This study is concerned with a two-dimensional electron-hole system in a strong perpendicular magnetic field with special attention devoted to the Rashba spin-orbit coupling. The influence of this interaction on the chemical potential of the Bose-Einstein condensed magnetoexcitons and on the ground state energy, and on the energy of the single-particle elementary excitations are investigated in the Hartree-Fock approximation. We demonstrate that chemical potential is monotonic function versus the value of the filling factor with negative compressibility, which leads to instability of the Bose-Einstein condensate of magnetoexcitons.
Journal of Nanoelectronics and Optoelectronics, Volume 7, Number 7, pp. 724-729(6)

The spontaneous breaking of the continuous symmetries of the two-dimensional (2D) electron–hole systems in a strong perpendicular magnetic field leads to the formation of new ground states and determines the energy spectra of the collective elementary excitations appearing over these ground states. In this review the main attention is given to the electron–hole systems forming coplanar magnetoexcitons in the Bose-Einstein condensation (BEC) ground state with the wave vector k =0, taking into account the excited Landau levels, when the exciton-type elementary excitations coexist with the plasmon-type oscillations. At the same time properties of the two-dimensional electron gas (2DEG) spatially separated as in the case of double quantum wells (DQWs) from the 2D hole gas under conditions of the fractional quantum Hall effect (FQHE) are of great interest because they can influence the quantum states of the coplanar magnetoexcitons when the distance between the DQW layers diminishes. We also consider in this review the bilayer electron systems under conditions of the FQHE with the one half filling factor for each layer and with the total filling factor for two layers equal to unity because the coherence between the electron states in two layers is equivalent to the formation of the quantum Hall excitons (QHExs) in a coherent macroscopic state. This makes it possible to compare the energy spectrum of the collective elementary excitations of the Bose-Einstein condensed QHExs and coplanar magnetoexcitons. The breaking of the global gauge symmetry as well as of the continuous rotational symmetries leads to the formation of the gapless Nambu-Goldstone (NG) modes while the breaking of the local gauge symmetry gives rise to the Higgs phenomenon characterized by the gapped branches of the energy spectrum. These phenomena are equivalent to the emergence of massless and of massive particles, correspondingly, in the relativistic physics. The application of the Nielsen-Chadha theorem establishing the number of the NG modes depending of the number of the broken symmetry operators and the elucidation when the quasi-NG modes appear are demonstrated using as an example related with the BEC of spinor atoms in an optical trap. They have the final aim to better understand the results obtained in the case of the coplanar Bose-Einstein condensed magnetoexcitons. The Higgs phenomenon results in the emergence of the composite particles under the conditions of the FQHE. Their description in terms of the Ginzburg-Landau theory is remembered. The formation of the high density 2D magnetoexcitons and magnetoexciton-polaritons with point quantum vortices attached is suggested. The conditions in which the spontaneous coherence could appear in a system of indirect excitons in a double quantum well structures are discussed. The experimental attempts to achieve these conditions, the main results and the accumulated knowledge are reviewed.
J. Nanoelectron. Optoelectron. 2012, Vol. 7, No. 7

The new results in the theory of Bose-Einstein condensation (BEC) of the two-dimensional (2D) magnetoexcitons formed by the high-density electron–hole (e–h) pairs created on the semiconductor mono-layer in a strong perpendicular magnetic field are reviewed. One of them is the metastable dielectric liquid phase (MDLP) formed by the 2D magnetoexcitons BEC-ed on the single-particle state with sufficiently large values of the wave vector k, so that its product kl with the magnetic length l equals about kl ≈ 3−4. This state was revealed in the conditions when the electrons and holes are situated on the lowest Landau levels (LLLs) and the polarizability of the Bose gas was calculated on the base of the Anderson-type coherent excited states. They give rise to correlation energy and to chemical potential displaying a nonmonotonous dependence on the filling factor v2 with a relative minimum and with positive compressibility in its vicinity. The influence of the excited Landau levels (ELLs) on the quantum states of the e–h system is due to the virtual quantum transitions of particles from the LLLs to ELLs during the Coulomb scattering processes and to their subsequent return back. These quantum transitions were taken into account in the frame of the second order perturbation theory giving rise to an effective Hamiltonian describing the supplementary indirect interactions between the particles lying on the LLLs. This interaction is characterized by a small parameter equal to the ratio r of the magnetoexciton ionization potential Iex
0 to the Landau quantization energy
c. The parameter r = Iex
0/
c, decreases as H−1/2 with the increasing the magnetic field strength H. The supplementary interaction is attractive, making the magnetoexcitons in the Hartree approximation more robust. Nevertheless its exchange, Fock terms as well as the Bogoliubov u–v transformation terms give rise to positive, repulsion-type contributions to the chemical potential. The Bose gas of magnetoexcitons with k =0 becomes weakly nonideal when the ELLs are taken into account. The collective elementary excitations of two ground states corresponding to BEC-ed magnetoexcitons forming either a nonideal Bose gas with k =0 or the MDLP with kl ≈3−4 were studied in the frame of the perturbation theory with the infinitesimal parameter v2
1−v2, chosen as a product of the filling factor v2 and of the phase space filling factor
1−v2. The collective elementary excitations in both cases consist from the exciton and plasmon branches. Due to the presence of the condensate there are energy and quasi-energy branches. The self-energy parts containing the unknown frequency in denominators increase the degree of the dispersion equations and give rise to mixed exciton-plasmon and exciton–exciton elementary excitation branches.
Journal of Nanoelectronics and Optoelectronics, Volume 6, Number 4, pp. 393-419(27)

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 Bose-Einstein condensed two-dimensional magnetoexcitons interacting with electron-hole(e-h) plasma in a strong perpendicular magnetic field are studied. The breaking of the gauge symmetry is introduced into the Hamiltonian following the Bogoliubov`s theory of quasiaverages. The motion equations for the summary operators describing the creation and annihilation of magnetoexcitons as well as the density fluctuations of the electron-hole(e-h) plasma were derived. They suggest the existence of magneto-exciton-plasmon complexes, the energies of which differ by the energies of one or two plasmon quanta. Starting with these motion equations one can study the Bose-Einstein Condensation (BEC) of different magneto-exciton-plasmon complexes introducing different constants of the broken symmetry correlated with their energies. The Green`s functions constructed from these summary operators are two-particle Green`s functions. They obey the chains of equations expressing the two-particle Green`s functions through the four-particle and six-particle Green`s functions. These chains were truncated in such a way that the six-particle Green`s functions, were expressed through the two-particle ones. At the same time the elementary excitations with different wave vectors were decoupled. As a result of these simplifications the Dyson-type equation in a matrix form for the two-particle Green`s functions was obtained. The 4x4 determinant constructed from the self-energy part Σij(Pω)gives rise to dispersion equation. The dispersion relations were obtained in analytical form, when in the self-energy parts Σij(Pω) only the terms linear in Coulomb interaction were kept. Taking into account also the terms quadratic in Coulomb interaction the dispersion equation becomes cumbersome and it can be solved only numerically.
Moldavian Journal of the Physical Sciences, Vol.4, N2, 2005, pp. 142-196

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