Pairing States of Spin- 32 Fermions: Symmetry-Enforced Topological Gap Functions

Abstract

We study the topological properties of superconductors with paired j ¼ 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-and triple-Dirac superconductors, with quadratic and cubic dispersion, respectively. Our approach, applied here to the case of j ¼ 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.

Reexamining Ginzburg-Landau theory for neutron P23 superfluidity in neutron stars

“…The cyclic and ferromagnetic phases are topological matter (Weyl semimetals) which can have gapless fermions in the bulk [65,86]. It is also an interesting to apply our formulation to superfluidity to higher spin systems [87].…”

Dielectric and electronic properties of three-dimensional Luttinger semimetals with a quadratic band touching

“…with θ k+q,k the angle between k + q and k. This overlap function is a key ingredient in the description of narrow bandgap semiconductors [47]. It does not only allow for interband transitions but also affects scattering within the same band, as discussed in the context of superconductivity with spin-orbit interaction [10,11,[48][49][50]. The analytic expression of polarizability is established for a single quadratic band [51], for Dirac bands [52,53] and for hole bands in zinc-blende semiconductors [54].…”

Nematic Superconductivity in Doped Bi2Se3 Topological Superconductors

“…Thus, the nematic feature of these compounds, if existing, is subtle compared with those observed in doped Bi 2 Se 3 superconductors. Theoretically, several other multi-comonent-superconductor candidates such as U 1−x Th x Be 13 [96] and half-Heusler compounds [97,98] were proposed to exhibit nematic superconductivity, and experimental verification is strongly called for.…”