Density of States in Graphene with Vacancies: Midgap Power Law and Frozen Multifractality
V. Häfner, J. Schindler, N. Weik, T. Mayer, S. Balakrishnan, R. Narayanan, S. Bera, F. Evers
- Datum: 2014
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 nonlinear 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)|^(−x), 1 ≤ x <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.