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

Abstract

Topological superconductors are exotic gapped phases of matter hosting Majorana mid-gap states on their boundaries. In conventional three-dimensional topological superconductors, Majorana in-gap states appear in the form of spin-1/2 fermions with a quasirelativistic dispersion relation. Here, we show that unconventional Majorana states can emerge on the surface of three-dimensional topological superconductors protected by rotational symmetry. The unconventional Majorana surface states are classified into three different categories: a spin-s Majorana fermion with (2s + 1)-fold degeneracy (s >= 3/2), 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 types, which go beyond conventional spin-1/2 fermions, are unique to topological superconductors and have no counterparts in topological insulators. We show that unconventional Majorana surface states can be obtained in the superconducting phase of doped Z(2) topological insulators or Dirac semimetals with rotational symmetry.