Polar hairs of mixed-parity nodal superconductors in Rarita-Schwinger-Weyl metals

TL;DR

This paper investigates the complex nodal structures and polar hairs in mixed-parity superconducting states of Rarita-Schwinger-Weyl metals, revealing how pairing amplitude influences gapless and gapped phases with specific topological features.

Contribution

It introduces the concept of polar hairs and detailed nodal structures in mixed-parity superconductors of RSW metals, highlighting their dependence on pairing strength and symmetry.

Findings

Polar hairs connect gapless poles on the same or different Fermi surfaces.

Small pairing amplitudes produce nodal rings between Fermi surfaces.

Large pairing amplitudes lead to a fully gapped superconducting state.

Abstract

Linearly dispersing Rarita-Schwinger-Weyl (RSW) fermions featuring two Fermi velocities are the key constituents of itinerant spin-3/2 quantum materials. When doped, RSW metals sustain two Fermi surfaces (FSs), around which one fully gapped $s$-wave and five \emph{mixed-parity} local pairings can take place. The intraband components of four mixed-parity pairings support point nodes at the poles of two FSs, only around which long-lived quasiparticles live. For weak (strong) pairing amplitudes ($\Delta$), gapless north and south poles belonging to the same (different) FS(s) get connected by \emph{polar hairs}, one-dimensional line nodes occupying the region between two FSs. The remaining one, by contrast, supports four nodal rings in between two FSs, symmetrically placed about their equators, but only when $\Delta$ is small. For large $\Delta$, this paired state becomes fully gapped. The transition temperature and pairing amplitudes follow the BCS scaling. We explicitly showcase these outcomes for a rotationally symmetric RSW metal, and contrast our findings when the system possesses an enlarged Lorentz symmetry and with those in spin-3/2 Luttinger materials.