Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals

TL;DR

This paper investigates how Coulomb repulsion can induce superconductivity in three-dimensional Luttinger semimetals with quadratic band touching, using numerical solutions of Eliashberg equations and analyzing mechanisms like plasmons and Kohn-Luttinger.

Contribution

It provides a detailed numerical analysis of Coulomb-driven superconductivity in spin-3/2 fermion systems with strong spin-orbit coupling, connecting results to experimental materials.

Findings

Good agreement with superconductivity in YPtBi

Critical temperature dependence on doping and dielectric function

Insights into plasmon and Kohn-Luttinger mechanisms

Abstract

We study superconductivity driven by screened Coulomb repulsion in three-dimensional Luttinger semimetals with a quadratic band touching and strong spin-orbit coupling. In these semimetals, the Cooper pairs are formed by spin-3/2 fermions with non-trivial wavefunctions. We numerically solve the linear Eliashberg equation to obtain the critical temperature of a singlet s-wave gap function as a function of doping, with account of spin-orbit and self-energy corrections. In order to understand the underlying mechanism of superconductivity, we compute the sensitivity of the critical temperature to changes in the dielectric function $\epsilon(i\Omega_n,q)$. We relate our results to the plasmon and Kohn-Luttinger mechanisms. Finally, we discuss the validity of our approach and compare our results to the litterature. We find good agreement with some bismuth-based half-Heuslers, such as YPtBi, and speculate on superconductivity in the iridate Pr2Ir2O7.