Pseudopotential carbon atom model in graphene lattice

This work is devoted to the formulation and approbation of the mathematical model describing an equilibrium state and properties of a graphene at a zero temperature. The model is based on integrated representation of pseudo-potential of hydrogen-like atom. This representation well is suitable for atoms of carbon in a graphene lattice. The model contains the parameters allowing to consider the local potential of an external field. Determination of parameters is made by a solution of a variation problem. Prospects of application of the developed model are connected with calculation of quantum states of carbon and silicon nanostructures. For example, use of the developed model will allow to connect a quantum state of atoms of a surface with emission current in a tunnel microscope or parameters of a virtual source of the edge emitter for probe electronoptical system.