Density of states in graphene with vacancies: midgap power law and frozen multifractality.
The density of states ϱ(E) of graphene is investigated numerically and within the self-consistent T-matrix approximation in the presence of vacancies within the tight binding model. The focus is on compensated disorder, where the concentration of vacancies n(A) and n(B) in both sublattices is the same. Formally, this model belongs to the chiral symmetry class BDI. The onlinear sigma model predicts for BDI a Gade-type singularity ϱ(E)∼|E|(-1)exp[-|log(E)|(-1/x)]. Our numerical data are comparable to this result in a preasymptotic regime that gives way, however, at even lower energies to ϱ(E)∼E(-1)|log(E)|(-x̃), 1≤x̃<2. We take this finding as evidence that, similar to the case of dirty d-wave superconductors, generic bipartite random hopping models may also 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.
Institute of Nanotechnology, Karlsruhe Institute of Technology, Campus North, D-76344 Karlsruhe, Germany and Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, Campus South, D-76128 Karlsruhe, Germany.
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Häfner
Institute of Nanotechnology, Karlsruhe Institute of Technology, Campus North, D-76344 Karlsruhe, Germany and Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, Campus South, D-76128 Karlsruhe, Germany.
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Schindler
Institute of Nanotechnology, Karlsruhe Institute of Technology, Campus North, D-76344 Karlsruhe, Germany and Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, Campus South, D-76128 Karlsruhe, Germany.
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Weik
Institute of Nanotechnology, Karlsruhe Institute of Technology, Campus North, D-76344 Karlsruhe, Germany and Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, Campus South, D-76128 Karlsruhe, Germany.
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Mayer
Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
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Balakrishnan
Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
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Narayanan
Institute Néel and Université Grenoble Alpes, F-38042 Grenoble, France.
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Bera
Institute of Nanotechnology, Karlsruhe Institute of Technology, Campus North, D-76344 Karlsruhe, Germany and Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, Campus South, D-76128 Karlsruhe, Germany and Center of Functional Nanostructures, Karlsruhe Institute of Technology, Campus South, D-76131 Karlsruhe, Germany.
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Evers