Bose condensation and superfluidity of excitons in a high magnetic field

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Abstract
In a high magnetic field, such that the distance between the Landau levels exceeds the binding energy of an exciton, an exciton gas in a semiconductor is capable of forming the Bose-Einstein condensate as well as a superfluid state even at a relatively high temperature. We consider the problem of excitonic interaction in a semiconductor in its multielectron formulation, starting from the second-quantization representation of the Hamiltonian of interacting electrons and holes in a high magnetic field. The expressions for the ground-state energy, the chemical potential, and the spectrum of elementary excitations of the system are obtained in a linear approximation in the concentration of excitons. It is shown that a system of excitons in a high magnetic field is similar to a weakly nonideal Bose gas. The existence and the stability of the Bose condensate due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field are established at a high density of excitons. The results obtained show that the excitation spectrum vanishes linearly, with a slope equal to a macroscopic speed of sound which depends on the direction of the magnetic field. Thus this spectrum satisfies the Landau criterion for superfluidity. The possible observable effects of the Bose condensate and the superfluidity of excitons in a high magnetic field are also discussed. It is shown that Bose condensation leads to unusual optical properties of a semiconductor, e.g., anomalous absorption of light, and to another mechanism of light amplification.