Majorana fermions and Z$_2$ vortices on a square lattice

TL;DR

This paper introduces a simple square lattice model of Majorana fermions, analyzing zero-energy states associated with Z$_2$ vortices and their topological properties through numerical and continuum approaches.

Contribution

It provides a new lattice model linking Majorana zero modes, Z$_2$ vortices, and topological invariants, with insights into spectral asymmetry and flux-induced topological changes.

Findings

Zero-energy states are related to the Chern number of the ground state.

Numerical calculations confirm the relationship between zero modes and topological invariants.

An effective continuum model demonstrates a topological transition at half-flux.

Abstract

We present a simple model of Majorana fermions on a square lattice, and study zero-energy states due to Z$_2$ vortices. We show the relationship between the Chern number of the ground state and the number of the zero-energy states by numerical calculations for finite systems. We also discuss the relationship for the bulk system by observing the change of the spectral asymmetry. We finally present an effective continuum model with O(2) gauge potential which shows a topological change of the index at a half-flux.