Topological Phases in Graphitic Cones

The electronic structure of graphitic cones exhibits distinctive topological features associated with the apical disclinations. Ahranov-Bohm magnetoconductance oscillations (period ${\Phi }_0$) are completely absent in rings fabricated from cones with a single pentagonal disclination. Close to the apex, the local density of states changes qualitatively, either developing a cusp which drops to zero at the Fermi energy, or forming a region of nonzero density across $E_F$, a local metallization of graphite.