Effect of Disorder in BCS-BEC Crossover

TL;DR

This paper studies how weak random disorder affects the BCS-BEC crossover, revealing nonmonotonic behavior of superfluid properties and robustness of superfluidity at unitarity through numerical solutions and sound mode analysis.

Contribution

It introduces a self-consistent numerical approach to analyze disorder effects across the BCS-BEC crossover, highlighting the stability of superfluidity at unitarity.

Findings

Depleted order parameter in BEC regime due to disorder

Nonmonotonic behavior of condensate fraction near unitarity

Suppressed sound velocity and nonmonotonic critical velocity

Abstract

In this article we have investigated the effect of weak random disorder in the BCS-BEC crossover region. The disorder is included in the mean field formalism through NSR theory of superconducting fluctuations. A self consistent numerical solution of the coupled equations involving the superfluid gap parameter and density as a function of the disorder strength, albeit unaffected in the BCS phase, yields a depleted order parameter in the BEC regime and an interesting nonmonotonic behavior of the condensate fraction in the vicinity of the unitary region, and a gradual depletion thereafter, as the pairing interaction is continuously tuned across the BCS-BEC crossover. The unitary regime thus demonstrates a robust paradigm of superfluidity even when the disorder is introduced. To support the above feature and shed light on a lingering controversial issue, we have computed the behavior of the sound mode across the crossover that distinctly reveals a suppression of the sound velocity. We also find the Landau critical velocity that shows similar nonmonotonicity as that of the condensate fraction data, thereby supporting a stable superfluid scenario in the unitary limit.