Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry

TL;DR

This paper predicts new types of propagating Majorana fermions on the surface of 3D topological superconductors protected by rotational symmetry, expanding the understanding of boundary states beyond conventional models.

Contribution

It introduces three categories of unconventional Majorana surface states, including higher-spin fermions and topological charges, which are unique to topological superconductors.

Findings

Unconventional Majorana states include spin-$S$ fermions with $(2S+1)$-fold degeneracy.

Discovery of Majorana Fermi lines with two topological charges.

Identification of a quartet of spin-1/2 Majorana fermions related by rotational symmetry.

Abstract

Topological superconductors are exotic gapped phases of matter hosting Majorana mid-gap states on their boundary. In conventional topological superconductors, Majorana in-gap states appear in the form of either localized zero-dimensional modes or propagating spin-1/2 fermions with a quasi-relativistic dispersion relation. Here we show that unconventional propagating Majorana states can emerge on the surface of three-dimensional topological superconductors protected by rotational symmetry. The unconventional Majorana surface states fall into three different categories: a spin-$S$ Majorana fermion with $(2S+1)$-fold degeneracy $(S\geq3/2)$, a Majorana Fermi line carrying two distinct topological charges, and a quartet of spin-1/2 Majorana fermions related by fourfold rotational symmetry. The spectral properties of the first two kinds, which go beyond the conventional spin-1/2 fermions, are unique to topological superconductors and have no counterpart in topological insulators. We show that the unconventional Majorana surface states can be obtained in the superconducting phase of doped $Z_2$ topological insulators or Dirac semimetals with rotational symmetry.