Exact Solution of the Problem of Bound Electronic States in Graphene

Abstract

In graphene with a gap in the electronic spectrum, the problem of bound states of an electron in the field of an impurity ion with the charge Z is considered. Parameter Z is the effective ion charge; it includes the permittivity of graphene. Analytical solution of the Schrödinger equation in the problem under consideration leads to a formula which contains two numbers determining the quantum state of the electron: the total pseudospin moment and the radial quantum number. The sign of the effective screening ion charge Z determines the positions of levels near the conduction or valence band of graphene. Accordingly, the energy levels can be interpreted as donor or acceptor electronic states in the gap.