On the phase diagram of a two-dimensional electron–hole system

•The phase transition in electron-hole bilayers is studied in the mean-field approximation.•The phase diagram for a system of spatially separated electrons and holes in coupled quantum wells or graphene double layers is obtained.•It was found a second order transition between an electron–hole plasma and a BCS phase.•It was found a first-order transition between the BCS phase and a bosonic Mott phase.

The phase diagram for a system of spatially separated electrons and holes in coupled quantum wells or graphene double layers is studied in the framework of a BCS-like mean-field approach and a Landau expansion in terms of the pairing order parameter. We find a second order transition between an electron–hole plasma and a BCS phase, as well as a first-order transition between the BCS phase and a bosonic Mott phase of tightly bound electron–hole pairs without phase coherence. The electron–hole plasma exists at low and at high densities for weak interaction, the BCS phase at moderate density and the Mott phase at high density and strong interaction.