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!