Keldysh Field Theory of Dynamical Exciton Condensation Transitions in Nonequilibrium Electron-Hole Bilayers

Recent experiments have realized steady-state electrical injection of interlayer excitons in electron-hole bilayers subject to a large bias voltage. In the ideal case in which interlayer tunneling is negligibly weak, the system is in quasiequilibrium with a reduced effective band gap. Interlayer tunneling introduces a current and drives the system out of equilibrium. In this work we derive a nonequilibrium field theory description of interlayer excitons in biased electron-hole bilayers. In the large bias limit, we find that p-wave interlayer tunneling reduces the effective band gap and increases the effective temperature for intervalley excitons. We discuss possible experimental implications for InAs/GaSb quantum wells and transition metal dichalcogenide bilayers.