Effects of Spin-Orbit Coupling on the Berezinskii-Kosterlitz-Thouless Transition and the Vortex-Antivortex Structure in Two-Dimensional Fermi Gases

We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a 2D Fermi gas with spin-orbit coupling (SOC), as a function of the two-body binding energy and a perpendicular Zeeman field. By including a generic form of the SOC, as a function of Rashba and Dresselhaus terms, we study the evolution between the experimentally relevant equal Rashba-Dresselhaus (ERD) case and the Rashba-only (RO) case. We show that in the ERD case, at a fixed nonzero Zeeman field, the BKT transition temperature $T_{\mathrm{BKT}}$ is increased by the presence of SOC for all values of the binding energy. We also find a significant increase in the value of the Clogston limit compared to the case without SOC. Furthermore, we demonstrate that the superfluid density tensor becomes anisotropic (except in the RO case), leading to an anisotropic phase-fluctuation action that describes elliptic vortices and antivortices, which become circular in the RO limit. This deformation constitutes an important experimental signature for superfluidity in a 2D Fermi gas with ERD SOC. Finally, we show that the anisotropic sound velocities exhibit anomalies at low temperatures, in the vicinity of quantum phase transitions between topologically distinct uniform superfluid phases.

Figure 1

Berezinskii-Kosterlitz-Thouless temperature $T_{\mathrm{BKT}}/E_F$ as a function of the two-body binding energy $E_b/E_F$, at fixed values of the Zeeman field $h_z/E_F$: (a) $h_z/E_F=0$ and (b) $h_z/E_F=0.2$. The Rashba coupling strength is held fixed at $v_R/{\tilde{v}}_F=1$ (with ${\tilde{v}}_F=v_F/2$), while the Dresselhaus coupling strength $v_D/{\tilde{v}}_F$ is varied. The reference case without SOC ($v=0$) is also shown. (c) $T_{\mathrm{BKT}}/E_F$ as a function of $h_z/E_F$ for ERD SOC ($v_R/{\tilde{v}}_F=v_D/{\tilde{v}}_F=0.8$) and the reference case without SOC ($v=0$) at fixed $E_b$. (d) Sound velocities $c_x/{\tilde{v}}_F$ and $c_y/{\tilde{v}}_F$ for ERD SOC ($v_R/{\tilde{v}}_F=v_D/{\tilde{v}}_F=0.8$) as a function of $h_z$, at fixed $E_b$ and varying $T$. The quantum phase transitions at $T=0$ between the indirect gapped state (i-US-0) and the gapped state with four (US-2) and two (US-1) nodes are indicated.

Figure 2

The components of the anisotropic superfluid density tensor ${\rho }_{xx}/E_F$ and ${\rho }_{yy}/E_F$ as a function of the binding energy $E_b/E_F$, for fixed Rashba coupling strength $v_R/{\tilde{v}}_F=1$ and varying Dresselhaus coupling strength $v_D/{\tilde{v}}_F$: (a) $h_z/E_F=0$ and (b) $h_z/E_F=0.2$.

Figure 3

Single antivortex and vortex-antivortex structure for RO SOC [(a) and (c)], and ERD SOC [(b) and (d)]. In the former case, the antivortex exhibits circular symmetry around its core, whereas in the latter case the antivortex is elongated along one axis and contracted along the other. The parameters used are $h_z/E_F=0.2$, $E_b/E_F=0.01$, $T\approx T_{\mathrm{BKT}}$, with $v_R/{\tilde{v}}_F=1$ and $v_D/{\tilde{v}}_F=0$ in (a) and (c), and $v_R/{\tilde{v}}_F=v_D/{\tilde{v}}_F=1$ in (b) and (d).