Interplay of Coulomb repulsion and spin-orbit coupling in superconducting 3D quadratic band touching Luttinger semimetals

TL;DR

This paper explores how Coulomb repulsion and spin-orbit coupling influence superconductivity in 3D Luttinger semimetals, analyzing critical temperature dependence and potential for higher T_c with different order parameters.

Contribution

It introduces a detailed analysis of Coulomb-driven pairing mechanisms in 3D Luttinger semimetals considering spin-orbit effects, expanding understanding beyond phonon-mediated pairing.

Findings

Critical temperature varies with doping levels.

Superconductivity is sensitive to dielectric permittivity.

Alternative order parameters may enhance T_c due to spin-orbit coupling.

Abstract

We investigate the superconductivity of 3D Luttinger semimetals, such as YPtBi, where Cooper pairs are constituted of spin-3/2 quasiparticles. Various pairing mechanisms have already been considered for these semimetals, such as from polar phonons modes, and in this work we explore pairing from the screened electron-electron Coulomb repulsion. In these materials, the small Fermi energy and the spin-orbit coupling strongly influence how charge fluctuations can mediate pairing. We find the superconducting critical temperature as a function of doping for an s-wave order parameter, and determine its sensitivity to changes in the dielectric permittivity. Also, we discuss how order parameters other than s-wave may lead to a larger critical temperature, due to spin-orbit coupling.