Vacancy Induced Splitting of Dirac Nodal Point in Graphene

We investigate the vacancy effects on quasiparticle band structure of graphene near the Dirac point. It is found that each Dirac nodal point splits into two new nodal points due to the coherent scattering among vacancies. The splitting energy between the two nodal points is proportional to the square root of vacancy concentration. In addition, an extra dispersionless impurity band of zero energy due to particle-hole symmetry is found. Our theory offers an excellent explanation to the recent experiments.