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

TL;DR

This paper investigates how superconductivity emerges and is characterized in a low-density two-dimensional Rashba Fermi gas with repulsive interactions, revealing enhanced superconductivity and topological phases with Majorana modes under Zeeman coupling.

Contribution

It demonstrates the enhancement of superconductivity at low electron densities and identifies topological superconducting states with Majorana modes in a 2D Rashba system.

Findings

Superconductivity is enhanced as the Fermi energy decreases.

The superconducting state has a total angular momentum $j_z=±2$ with Chern number $±4$.

Majorana zero modes can be realized with Zeeman coupling.

Abstract

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 (namely the Fermi energy $E_F$ is lower than the energy $E_R$ of the Dirac point induced by Rashba coupling). We find that superconductivity is enhanced as the dimensionless Fermi energy $\epsilon_F$ ($\epsilon_F\equiv E_F/E_R$) decreases, due to the following two reasons. First, the density of states at $\epsilon_F$ increases as $1/\sqrt{\epsilon_F}$. Second, the particle-hole bubble becomes more anisotropic, resulting in an increasing effective attraction. The superconducting state is always in the total angular momentum $j_z=+2$ (or $j_z=-2$) channel with Chern number $C=4$ (or $C=-4$), breaking time reversal symmetry spontaneously. Although a putative Leggett mode is expected due to the two-gap nature of the superconductivity, we find that it is always damped. More importantly, once a sufficiently large Zeeman coupling is applied to the superconducting state, the Chern number can be tuned to be $\pm1$ and Majorana zero modes exist in the vortex cores.