Interplay of Coulomb Repulsion and Spin–Orbit Coupling in Superconducting 3D Quadratic Band Touching Luttinger Semimetals
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.