This so-called magnetic Lifshits tail is determined for the case of two space dimensions with a perpendicular magnetic field and for all single-impurity potentials with either super-Gaussian, Gaussian or regular sub-Gaussian decay at infinity. While the result for regular sub-Gaussian decay coincides with the corresponding classical one, the Lifshits tail caused by super-Gaussian decay exhibits a universal quantum behaviour. As a consequence, Gaussian decay is proven to discriminate between quantum and classical tailing. We also give results for the Lifshits tail of the integrated density of states restricted to a single Landau band.
In the case of three space dimensions, the magnetic Lifshits tail is investigated for all impurity potentials with super-Gaussian or Gaussian decay. Its precise form is determined for all impurity potentials with stretched (sub-) Gaussian decay. In this case it turns out that the tail is independent of the magnetic field and coincides, up to a logarithmic acceleration, with that for one dimension and not too slowly decaying impurity potentials.
As a by-product we determine the strong-magnetic field asymptotics of the integrated density of states for the two-dimensional and three-dimensional situation.
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