Electronic Structure of Negatively Curved Graphene

We study the electronic structure of graphene in the presence of either sevenfolds or eightfolds by using a gauge field-theory model. The graphene sheet with topological defects is considered as a negative cone surface with infinite Gaussian curvature at the center. The density of electronic states is calculated for a single seven-and eight-fold as well as for a pair of sevenfolds with different morphology. The density of states at the Fermi energy is found to be zero in all cases except two sevenfolds with translational factor M = 0. Nowadays graphene and related graphene-based nanostructures are the subject of great interest. It is well known that some number of fivefolds must be included in the honeycomb graphene lattice to produce various nanostruc-tures with positive Gaussian curvature of the surface: nanocones, nanohorns, closed nanotubes, fullerenes, etc. There is another type of possible defects, sevenfolds and eightfolds, which results in a surface with negative Gaussian curvature. Experimentally the presence of sevenfolds in various nanostruc-tures was observed by Iijima [1]. The structures with sevenfolds only are rather exotic [2], however, the presence of fivefold-sevenfold pairs is expected 1