Sobol O. Supercritical instability in graphene with charged impurities

The thesis is devoted to the theoretical study of the properties of electronic states in graphene with charged impurities. In particular, the phenomenon of supercritical instability and conditions of its appearance in the systems with similarly or oppositely charged impurities are investigated. It was shown that in a cluster of two identically charged impurities an instability occurs if the distance between impurities is smaller than the critical one. It was found a new manifestation of supercritical instability in the potential of two oppositely charged impurities, when an electron and a hole are created from a vacuum in bound states with corresponding impurities. In addition, it was studied a possibility of realizing of the supercritical instability in systems with discrete electron spectrum: graphene flake of a finite area and graphene in an external magnetic field. Taking into account the polarization effects in a magnetic field, it was proved the possibility of regulating the effective charge of the impurity by means of the gate voltage.