  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 $H_0 := D_S
+ V_0$ is the sum of a Dirac-like operator $D_S$ plus a periodic matrix valued
potential $V_0$, and is assumed to have an open gap. The random potential
$V_\omega$ 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 $H_\omega := H_0 + V_\omega$ is dense pure point, with exponentially
decaying eigenfunctions, that give rise to dynamical localization.
