Vacancy-induced low-energy states in undoped graphene

Abstract

We demonstrate that a nonzero concentration n_v of static, randomly placed vacancies in graphene leads to a density w of zero-energy quasiparticle states at the band center ε=0 within a tight-binding description with nearest-neighbor hopping t on the honeycomb lattice. We show that w remains generically nonzero in the compensated case (exactly equal number of vacancies on the two sublattices) even in the presence of hopping disorder and depends sensitively on n_v and correlations between vacancy positions. For low, but not-too-low, |ε|/t in this compensated case, we show that the density of states ρ(ε) exhibits a strong divergence of the form ρ_Dyson(ε)∼|ε|⁻¹/[log(t/|ε|)]^(y+1), which crosses over to the universal low-energy asymptotic form (modified Gade-Wegner scaling) expected on symmetry grounds ρGW(ε)∼|ε|⁻¹e^{−b[log(t/|ε|)]2/3} below a crossover scale ε_c≪t. ε_c is found to decrease rapidly with decreasing n_v, while y decreases much more slowly.