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.
Highlights
The superconductivity of semiconducting materials has been experimentally studied since the 1960’s [1]
The observed differences between the critical temperature of a single quadratic band and of the quadratic band touching Luttinger semimetal come from the wave-function overlap and the effect of interband coupling on the screening function random phase approximation (RPA)(i, q) (4)
We have investigated the superconductivity of the threedimensional quadratic band touching Luttinger semimetal from the screened Coulomb repulsion
Summary
The superconductivity of semiconducting materials has been experimentally studied since the 1960’s [1]. The origin of the superconducting instability is attributed to the electron-plasmon coupling because the screened Coulomb potential is negative for frequencies below the plasma frequency and above the region of electron-hole excitations [34] In this approach, most of the studies are based on a spin-degenerate quadratic band model without spin-orbit coupling, which is well suited for SrTiO3 [13,32] but not for Luttinger semimetals like YPtBi [11]. It was recently shown that, compared to a single quadratic band, the interband coupling increases the long-range screening of the electric field and reduces the effective plasma frequency [35,36,37,38] This would weaken superconductivity within the aforementioned mechanism. IV, we compare our results to the experimental observations on superconducting Luttinger semimetals such as YPtBi, and we discuss the applicability of our theoretical description
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