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∈ZdwγA2(⋅−γ))+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 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=−Δ+V and on A holds.