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

S. Tchoumakov; L. J. Godbout; W. Witczak-Krempa

doi:10.1103/PhysRevResearch.2.013230

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

S. Tchoumakov, L. J. Godbout, W. Witczak-Krempa

DOI 10.1103/PhysRevResearch.2.013230 · Physical Review Research

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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-32 fermions with nontrivial wave functions. 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 ε(iΩn,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 literature. We find good agreement with some bismuth-based half-Heuslers, such as YPtBi, and speculate on superconductivity in the iridate Pr2Ir2O7.

Source-reported materials — not catalogue approval

Formula	Reported Tc (K)	Pressure (GPa)	Type
YPtBi Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Pr2Ir2O7 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
SrTiO3 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
PbTe Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown