Wigner supersolid of excitons in electron-hole bilayers

Bilayer electron-hole systems, where carriers in one layer are electrons and carriers in the other are holes, have been actively investigated in recent years with the focus on Bose-Einstein condensation of excitons. This condensation is expected to occur when the layer separation $d$ is much smaller than the interparticle distance ${r}_{s}{a}_{B}$ within each layer. In this Brief Report, we argue for the existence of a state, Wigner supersolid, in which excitons are phase coherent but form a Wigner crystal due to dipolar repulsion. We present the qualitative phase diagram of a bilayer system and discuss properties and possible signatures of the Wigner supersolid phase.