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In this paper we study the electronic properties of carbon nanocones with oneand two nappes, with pentagonal and heptagonal defects in their lattices. Weuse the continuum model, which is based on a Dirac-like Hamiltonian with thetopological effects described by localized non-Abelian gauge field fluxes. Wedevelop a geometrical approach that can describe the two nappes of the doublecone surface simultaneously, by extending the radial coordinate to the completeset of real numbers. We show that, for some combinations of differentnanocones, forming the double conical surface, the local density of states nearthe apex of the cone does not vanish at the Fermi energy and presents a strongdependence on the angular momentum. We also obtain the energy spectrum forfinite-sized nanocones and verify that it depends on the choice of topologicaldefect on the surface, which suggests that a double nanocone can be used tocontrol the electronic transport in carbon-based electronic devices.

Electronic properties of single and double napped carbon nanocones