Semiclassical Analysis of Driven-Dissipative Excitonic Condensation

A theoretical study of excitonic condensation in a driven-dissipative semiconductor is presented. The system that we analyze is driven by a coherent light that creates electron-hole pairs and also includes the process of the annihilation of the pairs. To study the steady state realized in this nonequilibrium system. we employ the Schwinger-Keldysh path integral formalism, which is useful for discussing the semiclassical aspect. We derive an effective theory for the excitonic condensation in the driven-dissipative situation and present a condition on the amplitude and phase of the condensate.