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

TL;DR

This paper introduces a Z₂ index theorem for class D topological superconductors, linking zero modes to a topological invariant through an extended Hamiltonian approach, highlighting a modulo two relationship.

Contribution

It presents a novel Z₂ index theorem for class D superconductors by extending the Hamiltonian with a parameter, establishing a topological invariant related to zero modes.

Findings

The index relates zero modes to a topological invariant.

Zero modes are characterized modulo two.

The approach applies to generic class D superconductors.

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.