Electrodynamic duality and vortex unbinding in driven-dissipative condensates

TL;DR

This paper explores how driven-dissipative two-dimensional Bose liquids, like polariton condensates, exhibit vortex unbinding behavior influenced by non-linear effects, revealing a crossover from Kosterlitz-Thouless transition to always unbound vortices due to non-equilibrium drive.

Contribution

It introduces a duality mapping between the compact KPZ equation and non-linear electrodynamics to analyze vortex unbinding in driven Bose liquids, extending understanding beyond equilibrium transitions.

Findings

Vortex unbinding occurs for non-zero non-linearity {bb} even when the system is superfluid.

The RG flow recovers the KT transition when the non-linearity {bb} vanishes.

Finite size scaling of superfluid stiffness shows a distinct crossover behavior from the KT transition.

Abstract

We investigate the superfluid properties of two-dimensional driven Bose liquids, such as polariton condensates, using their long-wavelength description in terms of a compact Kardar-Parisi-Zhang (KPZ) equation for the phase dynamics. We account for topological defects (vortices) in the phase field through a duality mapping between the compact KPZ equation and a theory of non-linear electrodynamics coupled to charges. Using the dual theory we derive renormalization group equations that describe vortex unbinding in these media. When the non-equilibirum drive is turned off, the KPZ non-linearity {\lambda} vanishes and the RG flow gives the usual Kosterlitz-Thouless (KT) transition. On the other hand, with non-linearity {\lambda} > 0 vortices always unbind, even if the same system with {\lambda} = 0 is superfluid. We predict the finite size scaling behavior of the superfluid stiffness in the crossover governed by vortex unbinding showing its clear distinction from the scaling associated with the KT transition.