Pairing of spin-3/2 carriers in three-dimensional a doped Luttinger semimetal: Confluence of topology, interaction and disorder

The search for charged topological superconductors (TSCs) in strong spin-orbit coupled metals is an ongoing venture, with most attention being paid thus far to doped Dirac semiconductors, such as Cu/Nb doped Bi₂Se₃. In this talk I will show that a three-dimensional Luttinger semimetal, capturing a bi-quadratic band touching of valence and conduction bands in the normal state, stands as a rich harbor of both gapless and gapped TSCs, specifically when doped away from the charge neutrality point. This model is relevant for the 227 pyrochlore iridates, half-Heuslers, HgTe, gray tin, to name a few. I will demonstrate that various incarnations of nodal Weyl superconductors are prominent candidates for gapless TSC, while a close cousin of ³He-B with higher winding number can be realized as a fully gapped class DIII TSC. The surface states of the latter consist of Majorana fermions with cubic dispersion. I will present numerical evidence that arbitrarily weak disorder induces critically delocalized surfaces for higher winding numbers, consistent with a certain family of conformal field theories. Signatures of bulk BdG-Weyl quasiparticles on thermal- and spin-Hall conductivity, NMR relaxation time, specific heat, and heat transport will be discussed in the clean as well as dirty limit. Relevance of our study in YPtBi and the possibility of realizing external strain engineered s+d pairing will also be presented. Finally, if time permits, I will highlight possible microscopic origin of various paired states.