Bose-Einstein condensation of excitons in a single quantum well

We study the problem of Bose-Einstein condensation of excitons in a single quantum well with infinitely high potential barriers. A BCS-like theory is used to describe the modification of the one-particle Green’s functions due to the presence of Bose-condensed excitons. By introducing those single-particle properties into the two-particle Bethe-Salpeter equation, we derive a system of two couple equations for the exciton wave functions, which is solved in the low-density limit in appropriate approximations. We obtain that in a single quantum-well structure, the ground-state quadratic exciton dispersion near $\mathbf{Q}=0$ is modified and starts linear with momentum in the presence of a Bose condensate. We have calculated the chemical potential of excitons in the quantum well in the low-density limit by the variational method. The first-order density correction to the chemical potential is calculated for different thicknesses. We obtain that in the low-density limit, when the electron-hole excitonic bound states can be considered as composite bosons, the critical temperature of the Bose-Einstein condensation scales linearly with two-dimensional (2D) density of excitons. In a strictly two-dimensional case a system of 2D excitons may undergo a phase transition to a superfluid state. We have calculated the critical temperature of the Kosterlitz-Thouless phase transition to exciton superfluidity as a function of the exciton density.