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arXiv · 1910.04189

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

Serguei Tchoumakov·Louis J. Godbout·William Witczak-Krempa
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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-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.

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Serguei Tchoumakov, Louis J. Godbout, William Witczak-Krempa. 2019-10-09. Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals. https://doi.org/10.1103/physrevresearch.2.013230

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