  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.
