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)