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