Particle-Hole Symmetry Protected Zero Modes on Vacancies in the Topological Insulators and Topological Superconductors on the Honeycomb Lattice

TL;DR

This paper investigates how vacancies in honeycomb lattice topological insulators and superconductors host zero energy modes, including Majorana modes, protected by particle-hole symmetry, revealing new insights into defect states in topological materials.

Contribution

It demonstrates the existence and protection of zero modes and Majorana modes at vacancies in honeycomb lattice topological phases, highlighting the role of particle-hole symmetry.

Findings

Vacancies host zero modes in Haldane and Kane-Mele models.

Majorana zero modes appear around vacancies in topological superconductors.

Zero modes are protected by particle-hole symmetry.

Abstract

In this paper we study the quantum properties of the lattice vacancy in topological band insulators (TBIs) and topological superconductors (TSCs) on honeycomb lattice with particle-hole symmetry. Each vacancy has one zero mode for the Haldane model and two zero modes for the Kane-Mele model. In addition, in TSCs on honeycomb lattice with particle-hole symmetry, we found the existence of the Majorana zero modes around the vacancies. These zero energy modes are protected by particle-hole symmetry of these topological sates.