Internal Lifshits tails for random magnetic Schrödinger operators

This paper is devoted to the study of Lifshits tails for weak random magnetic perturbations of periodic Schrödinger operators acting on L2(Rd ) of the form Hλ,w = (−i∇−λ γ ∈Zd wγ A(· − γ ))2 +V, where V is a Zd -periodic potential, λ is positive coupling constants, (wγ )γ ∈Zd are i.i.d and bounded random variables and A ∈ C1 0 (Rd ,Rd ) is the single site vector magnetic potential. We prove that, for λ small, at an open band edge, a true Lifshits tail for the random magnetic Schrödinger operator occurs if a certain set of conditions on H0 =− +V and on A holds. © 2007 Elsevier Inc. All rights reserved