Спонтанное нарушение непрерывных симметрий двумерной электронно-дырочной системы в сильном пер-пендикулярном плоскости магнитном поле приводит к образованию новых основных состояний и определяет энергетический спектр коллективных элементарных возбуждений, появляющихся над этими основными состояниями. В обзоре основное внимание уделено электронно-дырочной истеме,сформированной из компланарных магнитоэкситонов в условиях бозе-эйнштейновской конденсации в состояние с волновым вектором k = 0 при учете влияния возбужденных уровней Ландау, когда элементарные возбуждения экситонного типа сосуществуют с колебаниями плазмонного типа. В то же время представляют большой интерес свойства двухкомпонентной системы, состоящей из двумерного электронного газа и двумерного дырочного газа, пространственно разделенных в двойной квантовой яме, в условиях дробного квантового эффекта Холла, поскольку эти свойства могут повлиять на квантовые состояния магнитных экситонов, которые образуются когда расстояние между слоями стремится к нулю. Также рассмотрены двухслойные электронные системы в условиях дробного квантового эффекта Холла с фактором заполнения, равным половине для каждого слоя, и с общим фактором заполнения, равным единице. Когерентность между элек- тронными состояниями в двух слоях эквивалентна формированию экситонов, находящихся в когерентном макроскопическом состоянии. Это делает возможным сравнение энергетического спектра коллективных элементарных возбуждений бозе-эйнштейновских конденсированных экситонов в условиях квантового эффекта Холла и компланарных магнитоэкситонов. Нарушение глобальной калибровочной симметрии либо непрерывной вращательной симметрии приводит к образованию бесщелевого спектра типа Намбу– Голдстоуна, тогда как нарушение локальной калибровочной симметрии сопровождается появлением щели в энергетическом спектре (феномен Хиггса). Эти явления аналогичны образованию безмассовых и массивных частиц в релятивистской физике. Применение теоремы Нильсена и Чадхи, устанавливающей число мод Намбу–Голдстоуна в зависимости от числа нарушенных операторов симметрии, продемонстрировано на примере бозе-эйнштейновской конденсации спинорных атомных газов в оптической ловушке. Этот пример приведен для того, чтобы лучше понять результаты, полученные в случае бозе-эйнштейновской конденсации компланарных магнитоэкситонов. Феномен Хиггса приводит к появлению составных частиц в условиях дробного квантового эффекта Холла. Их описание дано в терминах теории Гинзбурга–Ландау.
Физика твердого тела, 2013, том 55, вып. 8

This study is concerned with a two-dimensional (2D) electron– hole (e–h) system in a strong perpendicular magnetic field with special attention devoted to the Rashba spin–orbit coupling (RSOC). The influence of this interaction on the chemical potential of the Bose–Einstein condensed magnetoexcitons and on the ground-state energy of the metallic-type electron–hole liquid (EHL) is investigated in the Hartree–Fock approximation (HFA). The magnetoexciton ground-state energy, and the energy of the single-particle elementary excitations were obtained. We demonstrated that chemical potential is a monotonic function versus the value of the filling factor with negative compressibility, which leads to instability of the Bose– Einstein condensate of magnetoexcitons. The energy per one e–h pair inside the electron–hole droplets (EHD) is found to be situated on the energy scale lower than the value of the chemical potential of the Bose–Einstein condensed magnetoexcitons with wave vector k ¼ 0 calculated in the HFA.

Phys. Status Solidi B 250, No. 7, 1432–1438 (2013)

The collective elementary excitations of the two-dimensional (2D) magnetoexcitons in the state of their Bose–Einstein condensation (BEC) with nonzero wave vector k and inplane parallel oriented motional dipole moments are investigated in the Hartree–Fock–Bogoliubov approximation (HFBA). The breaking of the gauge symmetry is achieved using the Bogoliubov theory of quasiaverages and the Keldysh–Kozlov– Kopaev (KKK) method. The starting Hamiltonian and the Green’s functions are determined using the integral twoparticle operators instead of the single-particle Fermi operators. The infinite chains of equations of motion for the multioperator four- and six-particle Green-s functions are truncated following the Zubarev method and introducing a small parameter of the perturbation theory related with the lowest Landau levels (LLLs) filling factor and with the phase-space filling factor. The energy spectrum of the collective elementary excitations consists of the mixed exciton–plasmon energy braches, mixed exciton–plasmon quasienergy branches as well as the optical and acoustical plasmon energy branches. The exciton branches of the spectrum have gaps related with the negative values of the chemical potential and attractive interaction between the 2D megnetoexcitons with inplane, parallel oriented motional dipole moments. The slopes of the mixed exciton–plasmon branches are determined by the group velocities of the moving condensed excitons in the laboratory reference frame. The acoustical and optical plasmon energy branches are gapless. Their dependence on the small wave vectors accounted from the condensate wave vector k is linear and quadratic, respectively, with saturation in the range of high values of the wave vectors.
Phys. Status Solidi B 250, No. 1, 115–127 (2013)

The article consists of two parts describing two associated properties of two-dimensional magnetoexcitons. In the first part, the theory of combined excitoncyclotron resonance in the quantum well structures is developed for a strong magnetic field. In the first part, we calculate the absorption band structure for optical quantum transitions with circularly polarized radiation creating a two-dimensional exciton and simultaneously exciting one of the resident electrons from the lowest to the first excited Landau level. In the second part, we discuss the collective elementary excitations of the system of two-dimensional magnetoexcitons in the ground state of Bose–Einstein condensation on the arbitrary wave vector k

0 in the Hartree–Fock approximation. The breaking of the gauge symmetry of the initial Hamiltonian was introduced following the idea proposed by Bogoliubov in his theory of quasi-averages. The energy spectrum of the collective elementary excitations is characterized by the interconnection of the exciton and plasmon branches.
International Journal of Quantum Chemistry, Vol 110, 177–194 (2010)

The collective elementary excitations of a system of two-dimensional magnetoexcitons in a state of Bose-Einstein condensation (BEC) with arbitrary wave vector was investigated in Hartree-Fock-Bogoliubov approximation. The breaking of the gauge symmetry of the Hamiltonian was introduced following the idea proposed by Bogoliubov in his theory of quasi-averages. The equations of motion were written in the frame of the starting electron and hole creation and annihilation operators. The chains of equations of motion for a set of Green’s functions describing the exciton-type excitations as well as the plasmon-type excitations were deduced. Their disconnections were introduced using the perturbation theory with a small parameter of the theory proportional to the filling factor multiplied by the phase space filling factor. The energy spectrum of the collective elementary excitations is characterized by the interconnection of the exciton and plasmon branches, because the plasmon-type elementary excitations are gapless and are lying in the same spectral interval as the exciton-type elementary excitations.
Journal of Nanoelectronics and Optoelectronics, Vol.4, N1, 52–75, (2009)

The indirect aftractive interaction between the electron and holes lying on the lowest Landau levels on the surface of a two-dimensional structure in the presence of a strong perpendicular magnetic field appears due to their virtual quantum transitions to excited Landau levels as a result of the Coulomb scattering. The influence of this indirect interaction on the ground state energy and on the chemical potential of the Bose-Einstein condensed magnetoexcitons is determined. The corrections to the energy spectrum and to the wave function of the lowest magnetoexciton band due to the influence of the first three excited exciton bands were investigated.
Proc. of SPIE Vol. 6256, 62560X(1-14), (2006) doi: 10.1117/12.682630

The study of the quantum states of a two-dimensional electron–hole system in a strong perpendicular magnetic field is carried out with special attention to the influence of virtual quantum transitions of interacting particles between the Landau levels. These virtual quantum transitions from the lowest Landau levels to excited Landau levels with arbitrary quantum numbers n and m and their reversion to the lowest Landau levels in second order perturbation theory result in an indirect attraction between the particles. The influence of the indirect interaction on the magnetoexciton ground state, on the chemical potential of the Bose–Einstein condensed magnetoexcitons, and on the ground state energy of the metallic-type electron–hole liquid is investigated in the Hartree–Fock approximation. The coexistence of different phases is suggested.
Solid State Communications 140 (2006) 236–239

This study is concerned with a two-dimensional electron–hole system in a strong perpendicular magnetic field with special attention devoted to the influence of the virtual quantum transitions of interacting particles between the Landau levels. It is shown that virtual quantum transitions of two Coulomb interacting particles from the lowest Landau levels to excited Landau levels with arbitrary quantum numbers n and m and their transition back to the lowest Landau levels in the second order of the perturbation theory result in indirect attraction between the particles supplementary to their Coulomb interaction. The influence of this indirect interaction on the chemical potential of the Bose–Einstein condensed magnetoexcitons and on the ground state energy of the metallic-type electron–hole liquid (EHL) is investigated in the Hartree–Fock approximation. The supplementary electron–electron and hole–hole interactions being averaged with direct pairing of operators increases the binding energy of magnetoexciton and the energy per pair in the EHL phase. The terms obtained in the exchange pairing of operators give rise to repulsion. Together with the Bogoliubov self-energy terms arising from the electron–hole supplementary interaction they both influence in the favor of BEC of magnetoexcitons with small momentum. The influence of the excited exciton bands on the energy spectrum and on the wave function of the lowest magnetoexciton band is studied in the second order of the perturbation theory. The BEC of magnetoexcitons in the superposition state is considered. The generalized Bogoliubov transformations, the BCS-type ground state wave function and the phase-space filling factors of the lowest and first excited Landau levels are determined.
Physica E 39 (2007) 137–149