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Due to its unique structure, graphene provides a condensed-matter model ofparticle physics phenomena. One is the critical charge which is highlyinterested. The investigation of critical charge in gapped graphene isperformed within single particle approach by means of Dirac equationintegration. The screened Coulomb interaction between charged defect andgraphene electron excitations is investigated. Two kinds of mass gap generationand various values of substrate dielectric permittivities are considered. It isshown that the critical charge phenomenon can be observed even with quite smallcharges for physically motivated parameters.

Critical Charge in Gapped Graphene: the role of the screening of the interaction potential by $\sigma$-orbitals