Modeling of the Energy Spectrum of a Carbon Sphere in the Continuous Medium Limit

Abstract—An approach to the calculation of the energy spectrum of a monolayer carbon nanoshell (monolayer and multilayer sphere is proposed based on the application of the Hubbard model and the continuous medium approximation with account for the possible deposition of impurity atoms on the carbon surface. A discrete spectrum of energy levels is realized in the limit of infinite radius of shell curvature, which corresponds to the structure of graphene energy levels. The presence of high-concentration impurity ions on the carbon surface leads to the emergence of a bandgap of width up to several electronvolts. The Coulomb repulsion of electrons at lattice sites enhances this effect and determines asymmetry of spectral branches. In the optical radiation spectrum, absorption bands are formed in the visible and ultraviolet spectral regions separated by broad intervals with a relatively small number of allowed transitions. The result obtained in this study are in conformity with the known spectroscopic data for fullerenes C₆₀ and C₇₀, as well as with their theoretical models.