Electronic Structure in Gapped Graphene with Coulomb Potential
  In this paper, we numerically study the bound electron states induced by long range Coulomb impurity in gapped graphene and the quasi-bound states in supercritical region based on the lattice model. We present a detailed comparison between our numerical simulations and the prediction of the continuum model which is described by the Dirac equation in (2+1)-dimensional Quantum Electrodynamics (QED). We also use the Fano's formalism to investigate the quasi-bound state development and design an accessible experiments to test the decay of the supercritical vacuum in the gapped graphene. 
W. Zhu, M. L. Liang, Q. W. Shi, Z. F. Wang, J. Chen, J. G. Hou