Post on 13-Jul-2020
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).