Superconductivity in three-dimensional spin-orbit coupled semimetals

Abstract

The discovery of superconductivity in the $j$=$\frac{3}{2}$ spin-orbit coupled half-Heusler semimetals has given the field of low-density superconductivity a new twist. Exotic pairings are likely, yet the favored superconducting instabilities remain to be determined. The authors provide a method to analyze superconductivity in systems with symmetry-protected band touchings. They apply it to $j$=$\frac{3}{2}$ systems to find that polar phonons play an important role in the superconducting mechanism of the half-Heusler compounds. They also explicitly show a number of new features associated with such band structures, such as the strong dependence on hole or electron doping in the determination of the leading odd-parity superconducting instability.