КВАНТОВЫЙ ТРАНСПОРТ В ПОЛУПРОВОДНИКОВЫХ МИКРОСТРУКТУРАХ

1. КВАНТОВЫЙ ТРАНСПОРТ В ПОЛУПРОВОДНИКОВЫХ МИКРОСТРУКТУРАХ • 1.ГЕТЕРОСТРУКТУРЫ. Home made quantum mechanics • 2.ОТКУДА БЕРЕТСЯ СОПРОТИВЛЕНИЕ ПРИ Т=0.Формула Ландауэра-Буттикера • 3. Как считать. ТРАНСПОРТ ЧЕРЕЗ КВАТОВЫЕ ДОТЫ

2. Полупроводниковые гетероструктуры

3. gates U 2DEG z 2 D E G GaAs AlGaAs n - AlGaAs GaAs Полупроводниковые гетероструктуры

6. SupriyoDatta • SpecialIssue:Physicsofelectronictransportinsingleatoms, • molecules,andrelatednanostructures, • Nanotechnology15(2004)S433

7. Проводимость Ландауэра • Rolf Landauer (1957)

8. Проводимость Ландауэра • T=0

9. Унитарность S-матрицы • S и T матрицы S-mattix Ток сохраняется

10. Т-матрица

12. Амплитуда трансмиссии

13. T-matrix

14. T-matrix

15. Resonant tunneling, LED

16. LED

17. LED

18. LED

19. отражается Multichannel conductance

20. Quantum point contacts (QPC)

21. QPC From A. Cserti, J. Appl. Phys. (2006)

22. QPC

24. Подход эффективного гамильтониана • 1. М. С. Лифшиц, ЖЭТФ (1957). • 2. U.Fano, Phys. Rev. 124, 1866 (1961). • 3. H. Feshbach,, Ann. Phys. (New York) 5 (1958) 357; 19 (1962) 287. • 4. C. Mahaux, H.A. Weidenmuller, (Shell-Model Approach to Nuclear • Reactions), (1969). • 5. I.Rotter, Rep. Prog. Phys., 54, 635 (1991). • 6. S.Datta, (Electronic transport in mesoscopic systems) (1995). • 7. Sadreev and I. Rotter, JPA (2003). • 8. Sadreev, JPA (2012). • Coupled mode theory (оптика) H.A.Haus, (Waves and Fields in Optoelectronics) (1984). C. Manolatou, et al, IEEE J. Quantum Electron. (1999). S. Fan, et al, J. Opt. Soc. Am.A20, 569 (2003). S. Fan, et al, Phys. Rev. B59, 15882 (1999). W. Suh, et al, IEEE J. of Quantum Electronics, 40, 1511 (2004). Bulgakov and Sadreev, Phys. Rev. B78, 075105(2008).

25. Одно модовый резонатор Coupled mode theory

26. Инверсия по времени Одно-модовый резонатор CMT • Х. Хаус, Волны и поля в оптоэлектронике

27. CMT • Много-модовый резонатор IEEE J. Quantum Electronics, 40, 1511 (2004)

28. Зарядовые эффекты • 1. Кулоновские взаимодействия в 1d проволоке. • 2. Кулоновская блокада в квантовых дотах

29. The reason for the spin precession is that the spin operatorsdo not commutate with the SOI operator, which leads to spinevolution for the electron transport. In particular the SOI hasa polarization effect on particle scattering processes, andthis effect was considered for different geometries of confinement of the 2DEG: S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990). E.N.Bulgakov, K.N.Pichugin, A.F.Sadreev, P.Streda, and P.Seba, Phys. Rev. Lett. 83, 376 (1999). A.Voskoboynikov, S.S.Liu, and C.P.Lee, Phys. Rev. B 58,15397 (1998), Phys. Rev. B 59, 12514 (1999). A.V.Moroz and C.H.W.Barnes, Phys. Rev. B60, 14272 (1999). F.Mireles and G. Kirczenow,Phys. Rev. B64, 024426 (2001). L.W.Molenkamp and G.Schmidt, cond-mat/0104109. Let it be 1d or quasi one-dimensional wire.

30. E ky1 ky2 Particular solutions of the Shrödinger equation are The total solution The angle of spin presession

31. Spin evolution for movement along curvilinear wire

32. For the straight wire RL (β→∞) we again obtain a simple spin precession

33. Two-dimensional curved waveguide

35. Spin evolution in the 2d curved waveguide R=d, β = 1 ε=25, the first-channel transmission ε=39.25, near an edge of the second-channel transmission

36. We prove that for a transmission through arbitrary billiard with two attached leads there is no spin polarization, if electrons incident in the single energy subband and were spin unpolarized The same result was obtained in more elegant way by use of spin dependent S-matrix theory by Kisilev and Kim (cond-mat/411070) and Zhai and Hu (to be published)

37. Numerical results Different way to define spin polarization via Transmission probabilities Bulgakov et al, PRL, 83, 376 (1999) Mireles and Kirczenow, PRB66, 214415 (2002) Hu and Zhai (to be published)

38. E.N.Bulgakov and A.F.Sadreev, Phys. Rev. B 66, 075331 (2002) Spin transistor T-shaped ballistic spin filter Kiselev and Kim, Appl. Phys. Lett. (2001)

39. QD with Rashba SOI - exact solutionBulgakov and Sadreev, JETP Lett. 73, 505 (2001)Tsitsishvili, Lozano, and Gogolin, PRB, 70, 115316 (2004) + mag. field

41. Resonant transmission through the QD,weak coupling

42. Radiation field with circular polarization • It is well known in atomic spectroscopy that atomic spectroscopy that circularly polarized radiationfield can transmit an electron from a multiplet statewith a half-integer total angular momentum to a continuumwith a definite spin polarization (Delone and Krainov, Sov. Phys. Usp. 127, 651 (1979). • We consider similar phenomenon for the electron ballistic transport in quantum dots and in microelectronic devices with bound states.

43. Similar to the two-level system, an effect of this radiation field can be considered exactly by transformation to the rotating coordinate system by the unitary operator exp(iwtJz) to give rise to the following effective Hamiltonian: Therefore the radiation field with circularpolarization effects the QD like anexternal magneticfield, i.e., lifts the Kramers degeneracy. This phenomenonfirstly was considered by Ritus for an atom (Sov.Phys. JETP 24, 1041 (1967)). Second, it obviously follows that the radiation field mixes only states M and M‘differing by M = ±1.

44. Effect of radiation field with circular polarization

45. The transmission probability through QD

46. Chaotic billiards with account of spin-orbit interaction (SOI) • Bulgakov and Sadreev, • JETPLett.78, 911 (2003); • PRE 70, 56211 (2004)

47. For

48. Distributions of

49. b=0.25 Saichevet al,J. Phys. A35, L87 (2002); Barth and Stockmann, Phys. Rev. E 65, 066208 (2002). Kim et al, Progr. Theort. Phys. Suppl. 150, 105 (2003). Sadreev and Berggren, Phys. Rev. E70, 26201(2004).

50. Exact relations for arbitrary QD with SOI