Institute for Information Management in Engineering

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

  • Author:

    V. Haefner, J. Schindler, N. Weik, T. Mayer, S. Balakrishnan, R. Narayanan, S. Bera, F. Evers 

  • Source: > Condensed Matter > Mesoscale and Nanoscale Physics

  • Date: April 2014
  • The density of states (DoS), ϱ(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, nA and nB, 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 ϱ(E)∼|E|−1exp(−|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 ϱ(E)∼E−1|log(E)|−x, 1≤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.