The collective elementary excitations of 2D magnetoexcitons in the BEC state with wave vector k=0

Abstract

The energy spectrum of the collective elementary excitations of a 2D electrom-hole (e-h) system situated in a strong perpendicular magnetic field in a state of Bose-Einstein condensation (BEC) with wave vector k=0 was investigated in the frame of Bogoliubov theory of quasiaveraes. The starting Hamiltonian describing the e-h system contains not only the Coulomb interaction between the particles lying on the lowest Landau levels(LLLs), but also the supplementary interaction due to their virtual quantum transitions from the LLLs to the excited Landau levels and return back. This supplementary interaction generates after the averaging on the ground BCS-type state wave function the direct Hartree-type terms with attractive character, the exchange Fock-type terms giving rise to repulsion as well as the similar terms arising after the Bogoliubov u - v transformation. The interplay of these three parameters gives rise to the resulting different from zero interaction between the magnetoexcitons with wave vector k=0 and to stability of their BEC as regards the collapse. It influences also on the single particle energy spectrum as well as on the collective elementary excitations. It consists from six branches. Four of them are excitonic-type branches, two of them being of exciton origin whereas the second two are the quasienergy branches representing the mirror reflection of previous two branches. Another two branches are the optical and acoustical plasmon branches.