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

TL;DR

This paper investigates the critical charge phenomenon in gapped graphene, analyzing how screening effects from $\sigma$-orbitals influence the interaction potential and the conditions under which critical charge can be observed.

Contribution

It provides a detailed analysis of critical charge in gapped graphene considering screening effects and various substrate dielectric permittivities using a Dirac equation approach.

Findings

Critical charge can be observed with small charges under realistic parameters.

Screening by $\sigma$-orbitals significantly affects the interaction potential.

Different mass gap generation mechanisms influence the critical charge threshold.

Abstract

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.