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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.
S. A. Moskalenko,M. A. Liberman, andE. V. Dumanov
"The collective elementary excitations of 2D magnetoexcitons in the BEC state with wave vector k=0", Proc. SPIE 7993, ICONO 2010: International Conference on Coherent and Nonlinear Optics, 79930D (6 January 2011); https://doi.org/10.1117/12.881324
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S. A. Moskalenko, M. A. Liberman, E. V. Dumanov, "The collective elementary excitations of 2D magnetoexcitons in the BEC state with wave vector k=0," Proc. SPIE 7993, ICONO 2010: International Conference on Coherent and Nonlinear Optics, 79930D (6 January 2011); https://doi.org/10.1117/12.881324