1. Interactions between electrons, mesoscopic Josephson effect and
asymmetric current fluctuations
B. Huard
& Quantronics group

2. important for L < Lj : phase coherence length
Quantum electronics
Macroscopic conductors
2 I I
DC AMPS
DC AMPS L
L/2
R  L
Mesoscopic conductors
R  L
Quantum mechanics
changes the rules
important for L < Lj : phase coherence length

3. Overview of the thesis d Tool for measuring
1) Phase coherence and interactions between electrons in a disordered metal
150 nm
2) Mesoscopic Josephson effects ) Measuring high order current noise
superconductor V B I I t d
Tool for measuring
the asymmetry of I(t) ?
I(d) for elementary conductor

4. Overview of the thesis d Tool for measuring
1) Phase coherence and interactions between electrons in a disordered metal
150 nm
2) Mesoscopic Josephson effects ) Measuring high order current noise
superconductor V B I I t d
Tool for measuring
the asymmetry of I(t) ?
I(d) for elementary conductor

5. Electron dynamics in metallic thin films+ le
150 nm
Grain boundaries
Film edges
Impurities
Elastic scattering
- Diffusion
- Limit conductance
Inelastic scattering
Coulomb interaction
Phonons
Magnetic moments
- Limit coherence (Lj)
- Exchange energy
Typically, lF  le  Lj ≤ L

6. How to access e-e interactions ?
1st method : weak localization
R(B) measures Lj B
In a wire
Pierre et al., PRB (2003)
B (mT)
First measurement: Wind et al. (1986)

7. How to access e-e interactions ?
2nd method : energy relaxation U
Diffusion time : (20 ns for 20 µm)
Occupied
states E ? eU
U=0
f(E)

8. Distribution function and
energy exchange rates
« weak interactions » U
tD  tint. E eU
f(E)

9. Distribution function and
energy exchange rates
« strong interactions » U
tD  tint. E eU
f(E)

10. Distribution function and
energy exchange rates
« weak interactions »
« strong interactions »
tD  tint.
tD  tint. E E
f(E)
f(E)
f(E) interactions

11. Understanding of inelastic scattering
1st method
Weak localization
2nd method
Energy relaxation
Interaction
stronger than
expected OK
Coulomb interaction
Wind et al. (1986)
Pierre et al. (2000)
e (µeV)
Probed energies :
0.01
0.1 1 10
100
dependence on B as expected
Magnetic moments OK
Pierre et al. (2003)
Anthore et al. (2003)

12. several explanations dismissed Quantitative experiment
Understanding of inelastic scattering
1st method
Weak localization
2nd method
Energy relaxation
Interaction
stronger than
expected OK
Coulomb interaction
Wind et al. (1986)
Pierre et al. (2000)
dependence on B as expected
Magnetic moments OK
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)

13. Access e-e interactions : measurement of f(E)
Dynamical Coulomb
blockade (ZBA) R I
U=0 mV

14. Measurement of f(E) Dynamical Coulomb blockade (ZBA) weak interaction
strong interaction
U=0.2 mV
U=0 mV

15. Quantitative investigation of the effects of magnetic impurities
0.65 ppm Mn
implantation
implanted 
bare Ag
( %)
Left as is
Comparative experiments
using methods 1 and 2
Huard et al., PRL 2005

16. 1st method : weak localization
spin-flip
Coulomb
phonons
0.65 ppm Mn
0.65 ppm consistent with implantation
0.03 ppm compatible with < 1ppm dirt
Best fit of Lj(T) for

17. 2nd method : energy relaxation
implanted
0.65 ppm Mn
strong interaction
U = 0.1 mV
B = 0.3 T
T= 20 mK
bare
weak interaction

18. * Spin-flip scattering on a magnetic impurity energy E E f(E)
- dephasing
- no change of energy
At B=0
energy E E
f(E) E E *
rate maximal at Kondo temperature

19. * Interaction between electrons mediated by a magnetic impurity
Virtual state E
E-e
E’+e E’
f(E) E
E-e E’
E’+e *
Enhanced by Kondo effect
Kaminski and Glazman, PRL (2001)

20. * Interaction mediated by a magnetic impurity :
effect of a low magnetic field (gµBeU)
Virtual state E
E-e
E’+e
E-EZ
EZ=gµB E’
f(E) E
E-e E’
E’+e *
Modified rate
(e-EZ)-2

21. Spin-flip scattering on a magnetic impurity :
effect of a high magnetic field (gµB  eU)
Virtual state E eU EZ
E-e
E’+e E’
E-EZ
f(E)
Reduction of the energy exchange rate
Modified rate
(e-EZ)-2

22. Experimental data at low and at high B
implanted
0.65 ppm Mn
U = 0.1 mV
B = 0.3 T
(gµBB = 0.35 eU)
B = 2.1 T
(gµBB = 2.4 eU)
Very weak
interaction
bare
U = 0.1 mV
T= 20 mK

23. Various B and U
T= 20 mK

24. Comparison with theory
Using theory of Goeppert, Galperin, Altshuler and Grabert PRB (2001)
Only 1 fit parameter for all curves : ke-e=0.05 ns-1.meV-1/2 (Coulomb interaction intensity)

25. Unexplained discrepancy
Coulomb interaction intensity ke-e
Experiments on 15 different wires:
e (µeV) 1 )
-1/2
100
meV -1 10
0.1 1
best fit for ke-e (ns
energy relaxation
weak localization
0.1
0.01
0.02
0.02
0.1 1
expected for ke-e (ns -1
meV
-1/2 )
Unexplained discrepancy

26. Conclusions on interactions
Quantitative understanding of the role played by magnetic impurities
but Coulomb interaction stronger than expected
Coulomb
spin-flip
phonons

27. Overview of the thesis d Tool for measuring
1) Phase coherence and interactions between electrons in a disordered metal
150 nm
2) Mesoscopic Josephson effects ) Measuring high order current noise
superconductor V B I I t d
Tool for measuring
the asymmetry of I(t) ?
I(d) for elementary conductor

28. Unified theory of the Josephson effect
Case of superconducting electrodes B I
Supercurrent through a weak link ?
Unified theory of the Josephson effect
Furusaki et al. PRL 1991, …

29. Transmission probability
Conduction channels
Coherent Conductor (L«Lj) V I
Landauer
Collection of independent channels r r’ t t’
Transmission probability

30. probability amplitude
Andreev reflection
(1964) N S
"e"
"h"
a(E)e-if
"e"
 "h"
a(E)eif
a(E)e-if
Andreev reflection
probability amplitude

31. Andreev bound states t = 1 fR fL 2 current carrying bound states
in a short ballistic channel ( < x )
t = 1 fL fR
a(E)eif
"e"
a(E)e-if L R
"h"
 "h"
"e"
E(d)
2 current carrying bound states +D E→ d p 2p E← -D ← →

32. Andreev bound states t < 1
in a short ballistic channel ( < x )
t < 1 fL fR
a(E, fL)
a(E, fR)
"e"
"h"
 "h"
E(d) +D E+ d p 2p
Central prediction of the mesoscopic theory
of the Josephson effect -D E-
A. Furusaki, M. Tsukada (1991)

33. Andreev bound states t < 1 d I(d,t)
in a short ballistic channel ( < x )
t < 1 fL fR
a(E, fL)
a(E, fR)
"e"
"h"
 "h"
CURRENT
I(d,t)
E(d) d p 2p d 2p
Central prediction of the mesoscopic theory
of the Josephson effect -D
A. Furusaki, M. Tsukada (1991)

34. Quantitative test using atomic contacts .
Atomic orbitals I V S S
{ t1 … tN }
A few independent conduction channels
of measurable and tunable transmissions
J.C. Cuevas et al. (1998)
E. Scheer et al. (1998)
I-V  { t1 … tN }
Quantitative test

35. Atomic contact pushing rods sample counter-support with shielded coil
metallic film
pushing
rods
Flexible
substrate
insulating
layer
counter-
support
counter-support
with shielded coil
3 cm

36. How to test I(d) theory It Strategy : Measure {t1,…,tM} Measure I(d)V
Tunnel junction j Al It
Metallic bridge
(atomic contact) Ib
Strategy :
Measure {t1,…,tM}
Measure I(d)
V>0
V=0 

37. Switching of a tunnel junction .Ib It V Ib
(circuit breaker) I
open circuit : 2D/e >V>0
2D/e V
circuit breaker : Ib>I  V>0 stable

38. Measure {t1,…,tM} It V Measure I(V) Ib Transmissions AC3 0.992 ± 0.003
method: Scheer et al. 1997
Transmissions
Measure I(V) It
AC3
0.992 ± 0.003
0.089
±0.06
0.088
±0.06 Ib
AC2
0.957 ± 0.01
0.185
±0.05
AC1
0.62 ± 0.01
0.12
±0.015
0.115
±0.01
0.11
±0.01
0.11
±0.01

39. Measure I(d) It d  j /f0 + p/2 V Ib I Ibare Ib j (circuit breaker)
2D/e V
d  j /f0 + p/2 

40. Measure I(d)
0.62 ± 0.01
0.957 ± 0.01
0.992 ± 0.003

41. Comparison with theory I(d)
Theory : I(d) + switching at T0
0.62 ± 0.01
0.957 ± 0.01
0.992 ± 0.003

42. Overall good agreement
Comparison with theory I(d)
Theory : I(d) + switching at T0
Overall good agreement
but with a slight deviation at t  1
0.62 ± 0.01
0.957 ± 0.01
0.992 ± 0.003

43. Overview of the thesis d Tool for measuring
1) Phase coherence and interactions between electrons in a disordered metal
150 nm
2) Mesoscopic Josephson effects ) Measuring high order current noise
superconductor V B I I t d
Tool for measuring
the asymmetry of I(t) ?
I(d) for elementary conductor

44. Full counting statisticsn Vm t
Average current
during t
ne/t=It
Pt(n) characterizes
It
pioneer: Levitov et al. (1993)
Need a new tool to measure it t

45. Well known case : tunnel junction
Independent tunnel events Poisson distribution
n
Log scale
Pt(n) n
Pt(n) is asymmetric
Simple distribution detector calibration

46. Which charge counter ?
Tunnel junction Vm It
It t

47. Charge counter: Josephson junction
Clarge
dIm
RlargeClarge 20 µs Vm
Im
Rlarge Im I G+
Im
Switching rates G- -I t
Proposal : Tobiska & Nazarov PRL (2004)

48. Charge counter: Josephson junction
dIm Ib
dIm+Ib Ib Vm
Im G+
dIm -Ib G-
dIm +Ib I I
Im -I -I t t

49. Asymmetric current fluctuations
Ib (µA) so that
G G 30 kHz
Im (µA)

50. Asymmetric current fluctuations
G+/ G- -1
|Ib| so that
G+  cste (30 kHz)
Gaussian noise
Im (µA)
There is an asymmetry

51. Asymmetric current fluctuations
G+/ G- -1
|Ib| so that
G+  cste (30 kHz)
Ankerhold (2006)
Im (µA)
Disagreement with existing theory

52. Conclusions Decoherence and interactions in Quantitative experiments
disordered metals
Quantitative experiments
Open : Coulomb intensity
Quantitative agreement
with fundamental relation
Persp. : spectro and manip.
of Andreev states
Unified theory of
Josephson effect
I (nA) j
Tool for measuring
high order
current noise
Tool sensitive to high
order noise  OK
Open : Interpretation ?

53. 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 ?
Magnetic impurities and 2 level systems cannot
explain the discrepancy (bad fits)
Slight error at the lowest probed energies
would furthermore reduce the intensity ke-e
Never been investigated
Strong enough if Ag very close to ferromagnetic instability
Yes, same result close to equilibrium
f(E) 1
Experiment near equilibrium E