Impurity levels in the electronic spectra of graphene

We calculate and analyze, within a model that allows to obtain an analytical approximation using the method of Jacobi matrices, the electronic spectra of graphene with impurity atoms, especially with boron substitutional impurity. We present analytical expressions for the conditions of the existence of electronic local discrete levels due to the presence of a substitutional impurity in graphene.

► Real and imaginary parts of the Green’s function for ideal graphene are calculated.
► We calculate and analyze the electronic spectra of graphene with impurity atoms.
► We achieved the expressions for conditions of appearing for local and quasi-local states.
► Parameters of damping of the amplitudes of local vibrations are determined.
► We report basic principles of calculational method of Jacobi matrices.