Verification of continuum-based model of carbon materials

The continuous medium approximation to the description of a carbon material previously used to model the properties of spherical carbon shells of nanometer diameter. This approach is based on the transition from lattice operators to field operators. The present study verifies the given model evaluating the energy spectrum of electrons in a perfect flat carbon monolayer. An implementation of the Dirac cones within the continuous medium framework is demonstrated. Its are close to the positions of the vertices of the Brillouin zone for graphene. Increase of the Taylor series expansion order of field operators makes the result precise, and the approximate positions of the Dirac cones match the exact data for graphene.