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In this paper we study the quantum properties of the lattice vacancy intopological band insulators (TBIs) and topological superconductors (TSCs) onhoneycomb lattice with particle-hole symmetry. Each vacancy has one zero modefor 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 theexistence of the Majorana zero modes around the vacancies. These zero energymodes are protected by particle-hole symmetry of these topological sates.

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