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Superconducting%20transport

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If due to some attractive interaction non included in H, the ... Cron, Goffman, Esteve and Urbina, Phys.Rev.Lett. 86, 4104, (2001). superconducting Al contact ... – PowerPoint PPT presentation

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Title: Superconducting%20transport


1
Superconducting transport
  • Superconducting model Hamiltonians
  • Nambu formalism
  • Current through a N/S junction
  • Supercurrent in an atomic contact
  • Finite bias current and shot noise
  • The MAR mechanism

2
Superconducting model Hamiltonians
  • Assume an electronic system with Hamiltonian
  • (in a site representation)
  • If due to some attractive interaction non
    included in H, the system
  • becomes superconducting

D local pairing potential gap parameter
(homogeneous system)
3
  • Diagonalization of HS Bogoliubov
    transformation

2x2 space (Nambu space)
  • A quasi-particle is a linear combination of
    electron and hole

4
  • Matrix notation spinor operator for a quasi
    particle of spin
  • The usual causal propagator in this 2X2 space
    will be
  • Which in an explicit 2x2 representation has the
    form

5
  • From a practical point of view of the quantum
    mechanical calculation
  • Doubling up of the Hilbert space
  • Formally like a normal system with two orbitals
    per site

6
  • Problem surface Green functions in the
    superconducting state

Simple model semi-infinite tight-binding chain
surface site
t
t
t
t
h0
h0
h0
h0
h0
e-h symmetry
7
  • Adding an extra identical site, , and
    solving the Dyson equation

Normal case
Superconducting case
  • In a superconductor the energies of interest are

Wide band approximation
Normal state
Superconducting state
BCS density of states
8
  • A word on notation Nambu space Keldish space

Superconductivity
Non-equilibrium
Keldish
Nambu
9
N/S superconducting contact
Single-channel model
perturbation
10
  • Superconducting right lead (uncoupled)

R
Nambu space
11
  • Normal metal left lead

L
  • Important point

hole distribution
12
N/S quasi-particle tunnel tunnel limit
Differential conductance
standard BCS picture
13
Conductance saturation
14
Andreev Reflection
Superconductor
Normal metal
15
perturbation
16
Current due to Andreev reflections (eVlt D)
17
Differential conductance
saturation value
18
Josephson current in a S/S contact
Zero bias case
Superconducting phase difference
BCS superconductors
19
SQUID configuration
transmission
Uncoupled superconductors
Nambu space
20
Superconductor
Superconductor
L
R
Left lead
Right lead
t
perturbation
21
  • The zero bias case, V0, is specially simple,
    because the system
  • is in equilibrium
  • Even in the perturbed system

22
Nambu space
Tunnel limit
Ambegaokar-Baratoff
23
Andreev states
24
Andreev states
Two level system
Supercurrent
25
Josephson supercurrent
Josephson (1962)
Kulik-Omelyanchuk (1977)
26
S/S atomic contact with finite bias
Multiple Andreev reflections (MAR)
Sub-gap structure qualitative explanation
c)
3 quasi-particles
eVgt2D/3
a)
1 quasi-particle
eVgt2D
b)
eVgtD
2 quasi-particles
e
e
h
h
2D
e
e
eVgt2D/n
n quasi-particles
I
a
2D
V
27
Conduction in a superconducting junction
EF,L
28
Experimental IV curves in superconducting
contacts
Al 1 atom contact
29
Andreev reflection in a superconducting junction
Superconductor
Superconductor
eVgtD
30
Multiple Andreev reflection
Superconductor
Superconductor
eV gt 2D /3
31
Theoretical model
time dependent perturbation
Gauge choice
32
Calculation of the current
  • Non-linear and non-stationary current

dc component of the current I0(V)
Experiments
33
Theoretical IV curves
34
Al one-atom contact
2D/3
2D
D
  • Sub-gap structure (SGS) in

35
Fitting of the curves I0(V)
36
I0(V) characteristics
Atomic Al contacts
Atomic Pb contacts
37
Determination of conduction channels of an atomic
contact
Mechanical break junction
Scheer et al, PRL 78, 3535 (97) (Saclay)
Superconducting IV in last contact before breaking
Theoretical curves
38
The PIN code of an atomic contact
39
Determination of conduction channels of an atomic
contact
  • Correlation between number of channels and
    number of valence atomic orbitals

3
  • Al

(Saclay)
MCBJ
3
  • Pb

(Madrid)
STM
5
  • Nb

(Leiden)
MCBJ
1
  • Au

(Saclay)
MCBJ
Proximity effect
40
Shot noise in superconducting atomic contacts
Poissonian limit
Charge of the carriers
  • What is the transmitted charge in a Andreev
    reflection?

41
Theoretical curves
  • Huge increase of S/2eI for V 0

42
  • Effective charge carried by a multiple Andreev
    reflection

43
Shot noise measurements in atomic contacts
superconducting Al contact
effective charge
  • Cron, Goffman, Esteve and Urbina, Phys.Rev.Lett.
    86, 4104, (2001).

44
Superconducting transport through a magnetic
region
S
S
F
Superconducting transport through a correlated
quantum dot
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