Dynamical instability of a driven-dissipative electron-hole condensate in the BCS-BEC-crossover region

TL;DR

This paper analyzes the stability of a driven-dissipative electron-hole condensate across the BCS-BEC crossover, revealing that pumping and decay induce instabilities and phase-dependent supercurrents, limiting the stable exciton-BEC phase.

Contribution

It extends the BCS-Leggett theory with GRPA to non-equilibrium conditions using Keldysh formalism, uncovering dynamical instabilities caused by pumping and decay effects.

Findings

Pumping and decay cause depairing of excitons.

Attractive exciton interactions emerge in the BEC regime.

The supercurrent flows anomalously opposite to the phase gradient.

Abstract

We present a stability analysis on a driven-dissipative electron-hole condensate in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-condensation)-crossover region. Extending the combined BCS-Leggett theory with the generalized random phase approximation (GRPA) to the non-equilibrium case by employing the Keldysh formalism, we show that the pumping-and-decay of carriers causes a depairing effect on excitons. This phenomenon gives rise to an attractive interaction between excitons in the BEC regime, as well as a supercurrent that anomalously flows anti-parallel to $\nabla \theta({\bf r})$ (where $\theta({\bf r})$ is the phase of the condensate) in the BCS regime, both leading to dynamical instabilities of an exciton-BEC. Our result suggests that substantial region of the exciton-BEC phase in the phase diagram (in terms of the interaction strength and the decay rate) is unstable.