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From Kondo problem to Transport Through a Quantum Dot. Yupeng Wang Institute of Physics, CAS, Beijing. 2005-7-1, IOP. Collaborators: Zhao-Tan Jiang, Ping Zhang, Qing-Feng Sun, X. C. Xie and Qikun Xue. Outline. Basic Issues Dephasing problem through a dot - PowerPoint PPT Presentation
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Yupeng Wang
Institute of Physics, CAS, Beijing
From Kondo problem to Transport Through a Quantum Dot
2005-7-1, IOP
Collaborators:
Zhao-Tan Jiang, Ping Zhang,
Qing-Feng Sun,
X. C. Xie and Qikun Xue
Outline
I. Basic Issues
II. Dephasing problem through a dot
III. Spin-dependent transport through a dot
IV.Further considerations
I. Basic Issues
What is the Kondo problem?
Conduction electrons +magnetic impurity
For a free moment
What is the Kondo problem?
Conduction electrons +magnetic impurity
For a free moment
SJHN
jjk
1
T
1~
Perturbation theory fails for Kondo problem
Tk is the energy scale distinguishing the strong coupling regime and the weak coupling regime
JNk
k
n
nk
eET
T
TnH
0
1
0
1
~
,max~
Theoretical methods developed from this problem
Poor man’s scaling J*=Local Fermi-liquid theory
Ximp~ConstWilson’s numerical RGSlave boson approachGutzwiller variationExact solution with Bethe ansatz
Scalar potential in Luttinger liquids [Kane-Fisher(92), Lee-Toner(90),
Furusaki-Nagaosa(94)]
J&V competing
PRL 77, 4934(96);79, 1901(97)
Some Basic issues of transport through a quantum dot
deV
d U
A dot coupled to two leads
Artificial
Kondo system!
A.Does the intra-dot Coulomb interaction
induce dephasing? How to test?
B.What’s the transport behavior of a
quantum dot with magnetic leads?
Dephasing is a basic problem in mesoscopic systems
Low temperature, , Mesoscopic
**
Which determines a system is macro or mesoscopicand affects the application of quantum devices
High temperature, Macro system
Phonons, temperature and magnetic impurity may inducedephasing but scattering with fixed phase shift does not.
Experiments showed partial coherence
R.Schuster, et.al. Nature 385, 417 (1997)
A. Yacoby, et.al. Phys.Rev.Lett. 74, 4047 (1995)
Former conclusion in AB-ring:
partial dephasing
incoherent :
coherent :
The direct physical picture for dephasing
,only 1 or 0 electron in the dot
Three second-order processes
coherent
coherent
dephasing
Theoretical result from the Anderson impurity model
*Partial dephasing
*Asymmetric amplitude
Flux dependent part
of the conductance
0 electron in the dot
1 electron in the dot
Asymmetry
New experiment demonstrated the asymmetry
H. Aikawa, et.al., Phys. Rev. Lett. 92 , 176802 (2004).
Now it seems that partial dephasing does exist!
(1) 、 A clear physical picture
(2) 、 A predicted asymmetric transmission amplitude
(3) 、 The asymmetry was
demonstrated in experiment
Our concern
(1) 、 Is the many-body effect unimportant ?
(2) 、 A static transport consists of a sequential tunneling processes which can be divided into many second- order tunneling in different ways!
(1)
(2)
(3)
(4)
(5)
(6)
Coherent !
(1)
(2)
(3)
(4)
(5)
(6)
Incoherent !
(3) 、 Does the AB amplitude reflect dephasing ?
The higher order processes have been discarded!
Reasonable ?
*AB ring is a closed and limited system! Higher-order tunneling important even is quite small
reft
Dot
A
* invalid!
* Phase locking
AB amplitude is irrelevantto dephasing! Two-terminalsystem is inappropriate to testdephasing!
For U=0, AB amplitude is zero but the process is coherent!
The situation is not clear!
Geometry induces asymmetry?
A multi-terminal system
The basic idea is to use side-way effect to reduce higher-order tunneling processes.
Z.T. Jiang et al, Phys. Rev. Lett. 93 , 076802 ( 2004 )
Coherence rate :
When higher order processes are unimportant
The model
2 、 Dyson and Keldysh equations for
Gr and G<
4 、 Electron number in dot is determined self-consistently
Non-equilibrium Green’s function method
1 、 Equation of motion for dot gr
3 、 Current and conductance :
Coherence rate
0U 5U
U
Far away from the peak, r=1, coherent!
Close to the peak, higher order important!
4 / 5
(1) 、 In the limit , all higher order processes tend to 0.
For any value of
(2) 、 For finite , the first order contains while the higher orders contain etc. Distinguishable in the formula! we have
4 / 0
We get the asymmetric conductance
2no| | +Ti
ref coG t e t
Multi-terminal to two-terminal:
With magnetic field
Even , is less than1 !!!
U&B induce dephasing?
U=0 case must be coherent
An adequate description: spin-dependent rate
When
• Intra-dot Coulomb interaction does not induce dephasing!
• The two-terminal AB-ring system is inappropriate to test the dephasing effect!
Our Conclusion
Spin dependent transportP. Zhang et al, Phys. Rev. Lett. 89, 286803(2002)
Physics World Jan. 33 (2001) by L. Kouwenhoven and L. Glazman
The modified Anderson model
, , ,
, , ,
( ) ( . .)
k k k dk L R
k kk L R
H a a d d Ud d d d
R d d d d V a d H c
Transformation : )(2
1)( ccd
Local density of states of the quantum dot
0.0
0.1
0.2
0.3
0.4
(a)
LDOS
-8 -6 -4 -2 0 2 4 6 80.0
0.1
0.2
Fig. 2
(b)
LDOS
Energy
Parallel
Antiparallel
Spin-down
)()()()(Im1
)()(rc
rc
rc
rc GGGG
Parallel Configuration , level splitting in the dot :
Tki
W
Tk
fV
B
dBd
k kd
kkdd
2
~
2
1Re
2ln
2
~)(||~
2
Local density of states with spin flip process
0.0
0.1
0.2
Parallel configuration (a)
-8 -6 -4 -2 0 2 4 6 80.0
0.1
0.2
Antiparallel configuration
Fig. 2
(b)
Linear conductance
0.0
0.5
1.0
1.5
2.0
(b)
T=2T=0.2T=0.02
G (
e2 /h)
0.0
0.5
1.0
1.5
2.0
(a)
G (
e2 /h)
T=2T=0.2T=0.02
-8 -4 0 4 80.0
0.5
1.0
1.5
2.0
(c)
G (
e2 )/h
d
T=2T=0.2T=0.02
-8 -4 0 4 80.0
0.5
1.0
1.5
2.0
G↑
G↓
Antiparallel
Parallel
Parallel 0R
Spin-valve
Conclusion
• In the mean-field framework, magnetic resistance is insensitive to the spin relaxation.
• For the parallel configuration, the spin splitting of the Kondo resonance peak can be controlled by the magnetization and therefore induces spin valve effect due to the correlation effect.
• The splitting of the Kondo resonance peak is induced by the intra-dot spin relaxation.
Further consideration
•The quantum dot array may simulate heavy fermion systems
•Orbital degeneracy to multi-channel Kondo effect: detect non-Fermi-liquid behavior with transport
感谢叶企孙奖励基金会Thank You!