Variational method for the calculation of critical distance between two   Coulomb centers in graphene
  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. 
Oleksandr Sobol
cond-mat.str-el cond-mat.mes-hall