Zero modes around vacancies in topological insulators and topological superconductors on the honeycomb lattice with particle-hole symmetry

Abstract
This paper studies the quantum properties of lattice vacancies in topological band insulators and topological superconductors (TSCs) on a honeycomb lattice with particle-hole symmetry. Each vacancy exhibits one “gauge-invariant” zero mode for the spinless Haldane model and two “gauge-invariant” zero modes for the Kane-Mele model. In addition, there exist Majorana zero modes around the vacancies in TSCs on honeycomb lattices with particle-hole symmetry. These zero-energy modes are protected by the particle-hole symmetry of these topological states.DOI: http://dx.doi.org/10.1103/PhysRevB.87.075126Received 10 October 2012Revised 3 February 2013Published 19 February 2013©2013 American Physical Society