Superconductivity in a two-dimensional repulsive Rashba gas at low density

We study the superconducting instability and the resulting superconducting states in a two-dimensional repulsive Fermi gas with Rashba spin-orbit coupling at low electron density. We find that the superconductivity is enhanced as the Fermi energy $E_F$ decreases, due to two reasons: first, the density of states at $E_F$ increases as $1/\sqrt{E_F}$; second, the particle-hole bubble gains a more magnificent structure, resulting in an increasing effective attraction. The superconducting state is always in the total angular momentum $j_z=\pm2$-channel, and breaks time-reversal symmetry. Once a sufficiently large Zeeman coupling is applied to the superconducting state, the spectrum Chern number becomes $\pm1$, depending on the direction of the Zeeman field, and Majorana zero modes appear in the vortex cores. Collective modes in this superconducting state are also studied.