p-wave superconductivity in Luttinger semimetals

TL;DR

This paper investigates the phase diagram and ground states of p-wave superconductivity in spin-orbit-coupled Luttinger semimetals, revealing multiple competing states that preserve time-reversal symmetry and exhibit diverse gap structures.

Contribution

It provides a detailed analysis of the low-temperature phase diagram and identifies the symmetry and angular momentum characteristics of the superconducting states in Luttinger semimetals.

Findings

Multiple competing p-wave states depend on doping and chemical potential sign.

All ground states preserve time-reversal symmetry despite different symmetry breakings.

The quasiparticle spectrum is either fully gapped or has point nodes, with no nodal lines.

Abstract

We consider the three-dimensional spin-orbit-coupled Luttinger semimetal of "spin" $3/2$ particles in presence of weak attractive interaction in the $l=1$ (p-wave) channel, and determine the low-temperature phase diagram for both particle- and hole-dopings. The phase diagram depends crucially on the sign of the chemical potential, with two different states (with total angular momentum $j=0$ and $j=3$) competing on the hole-doped side, and three (one $j=1$ and two different $j=2$) states on the particle-doped side. The ground state condensates of Cooper pairs with the total angular momentum $j=1,2,3$ are selected by the quartic, and even sextic terms in the Ginzburg-Landau free energy. Interestingly, we find that all the p-wave ground states that appear in the phase diagram, while displaying different patterns of reduction of the rotational symmetry, preserve the time reversal symmetry. The resulting quasiparticle spectrum is either fully gapped or with point nodes, with nodal lines being absent.