Vacancy Induced Splitting of Dirac Nodal Point in Graphene

TL;DR

This paper studies how vacancies in graphene cause the Dirac point to split into two, revealing a vacancy concentration-dependent splitting and an impurity band, explaining recent experimental observations.

Contribution

It introduces a theoretical model showing vacancy-induced splitting of Dirac points and the formation of impurity bands in graphene.

Findings

Dirac nodal points split into two due to vacancies

Splitting energy scales with the square root of vacancy concentration

An impurity band at zero energy appears due to particle-hole symmetry

Abstract

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.