Counting Majorana zero modes in superconductors

TL;DR

This paper develops a semi-classical counting formula for Majorana zero modes in topological superconductors, relating zero mode counts to Chern numbers, and applies it to systems like graphene and chiral p-wave superconductors.

Contribution

It introduces a new semi-classical method to count Majorana zero modes and links this count to topological invariants such as Chern numbers.

Findings

The counting formula accurately predicts zero modes in studied systems.

Zero modes are explicitly related to Chern numbers in examples.

The method applies to systems with charge-conjugation symmetry.

Abstract

A counting formula for computing the number of (Majorana) zero modes bound to topological point defects is evaluated in a gradient expansion for systems with charge-conjugation symmetry. This semi-classical counting of zero modes is applied to some examples that include graphene and a chiral p-wave superconductor in two-dimensional space. In all cases, we explicitly relate the counting of zero modes to Chern numbers.