Localized and quasi-localized energy levels in the electron spectrum of graphene with isolated boron and nitrogen substitutions

TL;DR

This paper investigates how boron and nitrogen impurities create localized energy levels in graphene, providing analytical conditions and analyzing their effects near the Fermi level.

Contribution

It introduces analytical expressions for impurity-induced energy levels in graphene and analyzes the formation of quasi-localized states for boron and nitrogen substitutions.

Findings

Boron creates discrete energy levels outside the conduction band.

Nitrogen induces quasi-localized states near the Fermi level.

Analytical conditions for impurity level formation are derived.

Abstract

Based on the calculation and analysis of local Green functions of impurity atoms of low concentration in a two-dimensional graphene lattice, the conditions for the formation and characteristics of local discrete levels with energies lying outside the band of the quasi-continuous spectrum and quasi-localized states with energies near the Fermi one are determined. Specific calculations were performed for boron and nitrogen impurity atoms, which can actually replace carbon in graphite and graphene nanostructures. For a boron impurity that forms local discrete levels outside the band of the quasi-continuous spectrum, sufficiently simple analytical expressions for the conditions for their formation, energy, intensity at the impurity atom, and damping parameter are obtained. An analysis of the formation of states quasi-localized on nitrogen impurities with energy near the Fermi level in graphene nanostructures was carried out.