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Phase transitions in the two-dimensional electron-hole gas

A first order phase transition between a BCS phase and an insulating Mott phase for a gas of spatially separated electrons and holes with tunable Coulomb interaction and variable density is predicted. In the framework of a BCS-like mean-field approach and a Landau expansion in terms of the pairing order parameter the phase diagram is studied. This indicates several phases and phase transitions, including an electron-hole plasma at low density and weak interaction, an intermediate BCS phase with Cooper pairs and an electron-hole plasma at high density and weak interaction. The insulating Mott phase appears for the strong interaction and low temperatures. We briefly discuss the possibilities to realize these phases in realistic systems such as coupled quantum wells and graphene double layers.