Density of states in graphene with vacancies: midgap power law and frozen multifractality

Abstract

The density of states (DoS), $\varrho (E)$, of graphene is investigated numerically and within the self-consistent T-matrix approximation (SCTMA) in the presence of vacancies within the tight binding model. The focus is on compensated disorder, where the concentration of vacancies, $n_{\text{A}}$ and $n_{\text{B}}$, in both sub-lattices is the same. Formally, this model belongs to the chiral symmetry class BDI. The prediction of the non-linear sigma-model for this class is a Gade-type singularity $\varrho (E)\sim |E{|}^{-1}\exp (-|\log (E){|}^{-1/x})$. Our numerical data is compatible with this result in a preasymptotic regime that gives way, however, at even lower energies to $\varrho (E)\sim E^{-1}|\log (E){|}^{-\mathfrak{x}}$, $1\le \mathfrak{x}<2$. We take this finding as an evidence that similar to the case of dirty d-wave superconductors, also generic bipartite random hopping models may exhibit unconventional (strong-coupling) fixed points for certain kinds of randomly placed scatterers if these are strong enough. Our research suggests that graphene with (effective) vacancy disorder is a physical representative of such systems.

References updated only

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