Polarizability, correlation energy, and dielectric liquid phase of Bose-Einstein condensate of two-dimensional excitons in a strong perpendicular magnetic field

Abstract

The coherent pairing of electrons and holes occupying only the lowest Landau level in a two-dimensional (2D) system with a strong perpendicular magnetic field is studied using the Keldysh-Kozlov-Kopaev method and generalized random phase approximation. Bose-Einstein condensation of the correlated pairs takes place in a single particle state with an arbitrary wave vector $\mathbf{k}$ in a symmetric 2D model. We show that the ground state energy per exciton and the chemical potential are nonmonotonic functions of the filling factor, so that metastable dielectric liquid states with positive compressibility exist, consisting of Bose-Einstein condensate of magnetoexcitons. It is shown that this dielectric liquid phase of the Bose condensed excitons is more stable than the metallic electron-hole liquid phase. The polarizability of the Bose-condensed magnetoexcitons is calculated using Anderson-type wave functions of the coherent excited states, which correspond to the appearance of one out-of-condensate electron-hole $(e\ensuremath{-}h)$ pair in the presence of the BCS-type ground state. The polarizability is characterized by a coherent factor which depends on $\mathbf{k}$ and vanishes when $\mathbf{k}$ tends to zero, as well as by a resonance frequency equal to the ionization potential of a magnetoexciton, and differs considerably from the polarizability of a noncondensed exciton gas. The condensate polarizability is used to determine the correlation energy of the system and the correction to the chemical potential beyond the Hartree-Fock-Bogoliubov approximation.