The collectiveelementaryexcitationsoftwo-dimensionalmagnetoexcitonsinaBose–Einsteincon- densate(BEC)withwavevector k ! ¼ 0 wereinvestigatedintheframeworkoftheBogoliubovtheoryof quasi-averages.TheHamiltonianoftheelectronsandholeslyinginthelowestLandaulevels(LLLs) containssupplementaryinteractionsduetovirtualquantumtransitionsoftheparticlestotheexcited Landaulevels(ELLs)andback.Asaresult,theinteractionbetweenthemagnetoexcitonswith k ! ¼ 0 does notvanishandtheirBECbecomesstable.Theenergyspectrumcontainsonlyonegapless,true Nambu–Goldstone(NG)modeofthesecondkindwithdependence oðkÞ  k2 at smallvalues k describingtheoptical-plasmon-typeoscillations.Therearetwoexciton-typebranchescorresponding to normalandabnormalGreen’sfunctions.Bothmodesaregappedwithroton-typesegmentsat intermediaryvaluesofthewavevectorsandcanbenamedasquasi-NGmodes.Thefourthbranchisthe acousticalplasmon-typemodewithabsoluteinstabilityintheregionofsmallandintermediaryvalues of thewavevectors.Allbrancheshaveasaturation-typedependenciesatgreatvaluesofthewave vectors.ThenumberandthekindofthetrueNGmodesareinaccordancewiththenumberofthe brokensymmetryoperators.
Solid StateCommunications155(2013)57–61

This study is concerned with a two-dimensional electron-hole system in a strong perpendicular magnetic field with special attention devoted to the Rashba spin-orbit coupling. The influence of this interaction on the chemical potential of the Bose-Einstein condensed magnetoexcitons and on the ground state energy, and on the energy of the single-particle elementary excitations are investigated in the Hartree-Fock approximation. We demonstrate that chemical potential is monotonic function versus the value of the filling factor with negative compressibility, which leads to instability of the Bose-Einstein condensate of magnetoexcitons.
Journal of Nanoelectronics and Optoelectronics, Volume 7, Number 7, pp. 724-729(6)

The new results in the theory of Bose-Einstein condensation (BEC) of the two-dimensional (2D) magnetoexcitons formed by the high-density electron–hole (e–h) pairs created on the semiconductor mono-layer in a strong perpendicular magnetic field are reviewed. One of them is the metastable dielectric liquid phase (MDLP) formed by the 2D magnetoexcitons BEC-ed on the single-particle state with sufficiently large values of the wave vector k, so that its product kl with the magnetic length l equals about kl ≈ 3−4. This state was revealed in the conditions when the electrons and holes are situated on the lowest Landau levels (LLLs) and the polarizability of the Bose gas was calculated on the base of the Anderson-type coherent excited states. They give rise to correlation energy and to chemical potential displaying a nonmonotonous dependence on the filling factor v2 with a relative minimum and with positive compressibility in its vicinity. The influence of the excited Landau levels (ELLs) on the quantum states of the e–h system is due to the virtual quantum transitions of particles from the LLLs to ELLs during the Coulomb scattering processes and to their subsequent return back. These quantum transitions were taken into account in the frame of the second order perturbation theory giving rise to an effective Hamiltonian describing the supplementary indirect interactions between the particles lying on the LLLs. This interaction is characterized by a small parameter equal to the ratio r of the magnetoexciton ionization potential Iex
0 to the Landau quantization energy
c. The parameter r = Iex
0/
c, decreases as H−1/2 with the increasing the magnetic field strength H. The supplementary interaction is attractive, making the magnetoexcitons in the Hartree approximation more robust. Nevertheless its exchange, Fock terms as well as the Bogoliubov u–v transformation terms give rise to positive, repulsion-type contributions to the chemical potential. The Bose gas of magnetoexcitons with k =0 becomes weakly nonideal when the ELLs are taken into account. The collective elementary excitations of two ground states corresponding to BEC-ed magnetoexcitons forming either a nonideal Bose gas with k =0 or the MDLP with kl ≈3−4 were studied in the frame of the perturbation theory with the infinitesimal parameter v2
1−v2, chosen as a product of the filling factor v2 and of the phase space filling factor
1−v2. The collective elementary excitations in both cases consist from the exciton and plasmon branches. Due to the presence of the condensate there are energy and quasi-energy branches. The self-energy parts containing the unknown frequency in denominators increase the degree of the dispersion equations and give rise to mixed exciton-plasmon and exciton–exciton elementary excitation branches.
Journal of Nanoelectronics and Optoelectronics, Volume 6, Number 4, pp. 393-419(27)