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

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 $R_{\mathrm{cr}}$ between the impurities on their total charge is calculated. The $R_{\mathrm{cr}}$-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.

10 pages, 2 figures

References in corpus (7)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• The Coulomb impurity problem in graphene
• Observing Atomic Collapse Resonances in Artificial Nuclei on Graphene
• Supercritical Coulomb center and excitonic instability in graphene
• Supercritical instability in graphene with two charged impurities

Cited by in corpus (2)

• Electron states in the field of charged impurities in two-dimensional Dirac systems
• Supercritical instability of Dirac electrons in the field of two oppositely charged nuclei