In this paper we study random perturbations of first order elliptic operators with periodic potentials. We are mostly interested in Hamiltonians modeling graphene antidot lattices with impurities. The unperturbed operator is the sum of a Dirac-like operator plus a periodic matrix-valued potential , and is assumed to have an open gap. The random potential is of Anderson-type with independent, identically distributed coupling constants and moving centers, with absolutely continuous probability distributions. We prove band edge localization, namely that there exists an interval of energies in the unperturbed gap where the almost sure spectrum of the family is dense pure point, with exponentially decaying eigenfunctions, that give rise to dynamical localization.
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Jean-Marie Barbaroux, Horia D. Cornean, Sylvain Zalczer, Localization for Gapped Dirac Hamiltonians with Random Perturbations: Application to Graphene Antidot Lattices. Doc. Math. 24 (2019), pp. 65–93DOI 10.4171/DM/675