Effects of spin-orbit coupling on the Berezinskii-Kosterlitz-Thouless transition and the vortex-antivortex structure in two-dimensional Fermi gases

摘要

We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in atwo-dimensional (2D) Fermi gas with spin-orbit coupling (SOC), as a function ofthe two-body binding energy and a perpendicular Zeeman field. By including ageneric form of the SOC, as a function of Rashba and Dresselhaus terms, westudy the evolution between the experimentally relevant equalRashba-Dresselhaus (ERD) case and the Rashba-only (RO) case. We show that inthe ERD case, at fixed non-zero Zeeman field, the BKT transition temperature$T_{BKT}$ is increased by the effect of SOC for all values of the bindingenergy. We also find a significant increase in the value of the Clogston limitcompared to the case without SOC. Furthermore, we demonstrate that thesuperfluid density tensor becomes anisotropic (except in the RO case), leadingto an anisotropic phase-fluctuation action that describes elliptic vortices andantivortices, which become circular in the RO limit. This deformationconstitutes an important experimental signature for superfluidity in a 2D Fermigas with ERD SOC. Finally, we show that the anisotropic sound velocitiesexhibit anomalies at low temperatures, in the vicinity of quantum phasetransitions between topologically distinct uniform superfluid phases.