Variational method for the calculation of critical distance between two Coulomb centers in graphene

TL;DR

This paper develops a variational approach to determine the critical distance between two Coulomb impurities in gapped graphene, revealing how it depends on total charge and band gap, and compares with previous studies.

Contribution

It introduces a new variational method to calculate the critical impurity distance in graphene, accounting for combined impurity charge effects.

Findings

Critical distance increases with total impurity charge.

Critical distance decreases as the band gap narrows.

Results align with earlier research findings.

Abstract

The supercritical instability in a system of two identical charged impurities in gapped graphene described in the continuous limit by the two-dimensional Dirac equation has been studied. The case where the charge of each impurity is subcritical, but their sum exceeds the critical value calculated in the version with a single Coulomb center, is considered. Using the developed variational method, the dependence of the critical distance $R_{\rm cr}$ between the impurities on their total charge is calculated. The $R_{\rm cr}$-value is found to grow as the total impurity charge increases and the quasiparticle band gap decreases. The results of calculations are compared with those obtained in earlier researches.