Critical Charge in Gapped Graphene: the role of the screening of the   interaction potential by $\sigma$-orbitals
  Due to its unique structure, graphene provides a condensed-matter model of particle physics phenomena. One is the critical charge which is highly interested. The investigation of critical charge in gapped graphene is performed within single particle approach by means of Dirac equation integration. The screened Coulomb interaction between charged defect and graphene electron excitations is investigated. Two kinds of mass gap generation and various values of substrate dielectric permittivities are considered. It is shown that the critical charge phenomenon can be observed even with quite small charges for physically motivated parameters. 
A. A. Novoselov, O. V. Pavlovsky
cond-mat.str-el