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 eightfold 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 $M\neq0$.