Electrodynamic duality and vortex unbinding in driven-dissipative condensates

Abstract

Superfluidity in two dimensions relies on the stability of a vortex imposed by external rotation of the fluid. It is lost if the flow around the test vortex is screened by spontaneously generated free vortices. In thermal equilibrium, this occurs through a Kosterlitz-Thouless phase transition, where vortex-antivortex pairs bound by Coulomb-like forces unbind only above the critical temperature. Recent experiments with exciton-polariton fluids and other driven dissipative systems raise the question of how this physics changes away from thermal equilibrium. In this paper, the authors generalize the electrostatic duality, which represents vortices as Coulomb charges, to a full electrodynamic description of the nonequilibrium system. The unbinding of vortices is analyzed within this theory using a renormalization group framework. In contrast to the equilibrium case, it is found that vortices always unbind beyond a large emergent length scale due to nonlinearities in the field dynamics. Hence, there is no superfluidity in a truly infinite driven system, while a finite system may appear as a superfluid. The heuristic derivation of the dual electrodynamics presented in this paper is supplemented by a systematic one starting from a microscopic lattice theory in a companion paper.