Questions on mesoscopic physics

1
Interactions between electrons, mesoscopic
Josephson effect and asymmetric current
fluctuations
B. Huard Quantronics group
2
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 lt Lj phase coherence length
3
Overview of the thesis
1) Phase coherence and interactions between
electrons in a disordered metal
2) Mesoscopic Josephson effects 3)
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
1) Phase coherence and interactions between
electrons in a disordered metal
2) Mesoscopic Josephson effects 3)
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
Grain boundaries Film edges Impurities
Elastic scattering
- Diffusion - Limit conductance
Inelastic scattering
- Limit coherence (Lj) - Exchange energy
Coulomb interaction Phonons Magnetic moments
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
Occupied states
E
U0
f(E)
8
Distribution function and energy exchange rates
weak interactions 
U
tD ? tint.
E
f(E)
9
Distribution function and energy exchange rates
strong interactions 
U
tD ? tint.
E
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
OK
Magnetic moments
Pierre et al. (2003)
Anthore et al. (2003)
12
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
OK
Magnetic moments
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
U0 mV
14
Measurement of f(E)
Dynamical Coulomb blockade (ZBA)
R
I
weak interaction
strong interaction
U0 mV
15
Quantitative investigation of the effects of
magnetic impurities
0.65 ppm Mn implantation
implanted
?
bare
Left as is
Ag (99.9999)
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 lt 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
- dephasing - no change of energy
At B0
energy
E
E
f(E)
E
E
19
Interaction between electrons mediated by a
magnetic impurity
Virtual state
E
E-e
Ee
E
f(E)
Ee
E
E
E-e
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
Ee
E-EZ
E
EZgµB
f(E)
Ee
E
E
E-e
?(e-EZ)-2
Modified rate
21
Spin-flip scattering on a magnetic impurity
effect of a high magnetic field (gµB ? eU)
Virtual state
E
E-e
EZ
eU
Ee
E
E-EZ
f(E)
Reduction of the energy exchange rate
?(e-EZ)-2
Modified rate
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-e0.05
ns-1.meV-1/2 (Coulomb interaction intensity)
25
Coulomb interaction intensity ke-e
Experiments on 15 different wires
e (µeV)

1
)
-1/2
100
meV
-1
10

1
0.1
best fit for ke-e (ns
0.1
0.01
0.02
0.02
0.1
1
-1
-1/2
expected for ke-e (ns
meV
)
Unexplained discrepancy
26
Conclusions on interactions
Quantitative understanding of the role played by
magnetic impurities but Coulomb
interaction stronger than expected
27
Overview of the thesis
1) Phase coherence and interactions between
electrons in a disordered metal
2) Mesoscopic Josephson effects 3)
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
Case of superconducting electrodes
B
I
Supercurrent through a weak link ? Unified
theory of the Josephson effect
Furusaki et al. PRL 1991,
29
Conduction channels
Coherent Conductor (LLj)
Landauer
Transmission probability
30
Andreev reflection (1964)
S
N
"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
in a short ballistic channel ( lt x )
fR
fL
a(E)e-if
a(E)eif
"e"
R
L
"h"
E(d)
2 current carrying bound states
D
E?
0
d
2p
p
E?
-D
32
Andreev bound states
t lt 1
in a short ballistic channel ( lt x )
E(d)
0
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 lt 1
in a short ballistic channel ( lt x )
CURRENT
I(d,t)
E(d)
0
d
p
2p
0
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
metallic film
pushing rods
Flexible substrate
insulating layer
counter- support
counter-support with shielded coil
36
How to test I(d) theory
V
Tunnel junction
j
Al
It
Metallic bridge (atomic contact)
Ib

• Strategy
• Measure t1,,tM
• Measure I(d)

Vgt0 V0
37
Switching of a tunnel junction .
Ib
I
0
2D/e
V
38
Measure t1,,tM
V
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)
V
Ib
j
It
Ib
0
2D/e
V
d ? j /f0 p/2
40
Measure I(d)
41
Comparison with theory I(d)
Theory I(d) switching at T?0
42
Comparison with theory I(d)
Theory I(d) switching at T?0
Overall good agreement
but with a slight deviation at t ? 1
43
Overview of the thesis
1) Phase coherence and interactions between
electrons in a disordered metal
2) Mesoscopic Josephson effects 3)
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 statistics
Vm
Average current during t
ne/tIt
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
RlargeClarge? 20 µs
dIm
?Im?
Vm
Rlarge
Im
I
G
Switching rates
?Im?
G-
-I
t
Proposal Tobiska Nazarov PRL (2004)
48
Charge counter Josephson junction
dIm
Ib
dImIb
Ib
?Im?
Vm
G
dIm -Ib
dIm Ib
G-
I
I
?Im?
0
-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 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 sensitive to high order noise ? OK Open
Interpretation ?
Tool for measuring high order current noise
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
0
E