Abstract
We study the topological properties of superconductors with paired $j=\frac{3}{2}$ quasiparticles. Higher spin Fermi surfaces can arise, for instance, in strongly spin-orbit coupled band-inverted semimetals. Examples include the Bi-based half-Heusler materials, which have recently been established as low-temperature and low-carrier density superconductors. Motivated by this experimental observation, we obtain a comprehensive symmetry-based classification of topological pairing states in systems with higher angular momentum Cooper pairing. Our study consists of two main parts. First, we develop the phenomenological theory of multicomponent (i.e., higher angular momentum) pairing by classifying the stationary points of the free energy within a Ginzburg-Landau framework. Based on the symmetry classification of stationary pairing states, we then derive the symmetry-imposed constraints on their gap structures. We find that, depending on the symmetry quantum numbers of the Cooper pairs, different types of topological pairing states can occur: fully gapped topological superconductors in class DIII, Dirac superconductors and superconductors hosting Majorana fermions. Notably, we find a series of nematic fully gapped topological superconductors, as well as double-Dirac superconductors with quadratic dispersion. Our approach, applied here to the case of $j=\frac{3}{2}$ Cooper pairing, is rooted in the symmetry properties of pairing states, and can therefore also be applied to other systems with higher angular momentum and high-spin pairing. We conclude by relating our results to experimentally accessible signatures in thermodynamic and dynamic probes.
Highlights
In condensed matter physics, the study of superconductors has traditionally been guided by two defining characteristics of a bulk superconductor: the nature of the pairing order parameter and the mechanism of Cooper pairing [1,2,3,4]
III and IV, a gap structure classification developed on the basis of a rotationally symmetric model naturally includes the analysis of pairing states with discrete crystal symmetry, since the symmetry group which leaves stationary points of the free energy invariant may in principle be any subgroup of the full rotation group
We focus on the gap structures of order parameter configurations Δ 1⁄4 ðΔJ; ...; Δ−JÞT corresponding to the possible mean-field ground states which were obtained in the previous section; pairing states that do not correspond to free-energy extrema are not considered
Summary
The study of superconductors has traditionally been guided by two defining characteristics of a bulk superconductor: the nature of the pairing order parameter and the mechanism of Cooper pairing [1,2,3,4]. The class of topological superconductors—in much the same way as topological insulators and topological semimetals—can be distinguished from ordinary superconductors by gapless quasiparticle excitations on the boundary, protected by the bulk superconducting gap structure. Whereas previous work has focused primarily on the question of pairing symmetry, in the context of materials such as YPtBi, the aim of this paper is to provide a comprehensive topological gap structure classification of spin. Such classification, which encompasses all pairing channels, is desirable for the practical purpose of interpreting ongoing and future experiments, and stands to enable important progress in identifying the nature of the pairing order parameter in. Since our approach relies on symmetry arguments, the results of our work are relevant to a broad range of spin-orbit coupled systems with higher angular momentum pairing
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