Phonon-Mediated Phase Transitions in Two-Dimensional Driven-Dissipative Systems

We develop a two-dimensional stochastic dissipative theory for the description of the transport of exciton polaritons accounting for their interaction with the environment of acoustic phonons. Our approach is based on the explicit modeling of the corresponding microscopic processes using a Monte Carlo framework rather than modeling from phenomenological principles. We show the dynamic formation of a condensate and investigate its characteristics, including threshold-like behavior in populations and the formation of spatial and temporal coherence at different temperatures of the environment and accounting for the stimulated nonlinear scattering, caused by system-environment interaction. The spatial coherence reveals a transition from an exponential to polynomial decay which can be attributed to the Berezinskii-Kosterlitzh-Thouless-like phase.