BCS-BEC Crossover in 2D Fermi Gases with Rashba Spin-Orbit Coupling

TL;DR

This paper provides a comprehensive theoretical analysis of the BCS-BEC crossover in 2D Fermi gases with Rashba spin-orbit coupling, revealing how SOC influences bound state formation, superfluidity, and transition temperatures.

Contribution

It introduces an exact two-body problem solution and explores many-body effects, showing SOC enhances binding energy and modifies superfluid properties in 2D Fermi gases.

Findings

SOC increases bound state binding energy and effective mass.

The BKT transition temperature approaches that of a Bose gas with effective mass at large SOC.

SOC enhances condensate density but suppresses superfluid density.

Abstract

We present a systematic theoretical study of the BCS-BEC crossover in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). By solving the exact two-body problem in the presence of an attractive short-range interaction we show that the SOC enhances the formation of the bound state: the binding energy $E_{\text B}$ and effective mass $m_{\text B}$ of the bound state grows along with the increase of the SOC. For the many-body problem, even at weak attraction, a dilute Fermi gas can evolve from a BCS superfluid state to a Bose condensation of molecules when the SOC becomes comparable to the Fermi momentum. The ground-state properties and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature are studied, and analytical results are obtained in various limits. For large SOC, the BKT transition temperature recovers that for a Bose gas with an effective mass $m_{\text B}$. We find that the condensate and superfluid densities have distinct behaviors in the presence of SOC: the condensate density is generally enhanced by the SOC due to the increase of the molecule binding, the superfluid density is suppressed because of the non-trivial molecule effective mass $m_{\text B}$.