yupeng wang institute of physics, cas, beijing
DESCRIPTION
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 PresentationTRANSCRIPT
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Yupeng Wang
Institute of Physics, CAS, Beijing
From Kondo problem to Transport Through a Quantum Dot
2005-7-1, IOP
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Collaborators:
Zhao-Tan Jiang, Ping Zhang,
Qing-Feng Sun,
X. C. Xie and Qikun Xue
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Outline
I. Basic Issues
II. Dephasing problem through a dot
III. Spin-dependent transport through a dot
IV.Further considerations
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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~
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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~
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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
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Scalar potential in Luttinger liquids [Kane-Fisher(92), Lee-Toner(90),
Furusaki-Nagaosa(94)]
J&V competing
PRL 77, 4934(96);79, 1901(97)
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Some Basic issues of transport through a quantum dot
deV
d U
A dot coupled to two leads
Artificial
Kondo system!
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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?
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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
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Phonons, temperature and magnetic impurity may inducedephasing but scattering with fixed phase shift does not.
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Experiments showed partial coherence
R.Schuster, et.al. Nature 385, 417 (1997)
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A. Yacoby, et.al. Phys.Rev.Lett. 74, 4047 (1995)
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Former conclusion in AB-ring:
partial dephasing
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incoherent :
coherent :
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The direct physical picture for dephasing
,only 1 or 0 electron in the dot
Three second-order processes
coherent
coherent
dephasing
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Theoretical result from the Anderson impurity model
*Partial dephasing
*Asymmetric amplitude
Flux dependent part
of the conductance
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0 electron in the dot
1 electron in the dot
Asymmetry
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New experiment demonstrated the asymmetry
H. Aikawa, et.al., Phys. Rev. Lett. 92 , 176802 (2004).
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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
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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!
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(1)
(2)
(3)
(4)
(5)
(6)
Coherent !
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(1)
(2)
(3)
(4)
(5)
(6)
Incoherent !
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(3) 、 Does the AB amplitude reflect dephasing ?
The higher order processes have been discarded!
Reasonable ?
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*AB ring is a closed and limited system! Higher-order tunneling important even is quite small
reft
Dot
A
* invalid!
* Phase locking
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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?
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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 )
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Coherence rate :
When higher order processes are unimportant
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The model
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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 :
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Coherence rate
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0U 5U
U
Far away from the peak, r=1, coherent!
Close to the peak, higher order important!
4 / 5
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(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
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4 / 0
We get the asymmetric conductance
2no| | +Ti
ref coG t e t
Multi-terminal to two-terminal:
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With magnetic field
Even , is less than1 !!!
U&B induce dephasing?
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U=0 case must be coherent
An adequate description: spin-dependent rate
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When
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• Intra-dot Coulomb interaction does not induce dephasing!
• The two-terminal AB-ring system is inappropriate to test the dephasing effect!
Our Conclusion
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Spin dependent transportP. Zhang et al, Phys. Rev. Lett. 89, 286803(2002)
Physics World Jan. 33 (2001) by L. Kouwenhoven and L. Glazman
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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
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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
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Parallel Configuration , level splitting in the dot :
Tki
W
Tk
fV
B
dBd
k kd
kkdd
2
~
2
1Re
2ln
2
~)(||~
2
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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)
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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
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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.
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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
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感谢叶企孙奖励基金会Thank You!