Unconventional superconductivity in a two-dimensional repulsive gas of fermions with spin-orbit coupling

TL;DR

This paper explores how Rashba spin-orbit coupling influences superconductivity in a two-dimensional repulsive fermion gas, revealing enhanced and unconventional topological superconducting states with mixed pairing symmetries.

Contribution

It introduces a renormalization group analysis of superconductivity in a 2D fermion gas with spin-orbit coupling, identifying the evolution of angular momentum channels and topological properties.

Findings

Superconductivity is enhanced with increasing spin-orbit coupling parameter.

Unconventional superconducting states break time-reversal symmetry and are topologically nontrivial.

The angular momentum channel for pairing decreases with increasing spin-orbit coupling, following a specific sequence.

Abstract

We investigate the superconducting instability of a two-dimensional repulsive fermion gas with Rashba spin-orbit coupling $\al_R$. Using renormalization group approach, we find the superconducting transition temperature as a function of the dimensionless ratio $\Theta={1}{2}m\al_R^2/E_F$ where $E_F=0$ when the smaller Fermi surface shrinks to a (Dirac) point. The general trend is that superconductivity is enhanced as $\Theta$ increases, but in an intermediate regime $\Theta\sim0.1$, a dome-like behavior appears. At a very small value of $\Theta$, the angular momentum channel $j_z$ in which superconductivity occurs is quite high. With increasing $\Theta$, $j_z$ decreases with a step of 2 down to $j_z=6$, after which we find the sequence $j_z=6, 4, 6, 2$, the last value of which continues to $\Theta\rightarrow\infty$. In an extended range of $\Theta$, the superconducting gap predominantly resides on the large Fermi surface, while Josephson coupling induces a much smaller gap on the small Fermi surface. Below the superconducting transition temperature, we apply mean field theory to derive the self-consistent equations and find the condensation energies. The state with the lowest condensation energy is an unconventional superconducting state which breaks time reversal symmetry, and in which singlet and triplet pairings are mixed. In general, these states are topologically nontrivial, and the Chern number of the state with total angular momentum $j_z$ is $C=2j_z$.