Collective Elementary Excitations of 2D Magnetoexcitons Taking Into Account Excited Landau levels

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 the frame 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 from two exciton-type branches (energy and quasienergy branches) each of them with energy gap and roton-type section, from the gapless optical plasmon branch and from the acoustical plasmon branch, which reveals the absolute instability in the range of small wave vectors.