Topological Metallicity in Defective Graphene

Disordered graphene surfaces are presented which have a non-vanishing density of states at the Fermi level driven by topological defects in the sheet structure, i.e. heptagonal and pentagonal rings. We observe a crossover in the relative representation of five and seven-fold rings in the site-resolved density of states upon passing across the Fermi level, with signs that gapping near the Fermi surface is connected to the development of “tails” of reversed ring character that extend into these gaps. The generality of this phenomenon suggests that it may be a universal feature of disordered sp² carbons.