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 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 $(S\ge 3/2)$, 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 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.

6+15 pages, 4+3 figures

References in corpus (8)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topology of crystalline insulators and superconductors
• Multiple types of topological fermions in transition metal silicides
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Bogoliubov Fermi surfaces in superconductors with broken time-reversal symmetry
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Theory of optical responses in clean multi-band superconductors
• Topological number and Fermion Green's function of Strongly Interacting Topological Superconductors

Cited by in corpus (5)

• Topological Superconductivity in an s-wave Superconductor and Its Implication to Iron-based Superconductors
• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
• Surface density of states and tunneling spectroscopy of a spin-3/2 superconductor with Bogoliubov Fermi Surfaces
• Many-body selection rule for quasiparticle pair creations in centrosymmetric superconductors
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries