Topology and symmetry of surface Majorana arcs in cyclic superconductors

TL;DR

This paper investigates the topological properties and surface states of Majorana fermions in cyclic superconductors, revealing how their surface states evolve with orientation and are protected by topological invariants, with implications for experimental detection.

Contribution

It demonstrates the evolution of Majorana surface states from cones to arcs in cyclic superconductors and identifies the topological invariants protecting these states.

Findings

Majorana arcs are governed by Chern and winding numbers.

Surface states evolve with surface orientation from cones to arcs.

Tunneling spectra can distinguish between different pairing scenarios.

Abstract

We study the topology and symmetry of surface Majorana arcs in superconductors with nonunitary "cyclic" pairing. Cyclic $p$-wave pairing may be realized in a cubic or tetrahedral crystal, while it is a candidate for the interior $^3P_2$ superfluids of neutron stars. The cyclic state is an admixture of full gap and nodal gap with eight Weyl points and the low-energy physics is governed by itinerant Majorana fermions. We here show the evolution of surface states from Majorana cone to Majorana arcs under rotation of surface orientation. The Majorana cone is protected solely by an accidental spin rotation symmetry and fragile against spin-orbit coupling, while the arcs are attributed to two topological invariants: the first Chern number and one-dimensional winding number. Lastly, we discuss how topologically protected surface states inherent to the nonunitary cyclic pairing can be captured from surface probes in candidate compounds, such as U$_{1-x}$Th$_{x}$Be$_{13}$. We examine tunneling conductance spectra for two competitive scenarios in U$_{1-x}$Th$_{x}$Be$_{13}$---the degenerate $E_u$ scenario and the accidental scenario.