Unusual Zeeman-field effects in two-dimensional spin-orbit-coupled Fermi superfluids

We investigate the Zeeman field effects on the bulk superfluid properties and the collective modes in two-dimensional (2D) attractive atomic Fermi gases with Rashba-type spin-orbit coupling. In the presence of a large spin-orbit coupling, the system undergoes a quantum phase transition to a topological superfluid state at a critical Zeeman field. We show that the nonanalyticities of the thermodynamic functions as well as other physical quantities at the quantum phase transition originate from the infrared singularities caused by the gapless fermionic spectrum. The same argument applies also to the BCS-BEC evolution in 2D fermionic superfluids with $p$- or d-wave pairing. The superfluid density $n_s$ and the velocity of the Goldstone sound mode $c_s$ behave oppositely in the normal and the topological superfluid phases: they are suppressed by the Zeeman field in the normal superfluid phase, but get enhanced in the topological superfluid phase. The velocity of the Goldstone sound mode also shows nonanalyticity at the quantum phase transition. For large Zeeman field, we find $n_s\rightarrow n$ and $c_s\rightarrow \upsilon_{\rm F}$, where $n$ is the total fermion density and $\upsilon_{\rm F}$ is the Fermi velocity of noninteracting system. The unusual behavior of the superfluid density and the collective modes can be understood by the fact that the spin-orbit-coupled superfluid state at large Zeeman field can be mapped to the $p_x+ip_y$ superfluid state of spinless fermions.