Leçon #2: Systèmes S/N Norman Birge

Michigan State University

Résumé: Systèmes S/N

• L’éffet de proximité classique (des années 60’s)

• La réflection d’Andréev • Excitation picture of metals • Bogoliubov – deGennes equations • Blonder, Tinkham & Klapwijk • Détection de la reflection d’Andreev

• L’éffet de proximité moderne (des années 90’s)

• Andreev bound states (ABS) & the Josephson effect

• Experiences hors équilibre

L’éffet de proximité classique - 1 Hilsch, Z. Physik 167, 511 (1962)

Tc of Pb/Cu bilayers

L’éffet de proximité classique – 2a Adkins & Kington, Phil. Mag. 13, 971 (1966)

Tunneling density of states on normal side of Pb/Cu bilayers

L’éffet de proximité classique – 2b Toplicar and Finnemore, PRB16, 2072 (1977)

Tunneling density of states on normal side of Pb/Cd bilayers

L’éffet de proximité classique - 3 Clarke, Proc. Royal Soc. London, Ser. A, 308, 447 (1969)

Supercurrent in Pb/Cu/Pb (S/N/S) Josephson junction

k

E

kF

-kF

Old view of proximity effect: “leakage of Cooper pairs” from S to N

ballistic

diffusive Time before electron wavefunctions dephase with respect to each other:

S N

DN = diffusion constant in N

Tk

v

B

FN

2

Tk

D

B

NN

2

N = “normal metal coherence length“

~

2

Average over thermal distribution:

2

FF

vvL

Energy-dependent length scale:

ballistic

diffusive

2

NN

DDL

Microscopic picture:

How do electrons pass from N to S?

E >

quasiparticle states available

E <

no single-particle states in S

N S

electrons enter S as pairs;

(to conserve energy 1=-2)

Alternative view: Andreev reflection: hole is retro-reflected from NS interface

SN

h

e

At E=0, reflected hole follows time-

reversed path of incident electron

Switch to whiteboard!

• Blonder, Tinkham & Klapwijk, PRB 25, 4515 (1982)

• Klapwijk, J. Supercon. Incorp. Novel Magnetism 17, 593 (2004)

• Lambert, Hui & Robinson, J. Phys. C: Condens. Mat. 5, 4187 (1993).

-)

\ Eu

/t l/

€,Le //'.i,4) ^r'' Atr-'at!1

E:p +^^Fr/

t llth '

-t-- Ir- rl

-p,h,o<4"'I

n o . d k tk'k

e-p) + A 4^tu\'

n

L-atL

' (Err)-- A V- u

l= rA*"\?t" IA CA-q-\/ a) \"r,,

E, [' o + A V . e u- w--l at r (

F +elf:u'l ^,A r +rlrTf Frf

6n.rr l".lrlt^h^

>0 : \\ t,k')L i I

tN \ -,r

w

Ale

N*l

BUE

--Q*r---hAc-&ffitr

Semiclassical picture of normal reflection (a) and Andreev reflection (b) & (c) Lambert, Hui & Robinson (1993)

Blonder, Tinkham, & Klapwijk

Detection of Andreev Reflection

Pothier, Gueron, Esteve & Devoret, PRL 73, 2488 (1994).

Sub-gap conductance

is enhanced by

coherent multiple

Andreev reflections

“NS-QUID”

Proximity Effect from Andreev Reflection

Electron and reflected hole stay

in phase for time:

2

Length scale:

diffusive2

ballistic2

DL

vL F

Finite T: Tk

De

B

N

x N

2,

/

(assumes N < L )

Experiment: equilibrium proximity effect DOS in N near N/S interface

S. Gueron et al. PRL 77, 3025 (1996)

Energy width of dip in DOS: 2x

DE

Courtois et al., J. Low Temp. Phys. 116, 187 (1999)

Proximity Effect - Transport

Change in the

conductivity of N

N N

S

Petrashov, Antonov, Delsing & Claeson, PRL 74 5268 (1995).

Phase sensitivity of Proximity Effect

Change in conductance of N

modulated by interference of

superconducting phases

N N

S1, 1

S2, 2

Return to Whiteboard: Andreev Bound States (ABS)

and Josephson junctions

Kulik, Zh. Eksp. Theor. Fiz. 57, 1745 (1969); [Sov. Phys. JETP 30, 944 (1970)].

Ishii, Prog. Theor. Phys. 44, 1525 (1970).

J. Bardeen and J. L. Johnson, Phys. Rev. B 5, 72 (1972).

Summarized by Klapwijk in J. Supercon. Incorp. Novel Magnetism 17, 593 (2004)

AnJ...v E,**J SfJ",8J G

atrw ? f + {, +

8J6'!m

aa-(p.u( 7 4,\fi *

t

t1 - -U-t-f--- - -----%{.-,- - -W.yt4-

| .lrc-ra,tilt,fr fit

6J o

l

l'T A4"

?^

4ry,,V <

Crossed Andreev Reflection (CAR) Deutscher & Feinbert, Appl. Phys. Lett. 76, 487 (2000)

Experiments on Crossed Andreev Reflection (CAR) - 1 Beckmann, Weber & von Löhneysen, PRL 93, 197003 (2004).

Experiments on Crossed Andreev Reflection (CAR) - 2 Russo, Kroug, Klapwijk & Morpurgo, PRL 95, 1027002 (2005).