Density of States in Graphene with Vacancies: Midgap Power Law and Frozen Multifractality

V. Häfner (1) , J. Schindler (1) , N. Weik (1) , T. Mayer (1) , S. Balakrishnan , R. Narayanan , S. Bera (2) , F. Evers (1)

1 KIT - Karlsruher Institut für Technologie
2 NEEL - ThQC - Théorie Quantique des Circuits

The density of states (DoS), %(E), of graphene is investigated numerically and within the selfconsistent 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|−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 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 genericbipartite 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.

Domaines: Science des matériaux [cond-mat.mtrl-sci]

V. Häfner, J. Schindler, N. Weik, T. Mayer, S. Balakrishnan, et al.. Density of States in Graphene with Vacancies: Midgap Power Law and Frozen Multifractality. Physical Review Letters, 2014, 113 (18), pp.186802. ⟨10.1103/PhysRevLett.113.186802⟩. ⟨hal-01379305⟩