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Current issue   Ukr. J. Phys. 2014, Vol. 59, N 5, p.531-540

    Paper

Sobol O.O.

Taras Shevchenko National University of Kyiv
(2, Prosp. Academician Glushkov, Kyiv 03022, Ukraine; e-mail: sobololeks@ukr.net)

Variational Method for the Calculation of Critical Distance between Two Coulomb Centers in Graphene

Section: Nanosystems
Original Author's Text: Ukrainian

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 Rcr between the impurities on their total charge is calculated. The Rcr-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.

Key words: graphene, supercritical instability, critical distance, Kantorovich variational method.