Collective elementary excitations of two-dimensional magnetoexcitons in the Bose-Einstein condensation state with wave vector k = 0

Abstract

The collective elementary excitations of the two-dimensional magnetoexcitons in a state of Bose-Einstein condensation (BEC) with wave vector k =0 were investigated in terms of the Bogoliubov theory of quasiaverages. The starting Hamiltonian of the electrons and holes lying on the lowest Landau levels (LLLs) contains the supplementary interactions due to the virtual quantum transitions of the particles to the excited Landau levels (ELLs) and return back. As a result, the interaction between the magnetoexcitons with k 0����does not vanish and their BEC becomes stable as regards the collapse. The energy spectrum of the collective elementary excitations consists of two exciton-type branches (energy and quasienergy branches) each of them with energy gap and roton-type section, the gapless optical plasmon branch, and the acoustical plasmon branch, which reveals the absolute instability in the range of small wave vectors.