  A theoretical study of the electronic properties of nanodisks and nanocones
is presented within the framework of a tight-binding scheme. The electronic
densities of states and absorption coefficients are calculated for such
structures with different sizes and topologies. A discrete position
approximation is used to describe the electronic states taking into account the
effect of the overlap integral to first order. For small finite systems, both
total and local densities of states depend sensitively on the number of atoms
and characteristic geometry of the structures. Results for the local densities
of charge reveal a finite charge distribution around some atoms at the apices
and borders of the cone structures. For structures with more than 5000 atoms,
the contribution to the total density of states near the Fermi level
essentially comes from states localized at the edges. For other energies the
average density of states exhibits similar features to the case of a graphene
lattice. Results for the absorption spectra of nanocones show a peculiar
dependence on the photon polarization in the infrared range for all
investigated structures.
