Dirac fermions on graphite cones

The electronic structure of graphitic cones is investigated within the self-consistent field-theory model. The local and total density of states near the apex is found for cones of different opening angles. For extended electronic states, total density of states is found to vanish at the Fermi level at any opening angles more than $60^{\circ}$. In turn, for power-law localized states, normalized zero-energy modes are shown to emerge.