both ends clamped to substrate, which

applies a uniform strain along the c-axis. Single-domains of

insulating phase and metallic phase coexist, with the relative

portion of the two domains varying with temperature. Fig. 7b

shows that M1 and M2 have the same activation energy (0.6eV) 50

but the resistivity of M2 is about more than twice that of M1.

More surprisingly the insulating phase’s resistivity reaches a

constant (about 12 Ωcm) as long as the metallic phase nucleates.

This result implies a constant carrier density for the insulating

phase right at the transition point - a signature of a Mott insulator. 55

These experiments demonstrate that when the material’s

dimension has been reduced to be smaller than the characteristic

length of inhomogeneities in bulk such as strain, the inconvenient

parameter for bulk can actually be used as a nice tuning knob to

investigate the material’s extended region of intrinsic properties. 60

Manganites

Another family of transition metal oxides is the manganites,

such as that based on the perovskite LaMnO3. Like the cuprates,

the manganites have an extremely rich phase diagram depending

on their chemical doping, with many competing phases including 65

those with charge order, orbital order, ferromagnetic, and

antiferromagnetic order, and electronic conductivities from the

metallic to the strongly insulating65. Some of the best studied

manganites are the “colossal magnetoresistance” compounds,

which exhibit a (magnetic field-tunable, hence the name) phase 70

transition from a high temperature insulating state to a low

temperature ferromagnetic metallic state66. The ferromagnetic

interaction coincident with metallic conductivity has its origins in

the “double exchange” process, whereby an electron may be

transferred from Mn3+

to Mn4+

ions via an intervening O2−

ion, all 75

in one coherent step. The on-site Coulomb repulsion on the Mn

sites is not small, and neither is the coupling of the Mn4+

charge

to the lattice via the Jahn-Teller interaction65. In the clean limit,

competition is between the ferromagnetic metallic state and an

antiferromagnetic insulating state, and mild (perhaps 80

unavoidable) perturbations in the form of strain and other

quenched disorder can lead to phase separation67, 68 on the

nanoscale. The result is that the metal-insulator transition is very

often inhomogeneous on the nanoscale, as seen clearly via

scanned probe measurements69, 70. 85

As in the case of VO2, several experimental efforts have been

made to examine the metal-insulator transition in this series of

compounds by spatially confining the materal on a length scale

comparable to the scale of the inhomogeneities. Two particular

groups71, 72 concentrated on materials based on 90

(La,Pr,Ca)MnO3(LPCMO), a system between the ferromagnetic

(below 275 K) metal La5/8Ca3/8MnO3, and the charge-ordered

antiferromagnetic insulator Pr5/8Ca3/8MnO3. The mixed material

is known73-75 to exhibit a percolative, inhomogeneous (low T)

metal-insulator (high T) transition with inhomogeneities from 95

tens to hundreds of nanometers in extent.

Fig. 8a shows the result of patterning constrictions down to

widths of 1.6 µm using conventional photolithography and wet

etching. In wide strips of LPCMO, the resistance vs. temperature

shows a clear hysteresis over the temperature range of the 100

transition, but the curves are comparatively smooth, as seen in

extended films. However, as the constriction width is reduced

toward the inherent length scale of the percolation process in this


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material, extremely sharp, discrete switching transitions are

evident. The natural interpretation is that spatial confinement

allows the transport measurement to be sensitive to individual

conducting and insulating domains and the boundaries between

them.72 5

Fig. 7 Individual VO2 nanobeam devices as tools to study the MIT. (a) Five images of one suspended nanobeam between contacts at the top and bottom

separated by 20 µm. Above 68 °C the beam contains a single metallic domain (gray, lower portion of beam), which grows on warming until the insulating

domain (brighter, upper portion) disappears at about 105 ˚C. (b) Collected resistivity measurements for twelve nanobeams of various dimensions. The

insulator resistivity ρi follows two distinct curves, which we ascribe to the M1 and M2 phases, both of which exhibit an activation energy of 0.30 eV 10

(illustrated by the dotted line). Plotted using symbols are measurements of the resistivity ρic of the insulator in coexistence for ten different nanobeams. To

within error they show a universal temperature-independent value of 12± 2 Ωcm. The metal resistivity ρm was obtained from one section of a nanobeam

(H = 0.18, W = 0.9, L = 30 µm) from which two other different-length sections (L = 20 and 50 µm) gave almost identical results. Estimated errors in ρm

due to uncertainty in the cross-section are 25%. Adapted with permission from MacMillan Publishers, Ltd.: from J. Wei et al., Nature Nano. 4, 420-424

(2009). 15

This same approach and material system have further

underscored the importance of strain and disorder in the

transition, and highlighted concerns about the intrinsic vs.

extrinsic origins of inhomogeneities. Follow-up

measurements76shown in Fig. 8b show a surprising feature, the 20

presence of a second metal-insulator transition peak in R vs. T, at

a different transition temperature than in the unpatterned film. As

the authors point out, this reemergent transition most likely

results from local differences in epitaxial strain. In a large area

film such a region of lower transition temperature would not be 25

detected through transport measurements since percolation of the

higher transition temperature regions would already have

produced a metallic network. The restricted geometry reveals the

existence of this inhomogeneity by constraining transport to take

place through a greatly restricted path. A similar observation has 30

been reported in micron-scale La0.5Ba0.5MnO3wires77. The same

basic idea can be applied to examining time-variation in the

percolative network78. In the restricted geometry of such a

constriction, it is possible to observe the motion of individual

domain boundaries, manifested as telegraph-like switching in the 35

electronic transport.

Fig. 8 Geometric confinement to study the MIT in manganites. (a) Resistivity vs. temperature in manganite constrictions shows evidence of discrete

switching events as constriction size is reduced toward the spatial scale associated with phase inhomogeneity in this material. Adapted with permission

from H. Y. Zhai et al., Phys. Rev. Lett. 97, 167201 (2006). Copyright 2006 by the American Physical Society. (b, c) (b) A uniform manganite film shows 40

a single phase transition, as expected, for four different values of magnetic field. (c) A constricted wire of the same material shows a double transition,

ascribed to phase inhomogeneity, averaged over in the bulk film. Adapted with permission from T. Z. Ward et al., Phys. Rev. Lett. 100, 247204 (2008).

Copyright 2008 by the American Physical Society.






Nanoscale

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Recent experiments have considered the LPCMO system at

even smaller constricted widths, well below 1 µm, fabricated via

focused ion beam (FIB) etching. As shown in Fig. 9a, in transport

through such constrictions, Singh-Bhalla et al. 79 observe very

high resistances (~108

Ω, much larger than the quantum of 5

resistance h/2e2 ~ 13 kΩ) in the temperature range corresponding

to the metallic phase of the unpatterned film. Remarkably, the

temperature dependence of that resistance is very weak. This is in

contrast with expectations from the scaling theory of

localization80, which would lead to an expectation of a strongly 10

temperature-dependent hopping conduction (activated or

variable-range hopping) at such resistances. The authors deduce

that the essentially temperature-independent transport must be

dominated by direct tunneling between metallic regions, through

insulating regions with thicknesses near the atomic scale. This 15

conclusion is supported by the observed response to an external

magnetic field, as in Fig. 9b. As the external field is applied, the

transport remains only weakly dependent on T, but the resistance

drops considerably (while still remaining above h/2e2). The

sensible interpretation is that the external H leads to coalescence 20

of the metallic regions, so that transport through the constriction

at higher magnetic fields is dominated by fewer, thinner tunnel

barriers. These constrictions may then be used as tools to

examine transport tunneling through both charge-ordered and

charge-disordered insulating phases81. 25

It is clear that combining a micro or nanoscale restricted

geometry with the manganites has shed further light on the

percolative nature of the metal-insulator phase transition. It is

somewhat surprising that strong “single domain” percolative

effects have been apparent even in experiments with overall 30

constriction geometries considerably larger than the length scales

highlighted by scanned probe or electron microscopy methods.

This suggests that the patterning methods used to provide the

confinement may sufficiently modify the quenched disorder, local

stoichiometry, or strain environment to alter the balance between 35

the competing states. Still, these experiments demonstrate the

nanostructure approach’s ability to bring to the fore the

homogeneity of the sample properties and allow the examination

of single domains or individual domain walls. Given past

observations of electroresistive effects82, in which gating has 40

been used to tune the percolative transition, it is reasonable that

explorations combining gating with nanostructures of greater

sophistication may lead to further insights into these materials.

High temperature superconductors

We limit our discussion to the copper oxide superconductors, as 45

nanostructure-based studies of the more recently discovered iron

pnictides have not yet been published. The cuprate high

temperature superconductors are perhaps the most famous of all

SCMs, and like the materials already discussed, there are

questions of intrinsic and extrinsic homogeneity in their electrical 50

properties. The parent compounds of the cuprate high

temperature superconductors are antiferromagnetic Mott

insulators. When chemically doped, antiferromagnetism is

suppressed, and the materials become “bad metals”, with an

unusual temperature dependence of the normal state resistivity at 55

higher temperatures. Tunneling spectroscopy and other

characterization methods reveal a pseudogap in the density of

states below a characteristic temperature T*. At a lower

temperature, the materials undergo a transition into a d-wave

superconducting state. The nature of the pseudogap remains 60

controversial after 25 years of investigation, with one central

question at hand, “is the pseudogap a sign of incipient

superconductivity, or is it instead a signature of some other

competing phase, interfering with superconductivity by removing

spectral weight near the Fermi level?” 65

Fig. 9 Measurements of resistivity in nanoscale manganite constrictions

show strong evidence of discrete switching due to phase separation. The

weak temperature dependence observed even when resistance far exceeds 70

the quantum of resistance suggests transport is dominated by tunneling

through insulating boundaries between metallic domains. Adapted with

permission from G. Singh-Bhalla et al., Phys. Rev. Lett. 102, 077205

(2009). Copyright 2009 by the American Physical Society.

75

A motivation for nanostructure-based probes of these materials





is the profusion of relatively short length scales that are

physically significant 83. (See Fig. 10). Scanned probe

microscopy has established the existence of spatial

inhomogeneity in the high-Tc cuprates both above and below the

superconducting transition. The chemical disorder due to doping 5

is essentially unavoidable in these SCMs. In the pseudogap

regime, the magnitude and onset of the pseudogap are observed

to vary considerably on the few nanometer distance scale75. In

those experiments, regions with an enhanced pseudogap had

locally higher superconducting transition temperatures. These and 10

other measurements84 lend credence to the possibility that

electronic pairing begins locally above the global Tc, and the

overall superconducting transition corresponds to the coalescence

of local regions and the establishment of global phase coherence.

Other spatial inhomogeneities have been detected via scattering 15

experiments and observed via scanning tunneling microscopy85-

87, showing that modulations of the local electronic density

(stripes or checkerboard patterns) can appear with periodicity of a

few lattice sites and extents on the nanometer scale.

Other physically relevant length scales arise from the well 20

known physics of superconductivity. The coherence length, ξ, is

the rough spatial extent of an electron pair and is also the

minimum distance scale over which the superconducting order

parameter may change rapidly. In the cuprates this scale is ~ 1

nm. The London penetration depth, λ, describes the distance scale 25

over which weak magnetic fields are screened in a

superconductor, and is the characteristic length associated with

vortices and flux penetration. In the cuprates λ ~ 200 nm88, and is

anisotropic due to the layered character of the perovskite crystal

structure. 30

Nanostructure examinations of the cuprates have been

performed though the challenge of preserving the material

stoichiometry is ever present. As early as 199189, focused ion

beam etching was combined with photolithography to pattern

microbridges with transverse dimensions as small as 500 nm 35

from a YBCO (YBa2Cu3O7) film 200-500 nm thick deposited by

pulsed laser methods. The Tc of the nanobridges was ~ 90 K,

comparable to that seen in the unpatterned film. These structures

exhibited very high critical current densities, exceeding 109

A/cm2 for the smallest cross section bridge. These observations 40

are in contrast to those made in nanobridges in slightly oxygen

deficient YBCO90. In this more recent work, e-beam lithography

and patterned reactive ion etching were used to produce

nanobridges as narrow as 50 nm, in films 50 nm thick. No critical

current enhancement was observed, and a slight degradation in Tc 45

indicates some alteration of the stoichiometry as a result of the

device fabrication processing.

Micro and nanobridges have also been used to study the limits

of superconductivity in reduced dimensionality, looking at the

superconductor-insulator transition and phase slips. Long (5-10 50

µm) and narrow (50-500 nm width) nanoconstrictions from

YBCO made via FIB are an example91. As shown in Fig. 11, such

constrictions with a normal-state resistance larger than h/4e2 = 6.45 kΩ, the quantum of resistance for Cooper pairs, do not

exhibit a superconducting transition. This may be fortuitous, as 55

resistance per unit length has proven to be relevant in

observations in ultrathin nanowires fabricated from conventional

superconductors92. In the narrowest wire that examined with

superconductivity, the resistance as a function of temperature is

well described by the theory of thermally activated phase slips. 60

Fig. 10 Length scales in the high temperature superconductors. Reprinted

from Physica C, Vol 408-410, P. Mohanty et al., “Nanoscale high-

temperature superconductivity”, 666-669, Copyright 2004, with 65

permission from Elsevier.

Further study of phase slips in a more extreme geometry was

undertaken by Xu and Heath15. A YBCO film was coated with a

thin SiO2 film, and then an array of very narrow (~ 10 nm) Pt 70

nanowires (templated on a selectively-etched MBE grown

substrate93) was transferred onto the surface. The refractory

nanowires acted as a hard mask during Ar/O2 ion etching,

transferring the nanowire pattern to the YBCO. The

superconducting transition was observed to be broadened and 75

shifted in accordance with the theory of thermally activated phase

slips, and exhibited enhanced critical fields as wire width was

considerably smaller than λ.

The nanowire geometry has also been used to examine the

pseudogap regime in underdoped YBCO. Low frequency noise 80

measurements on 100-250 nm-wide nanowires14 find significantly

enhanced telegraph-like noise (discrete switching between small


http://dx.doi.org/10.1016/j.physc.2004.03.102

http://dx.doi.org/10.1016/j.physc.2004.03.102


numbers of resistance values) in the pseudogap regime between

Tc and T*. The authors suggest that this noise originates from

fluctuating domains of stripes or other broken symmetry phases

within the pseudogap regime. In this case the nanoscale

transverse dimensions magnify the importance of individual 5

fluctuating regions, enhancing the noise beyond the spatially

ensemble-averaged result that would be measured in large films.

Follow-up experiments94 in microstructured YBCO and doped

YBCO samples further support these inferrences.

10

Fig. 11 Constrictions of various transverse dimensions and lengths

patterned from YBCO films. Constrictions with resistances exceeding the

resistance quantum are found to lack a superconducting transition, while

others (3) show resistance vs. temperature consistent with expectations

from phase slips. Adapted with permission from P. Mikheenko et al., 15

Phys. Rev. B 72, 174506 (2005). Copyright 2005 by the American

Physical Society.

Spatial confinement approaching the nanoscale also allows

detailed studies of phase coherence and the effects of magnetic

fields in the high-Tc cuprates. Two recent investigations have 20

looked at magnetoresistance oscillations in small rings, either

individually16 or in a linked 2D array95. In both cases, working

with nanoscale rings and wire widths allows the investigations to

take place at comparatively large field scales (corresponding with

threading quanta of magnetic flux, h/2e, through the ring). The 25

physics examined was the Little-Parks effect96, 97, the oscillation

of Tc of the ring structure periodic in the flux, with period h/2e.

This periodicity arises because of circulating persistent currents

required to quantize the flux through the ring.

The single-ring investigations in YBCO16 show features 30

indicating beating of different, close field periodicities,

interpreted as a signature of nonuniform vorticity within the

finite-width superconducting ring (see Fig. 12a). In contrast, the

array measurements95 (see Fig. 12b) in La1.84Sr0.16CuO4 show

magnetoresistance oscillations two orders of magnitude larger 35

than those expected for Little-Parks. The authors are able to

explain both the magnitude and the temperature dependence of

this effect through interactions between the persistent currents

and vortices/antivortices in the superconductor.

Because the cuprates are inherently layered compounds, there 40

have also been investigations trying to manipulate individual,

exfoliated sheets of some of these materials, particularly those

related to the bismuth strontium copper oxide family11, 98.

However, this approach has not yet met with success, in terms of

producing structures that exhibit superconductivity. 45

Fig. 12 Nanoscale multiply connected high temperature superconductors.

(a) An example of a single nanoscale YBCO ring patterned for

investigating the Little-Parks effect. Adapted with permission from F. 50

Carillo et al., Phys. Rev. B 81, 054505 (2010). Copyright 2010 by the

American Physical Society. (b) An array of cuprate superconductor rings

observed to exhibit magnetoresistance oscillations much larger than those

expected from the simple Little-Parks effect. Adapted with permission

from I. Sochnikov et al., Phys. Rev. B 82, 094513 (2010). Copyright 55

2010 by the American Physical Society.

In contrast, field effect gating has been attempted numerous

times as an attempt to tune the superconducting properties of

these strongly correlated materials without chemical doping. An

extensive review99 highlights the challenge in this work. 60

Significant modulation of the correlated state properties requires

changing the charge distribution at a level approaching a charge

carrier per unit cell. This gated charge density is extremely

difficult to achieve with conventional gate dielectrics because of

the limits of breakdown electric field and relative dielectric 65

constant. The most successful approach in the cuprates has

employed a ferroelectric as the gate insulator100. With a 2 nm

thick GdBa2Cu3O7−x channel layer having Tc ≈ 50 K, the

ferroelectric remnant polarization of 10 µC/cm2 was sufficent to

modulate Tc by several Kelvin. More recently, electrolytic gating 70

has been put forward as a means of achieving similar surface

carrier densities101, with one report of its use in a cuprate

structure102 to shift Tc by tens of percent. More recently103,

electrolytic gating in a single-unit-cell-thick La2-xSrxCuO4 layer

has cleanly modulated the material from the insulating regime 75

through into superconductivity with Tc ~ 40 K.

Conclusions

The physics of strongly correlated materials remains rich,

fascinating, and a challenge to experimentalists as well as 80

theorists. Only recently have the hard-won nanofabrication skills

acquired as a result of decades of semiconductor research been

applied to these material systems. As has been described above,

nanostructure experiments that directly incorporate SCMs are on

the rise, and have much to reveal about the underlying physics of 85

these materials. Complementing scanned probe experiments,

nanodevice methods can examine intrinsic and extrinsic

inhomogeneities on their characteristic length scales.

Nanostructures can throw the effects of contacts, comparatively

unstudied and often actively avoided, into sharp relief, and 90

analysis of contact effects can further illuminate the bulk physics.

Nanostructures also enable nonequilibrium studies, with large








electric field perturbations achieveable even at modest applied

voltages.

Nanostructure-based investigations of SCMs are likely to

expand considerably in coming years. The availability of

nanofabrication resources is at an all-time high and is continually 5

increasing. Growth techniques for metal and semiconductor

nanoparticles (“molecular beaker epitaxy”) and nanowires

(vapor-liquid-solid growth; physical vapor deposition; chemical

vapor deposition) and 2d exfoliated nanomaterials are likely to be

turned to SCMs. Novel techniques such as electrolytic gating 10

present new opportunities for tuning the electronic properties of

such systems.

The primary obstacle standing in the way of rapid progress in

this area, both in materials growth and top-down processing, is

the often complicated stoichiometry of SCMs. This complexity of 15

composition as well as the extreme sensitivity of the relevant

physics to chemical doping has made the growth even of high

quality epitaxial films of many SCMs extremely difficult. While

there has been some recent progress in oxide film growth104, the

situation is likely to be more challenging in efforts at bottom-up 20

growth of nanowires and nanoparticles, given the high surface-to-

volume ratio and chemical reactivity of surfaces.

Top-down processing of SCMs, either to produce SCMs of

reduced dimensionality or to pattern electrodes and other surface

features, runs into the same road-block. Etching techniques 25

(reactive ion etching; ion milling; focused ion beam; wet

chemistry) can leave exposed surfaces available to react with

ambient surroundings. Lithographic patterning involves exposure

to multiple solvents, and processes common to the semiconductor

industry (e.g., oxygen plasma treatment to remove resist residue) 30

may be too aggressive to preserve SCM composition.

This is nonetheless an extremely exciting time, given the

promise of the science and the rapid pace of advancement in

nanopatterning and nanoscale materials growth. We believe that

in the coming years, nanostructure techniques will become as 35

much a part of the SCM characterization portfolio as scanned

probe methods and surface-sensitive spectroscopies, providing

insights into previously inaccessible physics.

The authors gratefully acknowledge the support of Department

of Energy grant DE-FG02-06ER46337. J.W. acknowledges the 40

support of the Evans Attwell/Robert A. Welch Postdoctoral

Fellowship, overseen by the R. E. Smalley Institute for Nanoscale

Science and Technology at Rice University.

45

Notes and references

a Rice University, Department of Physics and Astronomy MS 61, 6100

Main St., Houston, TX 77005. Fax: 1-713-348-4150; Tel: 1-713-348-

4547; E-mail: [email protected] b Rice University, Department of Physics and Astronomy MS 61, and 50

Department of Electrical and Computer Engineering, 6100 Main St.,

Houston, TX 77005. Fax: 1-713-348-4150; Tel: 1-713-348-3214; E-mail:

[email protected]

‡ Regarding figures reproduced from APS journals: Readers may view,

browse, and/or download material for temporary copying purposes only, 55

provided these uses are for noncommercial personal purposes. Except as

provided by law, this material may not be further reproduced, distributed,

transmitted, modified, adapted, performed, displayed, published, or sold

in whole or part, without prior written permission from the American

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