Complex tensor order in half-Heusler superconductors

A revolutionary new direction in the field of superconductivity emerged recently with the synthesis of superconductors with strong inherent spin-orbit coupling of electrons, such as the half-Heusler compounds YPtBi or LuPdBi. Due to band inversion, the low-energy degrees of freedom are electrons at a three-dimensional quadratic band touching point with an effective spin-3/2, which allows for higher-spin Cooper pairing and potentially topological superconductivity. I will illuminate how this system may undergo a transition into a phase with complex tensor order, which is a superconducting state captured by a complex second-rank tensor valued order parameter describing Cooper pairs having spin-2. The interplay of both tensorial and complex nature results in a rich and intriguing phenomenology. I will discuss the mean-field phase structure as a function of doping and temperature, and relate our finding to experiments in YPtBi. Further, the critical properties of this new paradigm for superconductivity will be addressed. (I. Boettcher and I. F. Herbut, arXiv:1707.03444)