Yupeng Wang Institute of Physics, CAS, Beijing

1. From Kondo problem to Transport Through a Quantum Dot Yupeng Wang Institute of Physics, CAS, Beijing 2005-7-1, IOP

2. Collaborators: Zhao-Tan Jiang, Ping Zhang, Qing-Feng Sun, X. C. Xie and Qikun Xue

3. Outline • Basic Issues • Dephasing problem through a dot • Spin-dependent transport through a dot • Further considerations

4. I. Basic Issues What is the Kondo problem? Conduction electrons +magnetic impurity For a free moment

5. Perturbation theory fails for Kondo problem Tk is the energy scale distinguishing the strong coupling regime and the weak coupling regime

6. Theoretical methods developed from this problem • Poor man’s scaling J*= • Local Fermi-liquid theory Ximp~Const • Wilson’s numerical RG • Slave boson approach • Gutzwiller variation • Exact solution with Bethe ansatz

7. Scalar potential in Luttinger liquids[Kane-Fisher(92), Lee-Toner(90), Furusaki-Nagaosa(94)] J&V competing PRL 77, 4934(96);79, 1901(97)

8. Some Basic issues of transport through a quantum dot A dot coupled to two leads Artificial Kondo system! eV

9. Does the intra-dot Coulomb interaction induce dephasing? How to test? • What’s the transport behavior of a quantum dot with magnetic leads?

10. * * Dephasing is a basic problem in mesoscopic systems High temperature, Macro system Low temperature, ，Mesoscopic Which determines a system is macro or mesoscopic and affects the application of quantum devices

11. Phonons, temperature and magnetic impurity may induce dephasing but scattering with fixed phase shift does not.

12. Experiments showed partial coherence R.Schuster, et.al. Nature 385, 417 (1997)

13. A. Yacoby, et.al. Phys.Rev.Lett. 74, 4047 (1995)

14. Former conclusion in AB-ring: partial dephasing

15. incoherent： coherent：

16. ,only 1 or 0 electron in the dot Three second-order processes The direct physical picture for dephasing coherent coherent dephasing

17. Theoretical result from the Anderson impurity model *Partial dephasing *Asymmetric amplitude Flux dependent part of the conductance

18. Asymmetry 0 electron in the dot 1 electron in the dot

19. New experiment demonstrated the asymmetry H. Aikawa, et.al., Phys. Rev. Lett. 92， 176802 (2004).

20. (1)、A clear physical picture (2)、A predicted asymmetric transmission amplitude (3)、The asymmetry was demonstrated in experiment Now it seems that partial dephasing does exist!

21. 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!

22. (1) (2) (3) (4) (5) (6) Coherent！

23. (1) (2) (3) (4) (5) (6) Incoherent！

24. (3)、Does the ABamplitude reflect dephasing？ The higher order processes have been discarded! Reasonable？

25. *AB ring is a closed and limited system! Higher-order tunneling important even is quite small A Dot * invalid! * Phase locking

26. AB amplitude is irrelevant to dephasing! Two-terminal system is inappropriate to test dephasing! For U=0, AB amplitude is zero but the process is coherent! The situation is not clear! Geometry induces asymmetry?

27. A multi-terminal system Z.T. Jiang et al, Phys. Rev. Lett. 93，076802（2004） The basic idea is to use side-way effect to reduce higher-order tunneling processes.

28. Coherence rate： When higher order processes are unimportant

29. The model

30. 1、Equation of motion for dot gr Non-equilibrium Green’s function method 2、 Dysonand Keldyshequations for Gr and G< 3、Current and conductance： 4、Electron number in dot is determined self-consistently

31. Coherence rate

32. Far away from the peak, r=1, coherent! Close to the peak, higher order important!

33. (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

34. Multi-terminal to two-terminal: We get the asymmetric conductance

35. With magnetic field Even ， is less than1 !!! U&B induce dephasing?

36. U=0 case must be coherent An adequate description: spin-dependent rate

37. When

38. Our Conclusion • Intra-dot Coulomb interaction • does not induce dephasing! • The two-terminal AB-ring system is • inappropriate to test the dephasing • effect!

39. Spin dependent transportP. Zhang et al, Phys. Rev. Lett. 89, 286803(2002) Physics World Jan. 33 (2001) by L. Kouwenhoven and L. Glazman

40. The modified Anderson model Transformation：

41. Local density of states of the quantum dot Parallel Spin-down Antiparallel

42. Parallel Configuration，level splitting in the dot：

43. Local density of states with spin flip process

44. Linear conductance Antiparallel Spin-valve Parallel Parallel

45. 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.

46. 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

47. 感谢叶企孙奖励基金会Thank You!