Comment on “Influence of induced interactions on superfluid properties of quasi-two-dimensional dilute Fermi gases with spin-orbit coupling”

In an article in 2013, Caldas et al. [Phys. Rev. A 88, 023615 (2013)] derived analytical expressions of the induced interaction within the Gorkov–Melik-Barkhudarov correction in quasi-two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). They claimed that the induced interaction is exactly the same as the one for the case without SOC when the SOC is weak, and in the region of strong SOC, it starts from a reduced value and then recovers the value for the zero SOC in the limit of large SOC. We point out that their calculations contain critical errors and inconsistencies that significantly affect the basis of these claims.

Figure 1

Fermi momentum of a two-dimensional Fermi gas with Rashba SOC. The particle density is fixed as $n=k_F^2/2\pi$. The sign change of chemical potential $\mu$ is marked by the vertical dotted line at $\lambda /v_F=1/\sqrt{2}$. At $\mu <0$, the Fermi sea is only from the ($-$) helicity branch and doughnutlike shaped with inner radius $k_{F,<}^{-}$ and outer radius $k_{F,>}^{-}$. The black solid and dotted lines of $k_F^{\pm }/k_F=\pm \alpha +\sqrt{{\alpha }^2+2m\mu /k_F^2}$ [Eq. (3.10)] with the use of $k_F=\sqrt{2m\mu }$ shown in Fig. 4 of Ref. [1] are given for direct comparison.