Vacuum polarization effects on graphitic nanocones

Abstract

Theory of vacuum polarization by singular background fields is applied to the study of electronic properties of the graphitic monolayer (graphene) with a topological defect. Graphene in the long-wavelength approximation is characterized by the linear dispersion law for the quasiparticle excitations, representing a unique example of the really two-dimensional ‘ultrarelativistic’ electronic system which in the presence of topological defects can possess rather unusual properties. A disclination that rolls up a graphitic sheet into a nanocone is represented by a pointlike pseudomagnetic vortex with a flux which is related to the deficit angle of the cone. The electronic system on a graphitic nanocone is found to acquire the ground state condensate and current of special type, and we determine the dependence of these quantities on the deficit angle of the nanocone, continuous parameter of the boundary condition at the apex, and the distance from the apex.