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.