B. Huard & Quantronics group Interactions between electrons, mesoscopic Josephson effect and...

B. Huard& Quantronics group

Interactions between electrons,mesoscopic Josephson effect and

asymmetric current fluctuations

Quantum electronics

DC AMPS

DC AMPS

L L/2

I 2 I

R L

Macroscopic conductors

Mesoscopic conductors

R L

Quantum mechanicschanges the rules

important for L < Lphase coherence length

Overview of the thesis1) Phase coherence and interactions between electrons in a disordered metal

2) Mesoscopic Josephson effects 3) Measuring high order current noise

150 nm

VI

Tool for measuring the asymmetry of I(t) ?

IB

superconductor

I() for elementary conductor

t

Electron dynamics in metallic thin films

+ +++

+++

++

le

L

Grain boundariesFilm edgesImpurities

Elastic scattering

- Diffusion- Limit conductance

Coulomb interactionPhononsMagnetic moments

Inelastic scattering

- Limit coherence (L)- Exchange energy

Typically, F le L ≤ L

150 nm

How to access e-e interactions ?

1st method : weak localization

B

R(B) measures L

In a wire

Pie

rre e

t al., P

RB

(20

03

)

First measurement: Wind et al. (1986)

B (mT)

Diffusion time : (20 ns for 20 µm)D

E

? eU

U

U=0

f(E)

Occupiedstates

How to access e-e interactions ?

2nd method : energy relaxation

U

E

eU

f(E)

Distribution function and energy exchange rates

« weak interactions »

D int.

U

E

eU

f(E)

« strong interactions »


D int.

f(E) interactions

E

f(E)

« weak interactions »

E

f(E)

« strong interactions »


D int.D int.

Understanding of inelastic scattering

Coulomb interaction

Magnetic moments

Interaction1st method

Weak localization2nd method

Energy relaxation

OK

Wind et al. (1986)

OK

stronger thanexpected

Pierre et al. (2003)

dependence on B as expected

Anthore et al. (2003)


µeV0.01 0.1 1 10 100

Probed energies:

Understanding of inelastic scattering

Coulomb interaction

Magnetic moments

Interaction1st method

Weak localization2nd method

Energy relaxation

OK

Wind et al. (1986)

OK

stronger thanexpected

Pierre et al. (2003) Anthore et al. (2003)


several explanations dismissed (Huard et al., Sol. State Comm. 2004)

Quantitative experiment(Huard et al., PRL 2005)

dependence on B as expected

UU

R

BVR

I

U=0 mV

Access e-e interactions : measurement of f(E)

Dynamical Coulombblockade (ZBA)

UU

R

BVR

Istrong interactionweak interaction

U=0.2 mVU=0 mV

Measurement of f(E)

Dynamical Coulombblockade (ZBA)

Quantitative investigation of the effects of magnetic impurities

Ag (99.9999%)

0.65 ppm Mn implantation

bare

implanted

Left as is

Comparative experimentsusing methods 1 and 2

Huard et al., PRL 2005

1st method : weak localization

Best fit of L(T) for 0.65 ppm consistent with implantation

0.03 ppm compatible with < 1ppm dirt

0.10.02 TK 1 10TK1

10

30

3

L µm

Coulomb

spin-flipphonons

0.65 ppm Mn

0.1 0 0.1 0.2 0.3VmV

0.9

0.92

0.94

0.96

0.98

RtIdVd

0.1 0 0.1 0.2 0.3VmV

0.75

0.8

0.85

0.9

RtIdVd

2nd method : energy relaxation

U = 0.1 mVB = 0.3 TT= 20 mK

weak interaction

strong interaction

bare

implanted0.65 ppm Mn

0.1 0 0.1 0.2 0.3VmV

0.9

0.92

0.94

0.96

0.98

RtIdVd

0.1 0 0.1 0.2 0.3VmV

0.75

0.8

0.85

0.9

RtIdVd

Spin-flip scattering on a magnetic impurity

energy

f(E)

E

E E

E

- dephasing- no change of energy

*rate maximal at Kondo temperature

At B=0

Interaction between electrons mediated by a magnetic impurity

f(E)

E

E- E’+

E’

E’+E’E E-

Virtual state

Kaminski and Glazman, PRL (2001)

* *Enhanced by Kondo effect

Interaction mediated by a magnetic impurity :effect of a low magnetic field (gµBeU)

f(E)

E

E- E’+

E’

E’+E’E E-

Virtual state

EZ=gµB

Modified rate* *

EZ

E-EZ

Spin-flip scattering on a magnetic impurity :effect of a high magnetic field (gµB eU)

f(E)

E

E-EZ

EZ

Reduction of the energy exchange rate

eU E-

EZModified rate

E’+

E’

Virtual state

0.1 0 0.1 0.2 0.3VmV

0.9

0.92

0.94

0.96

0.98

RtIdVd

0.1 0 0.1 0.2 0.3VmV

0.75

0.8

0.85

0.9

RtIdVd

0.1 0 0.1 0.2 0.3VmV

0.9

0.92

0.94

0.96

0.98

RtIdVd

0.1 0 0.1 0.2 0.3VmV

0.75

0.8

0.85

0.9

RtIdVd

B = 0.3 T(gµBB = 0.35 eU)

B = 2.1 T(gµBB = 2.4 eU)

Very weakinteraction

Experimental data at low and at high B

implanted0.65 ppm Mn

bare

U = 0.1 mV

U = 0.1 mV

T= 20 mK

B0.3 TB0.6 TB0.9 TB1.2 TB1.5 TB1.8 TB2.1 T

0 0.60.3VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.3 mV

Various B and U

0 0.40.2VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.2 mV

0 0.20.1VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.1 mV

0 0.60.3VmV0.9

1

1.1

RtIdVd

bareU0.3 mV

0 0.40.2VmV0.9

1

1.1

RtIdVd

bareU0.2 mV

0 0.20.1VmV0.9

1

1.1

RtIdVd

bareU0.1 mV

T= 20 mK

Comparison with theoryUsing theory of Goeppert, Galperin, Altshuler and Grabert PRB (2001)

0 0.60.3VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.3 mV

0 0.40.2VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.2 mV

0 0.20.1VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.1 mV

B0.3 TB0.6 TB0.9 TB1.2 TB1.5 TB1.8 TB2.1 T

0 0.60.3VmV0.9

1

1.1

RtIdVd

bareU0.3 mV

0 0.40.2VmV0.9

1

1.1

RtIdVd

bareU0.2 mV

0 0.20.1VmV0.9

1

1.1

RtIdVd

bareU0.1 mV

Only 1 fit parameter for all curves : e-e=0.05 ns-1.meV-1/2 (Coulomb interaction intensity)

Coulomb interaction intensity e-e

0.02 0.1 1

0.02

0.1

1

energy relaxation weak localization

best

fit

for

e-e

(ns -

1 m

eV

-1

/2

)

expected for e-e (ns -1 meV

-1/2 )

Unexplained discrepancy

µeV

0.01

0.1

1

10

100

1/ 232

2

cross section area2

resistance / lengthF

e e e

Experiments on 15 different wires:

0 0.20.1VmV

0.9

1

1.1

RtIdVd

bareU0.1 mV

0 0.40.2VmV

0.9

1

1.1

RtIdVd

bareU0.2 mV

0 0.60.3VmV

0.9

1

1.1

RtIdVd

bareU0.3 mV

0 0.20.1VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.1 mV

0 0.40.2VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.2 mV

0 0.60.3VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.3 mV

Conclusions on interactions

Quantitative understanding of the role played by magnetic impurities

but Coulomb interaction stronger than expected

0.10.02 TK 1 10TK1

10

30

3

L µm

Coulomb

spin-flipphonons



150 nm

VI


IB

superconductor


t

Case of superconducting electrodes

L R

L R

I

Supercurrent through a weak link ?

Unified theory of the Josephson effect

Furusaki et al. PRL 1991, …

B

VI

Coherent Conductor (L«L)

Transmission probability 2 2't t

Landauer

Collection of independent channels

r r’t

t’

Conduction channels

a(E)e-i

"e"

"h"

"h"

"e"

| | ieN S

Andreev reflection

probability amplitude

Andreev reflection (1964)

a(E)ei

a(E)e-i

E()

2

+

-

0

cos 2E

2 current carrying bound states

LR

"e"

"h"

"h"

"e"

= 1Andreev bound states

arg ( ) arg ( ) 0 mod 2R Li ia E e a E e

in a short ballistic channel ( < )

E→

E←

2arg mod 2a E

a(E)e-iR

a(E)eiL

←→

L R

a(E, L) a(E, R)"e"

"h"

"h"

"e"

< 1

-

0

E-

2

E()

+ E+

2 1

21 sin 2E

Central prediction of the mesoscopic theory

of the Josephson effect A. Furusaki, M. Tsukada (1991)

Andreev bound statesin a short ballistic channel ( < )

L R

a(E, L) a(E, R)"e"

"h"

"h"

"e"

< 1

-

02

E()

21 sin 2E

Central prediction of the mesoscopic theory

of the Josephson effect

A. Furusaki, M. Tsukada (1991)

Andreev bound statesin a short ballistic channel ( < )

0.5

0.99

0

),

1 ( ,I

E

CURRENT

0.5

0.99

I()

20

IS SV

{ 1 … N }

A few independent conduction channelsof measurable and tunable transmissions

J.C. Cuevas et al. (1998)E. Scheer et al. (1998)

Atomic orbitals

Quantitative test using atomic contacts .

,II

Quantitative test

I-V { 1 … N }

insulating layer

counter-support

Flexiblesubstrate

metallic film pushing rods

pushing rods

counter-supportwith shielded coil

sample

3 cm

Atomic contact

2 µm

Al

Metallic bridge(atomic contact)

Tunnel junction

max03 0.7 µ0 nA A tII

Ib

( )I

It

VHow to test I() theory

Strategy :

1)Measure {1,…,M}

2)Measure I()

V>0

V=0

Ib

V0

I

2/e

Switching of a tunnel junction .

It

V

Ib

circuit breaker : Ib>I V>0 stable

(circuit breaker)

open circuit : 2/e >V>0

0 0.1 0.2 0.3VmV0

15

30

45

60

IAn22e

23e

24e

AC1

AC2

AC3

0 0.1 0.2 0.3VmV0

15

30

45

60

IAn22e

23e

24e

Ib

I( )

It

VMeasure {1,…,M}

Measure I(V)

method: Scheer et al. 1997

0.957 ± 0.01

0.992 ± 0.003

AC3

AC2

AC1

Transmissions

0.089±0.06

0.185±0.05

0.12±0.015

0.115±0.01

0.088±0.06

0.11±0.01

0.11±0.01

0.62 ± 0.01

Ib

I( )

It

V

Measure I()

(circuit breaker)

max

03 0.7 µ0 nA A tII

swI ( ) I( )

bareswI ( ) ( )I I

V0

2/e

I Ibare

Ib

I( )

0

40

20

0

20

40

0

40

20

0

20

40

0

40

20

0

20

40

sw swI I

nA

Measure I()

0.957 ± 0.01 0.992 ± 0.0030.62 ± 0.01

0

40

20

0

20

40

0

40

20

0

20

40

0

40

20

0

20

40

sw swI I

nA

Theory : I() + switching at T0

Comparison with theory I()

0.957 ± 0.01 0.992 ± 0.0030.62 ± 0.01

0

40

20

0

20

40

0

40

20

0

20

40

0

40

20

0

20

40

sw swI I

nA

Comparison with theory I()

0.957 ± 0.01 0.992 ± 0.0030.62 ± 0.01

Overall good agreement

but with a slight deviation at 1

Theory : I() + switching at T0



150 nm

VI


IB

superconductor


t

0 n

Full counting statistics

P(n) characterizes

Average current

during

Vm

ne/=I

I

t

pioneer: Levitov et al. (1993)

Need a new tool to measure it

10 0 10 20 30 40 50

1010

107

104

101

Independent tunnel events Poisson distribution

P(n) is asymmetric

P(n)

n

n

Well known case : tunnel junction

Simple distribution detector calibration

Log scale

Which charge counter ?

Vm

I

I

t

Tunnel junction

Charge counter: Josephson junction

t

VmIm

Im

Im

Im

I

Rlarge

Clarge

RlargeClarge 20 µs

-I

Switching rates

Proposal : Tobiska & Nazarov PRL (2004)

Charge counter: Josephson junction

t

VmIm

Im

Im+Ib

0

Im -Ib

Ib

t

Im

I

-I

I

-I

Im +Ib

Ib

0.25 0.5 0.75 1 1.25 1.5 1.75ImµA

0

0.02

0.04

0.06

0.08

0.1

0.12

R

Asymmetric current fluctuations

Im (µA)

cste (30 kHz)

There is an asymmetry

|Ib| so that

Gaussian noise

0 0.25 0.5 0.75 1 1.25 1.5 1.75ImµA

0

0.02

0.04

0.06

0.08

0.1

0.12

R

Asymmetric current fluctuations

Im (µA)

Disagreement with existing theory

Ankerhold (2006)

cste (30 kHz)

|Ib| so that

0

40

20

0

20

40

0 0.20.1VmV

0.9

1

1.1R

tIdVdbare

U0.1 mV

0 0.40.2VmV

0.9

1

1.1

RtIdVd

bareU0.2 mV

0 0.60.3VmV

0.9

1

1.1

RtIdVd

bareU0.3 mV

0 0.20.1VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.1 mV

0 0.40.2VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.2 mV

0 0.60.3VmV

0.8

0.9

1

1.1

RtIdVd

implantedU0.3 mV

0 0.25 0.5 0.75 1 1.25 1.5 1.75ImµA

0

0.02

0.04

0.06

0.08

0.1

0.12

R

Conclusions

Decoherence and interactions indisordered metals

Quantitative experimentsOpen : Coulomb intensity

Unified theory ofJosephson effect

Quantitative agreementwith fundamental relationPersp. : spectro and manip.

of Andreev states

Tool for measuringhigh ordercurrent noise

Tool sensitive to high order noise OKOpen : Interpretation ?

I (nA

)

Coulomb interaction discrepancy explanations- Extrinsic energy exchange processes ?

- Quasi-1D model inappropriate ?

- Diffusive approximation invalid ?

- Hartree term stronger than expected ?

- Theory valid at equilibrium only ?

Experiment near equilibrium

E

f(E)

0

1

Magnetic impurities and 2 level systems cannotexplain the discrepancy (bad fits)

Slight error at the lowest probed energieswould furthermore reduce the intensity e-e

Never been investigated

Strong enough if Ag very close to ferromagnetic instability

Yes, same result close to equilibrium

B. Huard & Quantronics group Interactions between electrons, mesoscopic Josephson effect and...

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