金属/超导体异质结
Andreev reflection
11111
正常金属/超导体（N/S）界面的 Andreev 反射
electron
Cooper pair
electron hole
no barrier
N/S 界面上的正常反射（NR）和 Andreev 反射 （AR ） A.F. Andreev, Sov. Phys. JETP 19, 1228 (1964).
Why is it the retro-reflection?
Incident electron Andreev reflected hole
Ee,in kh, AR
Correspondence of electron and hole
2
2m ke,in
2 (k 2 k ) EF
H K i vF ( x x y y ) H K i vF ( x x y y )
K and K denote two inequivalent valleys at the corners
of BZ.
拓扑绝缘体
BiSb, Bi2Se3, Bi2Te3 Sb2Te3 ……. 体: 绝缘体能隙 表面: 金属态, “light-like” electrons are protected by time-reversal symmetry.
Andreev反射 Spin-up hole
S/N/S Josephson junction
Spin-up hole in the spin-down subband In the weak link region, an electron impinging on one of the interfaces is Andreev reflected and converted into a hole moving in the opposite direction, thus generating a Cooper pair with opposite spins in one S. This hole is consequently Andreev reflected at the second interface and is converted back to an electron, leading to the destruction of the Cooper pair in the other S. As a result of this cycle, a pair of correlated electrons with opposite spins is transferred from one S to another, creating a singlet
Vy , AR
Eh , AR ( k y )
v k y
Since
k y 0,
Vy , AR 0
II. Proximity Effect in Ferromagnet/Superconductor Junctions
铁磁和 singlet 超导的自旋序
有矛盾, 能否共存?
Andreev reflection and its applications
邢定钰
南京大学固体微结构物理国家重点实验室 06/11/2010
Andreev reflection
Proximity effect at F/S interfaces
非共线铁磁/铁磁/超导异质结的 自旋三重态超导关联 Half-metallic F/s-wave S contacts
Eh, AR EF vh, AR
2
2m
2 (k 2 k )
k h ke Eh (kh ) Ee (ke )
Eh , AR ( kh, AR )
ke,in / m
vh, AR ve,in
N/S结隧道电导的Andreev增强
N S S N
Conductance of an N/s-wave S junction Z=0 metallic contact Z=5 tunnel limit
p
p


if T=0
0 for Ep >0, 1 for Ep <0
n p
p
p
exp E / T 1

1
p


if T=0
In the region of Ep >0，electrons form pairs； In the region of Ep <0，unpaired electrons form M.
Virtual Andreev reflection
Virtual AR in the FM/SC interface
2 2 k k EF 2h 2m 2m
E
k k
2 2 2 2 k k k k 4mh
kf
kf
E
F
h h
k k , A N
F supercurrent flow across the junction. I
铁磁和超导结（F/S）
铁磁和超导界面Andreev反射示意图
Ferromagnetic metal/Superconductor (F/S) F/S 界面上的正常反射（NR）、Andreev 反射（AR ）、 ELQ 透射和 HLQ 透射
Crossed (non-local) AR in an N/S/N structure
量子点-超导复合系统中实现可控 Cooper pair 分裂
L. Hofstetter et al. Nature 461, 960 (2009)
Specular Andreev reflection
Due to the unique band structure of graphene, a new specular Andreev reflection will happen at the interface of graphenebased NS junction.
电子的动量和自旋关联
Andreev retro-reflection in F/S contacts
If the Andreev reflected hole is in the conduction band, there will be a conventional Andreev retro-reflection.
Blonder, Tinkham, and Kapwijk, PRB 1982
对N/S界面敏感性 AR点接触仪 对超导端的库柏对敏感性 对金属端的自旋极化敏感性
Tunneling spectra for
anisotropic d-wave
superconductors
PRB 53, 2667 (1996) 1982
H H BCS h (c c c c )
p p p p p
Bogoliubov transformation
H MF ( E p E p ) E0
p
p
p
p
p
E h0
2 p
p
2
E h
Linear dispersion relation of lowenergy excitations in graphene
The most interesting aspect of graphene is that its lowenergy excitation at the six corners of Brillouin zone is linearized and can be described by massless Dirac equations
Energy gap equation
1 n n g p 2 2 2
p
Байду номын сангаас
p
p
1 1 Magnetization M (n p n p ) (n p np ) 2 p 2 p
1 n p 0, exp E p / T 1
2 Ee,in v k x2 k y EF 2 Ee, AR v k x2 k y EF 2m
for the incident electron
Eh , AR EF v k k 2m for the AR hole
2 x 2 y
Metal/superconductor junction 金属/超导体异质结 Andreev reflection
metal superconductor Cooper pair
EF
Andreev reflection
正常反射 Spin-up 电子
interface no barrier
Spin-up电子入射
2 p
p
2
If Ep <0 ，the SC ground state will be unstable！ h comes from the FM background （ independent variable）or spontaneous magnetization of conduction electrons. arises from the SC pairing.
Eh, AR EF v k k 2m for the AR hole Vy , AR Eh, AR ( k y ) v k y
Vy , AR 0
Since