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

Полупроводниковые гетероструктуры

U z gates 2DEG Полупроводниковые гетероструктуры

SupriyoDatta Special Issue: Physics of electronic transport in single atoms, molecules,and related nanostructures, Nanotechnology 15 (2004) S433

Проводимость Ландауэра Rolf Landauer (1957)

Проводимость Ландауэра T=0

S и T матрицы Ток сохраняется S-mattix Унитарность S-матрицы

Т-матрица

Амплитуда трансмиссии

T-matrix

Resonant tunneling, LED

LED

Multichannel conductance отражается

Quantum point contacts (QPC)

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

QPC

Подход эффективного гамильтониана Coupled mode theory (оптика) 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) 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). 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, (1999). W. Suh, et al, IEEE J. of Quantum Electronics, 40, 1511 (2004). Bulgakov and Sadreev, Phys. Rev. B78, (2008).

Coupled mode theory Одно модовый резонатор

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

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

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

The reason for the spin precession is that the spin operators do not commutate with the SOI operator, which leads to spin evolution for the electron transport. In particular the SOI has a polarization effect on particle scattering processes, and this 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, (1998), Phys. Rev. B 59, (1999). A.V.Moroz and C.H.W.Barnes, Phys. Rev. B 60, (1999). F.Mireles and G. Kirczenow, Phys. Rev. B 64, (2001). L.W.Molenkamp and G.Schmidt, cond-mat/ Let it be 1d or quasi one-dimensional wire.

Particular solutions of the Shrödinger equation are The total solution The angle of spin presession E k y1 ky2ky2

Spin evolution for movement along curvilinear wire

For the straight wire R L (β) we again obtain a simple spin precession

Two-dimensional curved waveguide

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

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)

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

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

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

Resonant transmission through the QD, weak coupling

Radiation field with circular polarization It is well known in atomic spectroscopy that atomic spectroscopy that circularly polarized radiation field can transmit an electron from a multiplet state with a half- integer total angular momentum to a continuum with 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.

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(i w tJ z ) to give rise to the following effective Hamiltonian: Therefore the radiation field with circular polarization effects the QD like an external magnetic field, i.e., lifts the Kramers degeneracy. This phenomenon firstly 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.

Effect of radiation field with circular polarization

The transmission probability through QD

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

For

Distributions of

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

Exact relations for arbitrary QD with SOI

Strong SOI There are two characteristic scales in solution : and

Statistics of the eigenfunctions

Comparison of numerical statistics with analytical distributions for strong