Probing electronic interactions using electron tunneling

Probing electronic interactions using electron tunneling

Pratap Raychaudhuri

Electrons in a solidFormation of energy bands

E1

E2

E3

Free atoms

Solid

Energy

Individual levelsto nearly continuous bands

Allowed energy for an electron InsulatorsMetals

Electrons in a metal

Energy

~1-50meV

eV

Give rise to electrical

conduction

Superconductivity

(Nb,Pb,Al,Sn)

Novel quantum phenonmenon

Quantum criticality, Unconventional superconductivity

EF

Understanding the nature of electrons close to EF

Itinerant

Magnetism

(Fe,Co,Ni)

Quantum Hall effect

2D systems

V

Leo Esaki, b. 1925Nobel Prize, 1973

Tunneling in Solid State systems

The award is for their discoveries regarding tunneling phenomena in solids. Half of the prize is divided equally between Esaki and Giaever for their experimental discoveries regarding tunneling phenomena in semiconductors and superconductors respectively. The other half is awarded to Josephson for his theoretical predictions of properties in a supercurrent flowing through a tunnel barrier, in particular the phenomena generally known as the Josephson effects.

Ivar Giaever, b. 1929Nobel Prize, 1973

Brian Josephson, b. 1940Nobel Prize, 1973

Electron tunneling in solids

N1 N2

T(12) e-kd N1N2d(E1-E2)

d

Metal A Insulator Metal B

EF+d EF-d

E

Metal 1Metal 2

Electrons close to the Fermi level can tunnel from one metal to another

Electron tunneling does happen!!!

Fermi Energy(EF)

IntrinsicSemiconductor

n-dopedSemiconductor

p-dopedSemiconductor

Conduction band

Valence band

Heavily doped: >1019 cm-3

Leo Esaki, b. 1925Nobel Prize, 1973

The Esaki (Tunnel) dioden-doped p-doped

Potential barrier

n-doped p-doped

Potential barrier

No Bias Reverse bias: Electrons will tunnel from p-doped to n-

doped region

The Esaki (Tunnel) diode: Forward bias

n-doped p-doped

Potential barrier

Small forward bias

Electrons will tunnel from n-doped to p-doped region

Intermediate forward bias

No states available to tunnel to

Electrons will tunnel from n-doped to the conduction band of p-doped

region

Large forward bias

0dIdVRd

How to use tunneling as a spectroscopic probe?

Ivar Giaever, b. 1929Nobel Prize, 1973

What do we want to know about electrons?

E

N(E)

The number of electronic states available in an energy interval E to E+dE: Density of states: N(E)

Free electronsE

N(E)

Free electrons+ periodic potential

Bandgap

Principle of Tunneling spectroscopy as an energy resolved probe

( ( ( (

dEEfeVEfeVENENTAI 21

2

Metal A Insulator Metal B

EF

EFV=0

V>0

V<0

In a realistic situation V is limited to few hundred mV

In simple metals such as Cu, Ag, Au, Al, N(E) is almost constant over this range

( ( ( ( ( ( eVKNeVNNTAdVdIVGdEENNTAI

eV

1122

012

2 0 0

Superconductivity

The resistance is as close to zero as measurable

K Onnes (1911)

Perfect diamagnet:Meissner –Ochsenfeld effect

Superconductors

k

-kk -k

kBTc ~1-20meVT<Tc

2D

E

T>Tc

EF

E

T<TcNormal state DOS

Superconducting state DOS

Energy

N(E)3-4 meV

D 22Re

E

E

x0~5-50nm

Tunneling: ExperimentFabrication of a tunnel junction

Step 1: Deposit a metal such as Al, Pb, Nb which forms native surface oxide

Step 2: The surface of the metal is oxidized through controlled exposure to air

Step3: Deposit the counter-electrode

Step 4: Put gold pads for electrical contacts

Tunnel junction formed here

Tunneling measurement

I

V

Differential conductance measurement

Current: I=Idc+Iacsinwt

Voltage: Vdc+Vacsinwt

d.c. bias V=Vdc

G(V)=dI/dVIac/Vac

Advantage of this technique:

Direct measurement of differential conductance

Vac can be measured with a lock-in amplifier which greatly improves the sensitivity

Tunneling spectroscopy in superconductorsNormal metal/Superconductor tunneling

-6 -4 -2 0 2 4 6

0

1

2

3

4

5T = 0 K

Z = 3

G(V

)/Gn

V (mV)

VCalculated conductance Vs voltage

2D

-6 -4 -2 0 2 4 60.0

0.3

0.6

0.9

1.2

1.5

dI/d

V (

1

V (mV)

2.5K4K5.5K8.5K10 K11.5K12.9K14.4K15K

NbN/I/AgMadhavi Chand

Interactions of electrons with other excitations

Phonon density of states

-10 -5 0 5 100.0

0.4

0.8

1.2

1.6

2.21K

G(V)

/GN

V(mV)

Al/AlOx/Pb

“Clean” junction

Propionic acidCH3(CH2)COOH

Acetic acidCH3COOH

The Al/AlOx layer was exposed to a small amount of organic molecules before depositing the Pb counter-electrode

Tunneling through a nanometer sized particleQuantized levels of particles in a box

AtomNanoparticle Solid

Discrete energy levels

CB

VB

Atomic levels

Ralph et al, Phys. Rev. Lett., 1996

Superconductor-Superconductor TunnelingDissimilar superconductor

2D2

V=0

V>|(D1D2|/e

V>(D1+D2/e

2D1

Onset for the 1st channel of current is at

V=|(D1-D2)|/e

Onset for the 2nd channel of current is at

V=(D1+D2)/e

T0Thermally excited quasiparticle

-5 0 50.00.20.40.60.81.01.21.4

2.26K 5.5K 6.5K 7K 8K 12.5K

dI/dV

(

-1)

V (mV)NbN/Insulator/Pb junction

T0( ( ( (

dEEfeVEfeVENENTAI 21

2

(

D

22,1

22,1 ReE

EEN

Townsend & Sutton, PR128, 591 (1962)

(D1+D2)/e

|(D1-D2)|/e

0dIdVRd

The Josephson Effect

Dissipation-less current up to a certain current Ic

Current flows in a Josephson junction even

at V=02D2

V=0

2D1

T=0

Predicted: 1961-62, Nobel Prize in 1973

Macroscopic Quantum State

Random Phase approximation

+

Eti

ertr )(),(

Since energy/momentum of the electron is altered statistically after travelling a distance l does not matter

Superconductor

iertr )(),(

Phase important for Cooper pair tunneling

Josephson effect…

This effect is over and above the single particle tunneling current.

Where is the Josephson effect???

Anderson & Rowell, PRL10, 230 (1963)

I realized that actually doing physics is much more enjoyable than just learning it. Maybe 'doing it' is the right way of learning, at least as far as I am concerned.

Gerd Binnig, b. 1947Nobel Prize: 1986

Heinrich Rohrer, b. 1933Nobel Prize: 1987

The scanning tunneling microscope

7X7 reconstruction of Si (111)

Vacuum tunneling between two planar electrodes

V

I f(V) exp (-2k d)

For low bias voltage (eV << ):

hm /2]2[ 2/1 k

STM basis

V

Piezoceramic tube

Scanning Tunneling Spectroscopy

Graphite

The TIFR (low temperature high vacuum) STM

With active design help from Dr. Sangita Bose

Sourin Mukhopadhyay(currently post-doc in Cornell)

Anand Kamlapure and Garima Saraswat

V

Topographic image/spectroscopy

FeSe0.5Te0.5 single crystal: Grown by P. L. Paulose

Atomic steps on grapite surface GaAs epilayer by MOVPE: Grown by Arnab Bhattacharya

NbNTc~16K

x~5nm l~200nm

Grows as epitaxial thin film on (100) MgO substrate using reactive magnetron sputtering:

NaCl structure

MgO

NbN

Thickness of our films ~ 50nm >> x

Topographic image

Atomic step edges on a 6nm thick film

Strain relaxed structure on a 50 nm thick film

Superconducting tunneling using STM

-4 -2 0 2 40.0

0.3

0.6

0.9

1.2

1.5

G(V)

/G N

Bias (mV)

V (mV)

150nm

Bias

(mV)

G(V)/GN

G(V)

Superconducting Tunneling

-4 -2 0 2 40.0

0.5

1.0

1.5

G(V)

/GN

Bias (mV)

0 2 4 6 8 10 120.0

0.5

1.0

1.5

2.0

BCS D D (m

ev)

T (K)

150 nm

-4.55

0.00

4.55

0

1

2

3

4

08

162432dI

/dV

(arb

)

Point

Num

ber

V(mV)

The superconducting gap map

Topographic image

Superconducting gap map

Combining Spectroscopy with ImagingMapping inhomogeneities in a superconductor: BSCCO

A Pushp et al. Science 320, 196(2008)

Observation of shell effects in superconducting nanoparticles

Atomic shell structureMagic number of electrons : closed shells : Inert gas atoms

Superconducting nanoparticles : formation of shells

Discrete energy levels have a degeneracy depending on the symmetry of the grainEach degenerate energy level : SHELL

EFE+ED-ED

Discrete Energy level

d = mean energy level spacing

hi

EF

Pairing Region ED

Manifestation of shell structure : oscillation in the ionization energy

0 nm

11 nm

V

It

STM : single nanoparticle

Sangita Bose et al., Nature Materials (in press)

5 10 15 20 25 300.0

0.4

0.8

D 0 (m

eV)

Particle height (nm)

10 15 20 25 300.4

0.6

0.8

1.0

1.2

1.4

1.6

Experimental data Theory

Gap

(meV

)

Particle height (nm)

Sangita Bose et al., Nature Materials (in press)

Particle in a box (again)

M.F.Crommie et al. Nature 363, 524 (1993)

M.F.Crommie et al., Science (1993)

Imaging in the momentum space

20nm

1mV

Courtesy: Sangita Bose, MPI Stuttgart

7.3nmAu surface: Topography

How to accentuate spacial variation of the Local Density of States

E

N(E)

eV

( ( eV

dEeVENENTAI0

21

2

( (

( ( ( ( eVKNeVNNTAdVdIVG

dEENNTAIeV

112

2

012

2

0

0

1.6{1/nm}

k = 1.5 nm-1

( ( rkierur

Fourier Transform

Courtesy: Sangita Bose, MPI Stuttgart-2 -1 0 1 2

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4 subK STM; B = 0T subKSTM; B = 5T subKSTM; B = 8T

E [e

V]

k|| [nm]

dI/dV image

xikFAexikFBe

Unusual Superconducting states: Ca2−xNaxCuO2Cl2

Difference of conductance map +6 and -6 meV

Hanaguri et al.

Exploring Molecules: Homo Lumo gapPentacene

Theory

Repp and Meyer

Resolving spins: Spin polarized STMTip coated with ferromagnetic material

Make your own STM (Rs.50000/-)http://www.e-basteln.de/

http://sxm4.uni-muenster.de/introduction-en.html

http://web.archive.org/web/20021219052018/http://www.peddie.k12.nj.us/Research/STMProject/

Simple STM Project

http://www.geocities.com/spm_stm/

AMATEUR STM

http://www.angelfire.com/electronic2/spm/index.html