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

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Cited by in corpus (10)

• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Flat bands in topological media
• Vortices and Other Topological Solitons in Dense Quark Matter
• Flat band in the core of topological defects: bulk-vortex correspondence in topological superfluids with Fermi points
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• Fractional Quantum Hall Effect in Weyl Semimetals
• Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
• Index theorem for topological heterostructure systems
• $Z_2$ index for gapless fermionic modes in the vortex core of three dimensional paired Dirac fermions
• Trapping of Spin-0 fields on tube-like topological defects