Shape-driven conductivity in graphene

A graphene surface is presented which has a non-vanishing density of states at the Fermi level. This is driven by defects in the sheet structure: these defects are solely odd-membered rings, forced upon the system by topological constraints due to its shape, which is a series of cones and saddles. These defects sufficiently distort the electronic structure of pure graphene such that the density of states at the Fermi level is significant. The system, physically, is globally flat--there is no net gaussian curvature--and the density of states is calculated via first principles. The system further possesses multiple stable surface configurations accessible via mechanical inversion of the cones, each with different densities of states.