Mott transition, biexciton crossover, and spin ordering in the exciton gas in quantum wells

We present the phase diagram of exciton gas in single and coupled quantum wells. In the latter case, electrons and holes are spatially separated. In both single and coupled quantum wells there is a Mott transition from the exciton gas to electron-hole plasma. In temperatures below the Mott transition in a single quantum well, there is a crossover to a biexciton gas phase. The formation of biexciton gas rules out the Kosterlitz-Thouless transition of excitons. In coupled quantum wells, the strong direct repulsion between excitons prevents the biexciton formation. If the separation between the electrons and holes is large enough, the decrease of temperature leads to the transition to a ferromagnetic exciton phase with a spontaneous spin polarization. Further decrease of the temperature leads to the Kosterlitz-Thouless transition of the exciton gas. We discuss possible experiments that can distinguish different phases of the exciton gas.