Particle-Hole Symmetry Protected Zero Modes on Vacancies in the   Topological Insulators and Topological Superconductors on the Honeycomb   Lattice
  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. 
Jing He, Ying-Xue Zhu, Ya-Jie Wu, Lan-Feng Liu, Ying Liang, and   Su-Peng Kou
cond-mat.mes-hall cond-mat.str-el cond-mat.supr-con