Two-dimensional electron-hole fluid in a strong perpendicular magnetic field: Exciton Bose condensate or maximum density two-dimensional droplet

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Abstract
The two-dimensional (2D) electron-hole fluid is studied in a strong perpendicular magnetic field. In the ideal case (simple 2D electron and hole bands), the exact ground state is a Bose condensate of noninteracting magnetic excitons. In a quantum well the asymmetry of the transverse wave functions induces an attractive interaction between excitons, and the ground state is a 2D ‘‘droplet’’ of maximum local density. On the other hand, virtual transitions to excited Landau levels cause a repulsive interaction, and the ground state becomes a Bose condensate of interacting excitons. This condensate is a superfluid and moves under application of an electric field in a direction perpendicular to both the electric and magnetic fields. The influence of the spin-orbit coupling between hole bands in a GaAs or Ge quantum well is examined. Both types of ground state can occur, depending on the polarization of the pumping light. The luminescence properties are also discussed, both for the case of a direct- and an indirect-gap semiconductor.