Z${}_2$ index theorem for Majorana zero modes in a class D topological superconductor

Abstract

We propose a Z${}_2$ index theorem for a generic topological superconductor in class D. Introducing a particle-hole symmetry breaking term depending on a parameter and regarding it as a coordinate of an extra dimension, we define the index of the zero modes and corresponding topological invariant for such an extended Hamiltonian. It is shown that these are related with the number of the zero modes of the original Hamiltonian modulo two.

5 pages, 3 figures. v2: typos corrected

References in corpus (9)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Zero modes of two-dimensional chiral p-wave superconductors
• An Index Theorem for the Majorana Zero Modes in Chiral P-Wave Superconductors
• Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice
• Fermion structure of non-Abelian vortices in high density QCD
• Majorana zero modes bound to a vortex line in a topological superconductor

Cited by in corpus (1)

• Flat band in the core of topological defects: bulk-vortex correspondence in topological superfluids with Fermi points