Topological stability of Majorana zero-modes in superconductor-topological insulator systems

TL;DR

This paper develops an index theorem to classify and analyze the stability of Majorana zero-modes in superconductor-topological insulator systems across different dimensions and symmetries.

Contribution

It introduces a new index theorem applicable to systems with chiral and particle-hole symmetry, and proposes a Z$_2$ classification for more generic models without chiral symmetry.

Findings

Derived an index theorem for zero-energy Majorana modes in 2D and 3D systems.

Established a Z$_2$ classification for Majorana zero-modes in models lacking chiral symmetry.

Provided theoretical framework for understanding topological stability of Majorana modes.

Abstract

We derive an index theorem for zero-energy Majorana fermion modes in a superconductor-topological insulator system in both two and three dimensions, which is valid for models with chiral symmetry as well as particle-hole symmetry. For more generic models without chiral symmetry, we suggest that Majorana zero-modes are classified by Z$_2$.