Dynamical exciton condensates in biased electron-hole bilayers

Bilayer materials may support condensates of interlayer excitons formed by electrons in one layer and holes in the other. The condensates are often induced by a voltage bias applied by electrical contacts that impose an interlayer chemical potential difference, driving the system out of equilibrium and causing the condensate phase to wind in time. We show that if charge can tunnel between the layers, this dynamical condensate has physical consequences including an ac Josephson effect which leads to parametric generation of collective phase modes in pairs, and in appropriate circumstances, an oscillating in plane electrical polarization that emits coherent photons with a frequency set by the bias: coherent electroluminescence. This non-equilibrium steady state may also be viewed as a time crystal that spontaneously breaks continuous time translational symmetry. If the system is placed in an optical cavity, coupling with cavity photons favors different dynamical states depending on the bias, realizing superradiant phases. We demonstrate these phenomena in biased transition metal dichalcogenide bilayers.