Reentrant localization and a mobility gap in superlattice minibands

We develop a theory of the mobility edge for transport in superlattice minibands. For small W, where 2W is the bandwidth, the mobility edge ${\mathit{E}}_{\mathit{c}}$ diverges as ln1/W, so that all states are localized in the limit W→0. For large values of W, we find ${\mathit{E}}_{\mathit{c}}$∼1/W, and the system behaves as an anisotropic conductor. For intermediate values of W, the system can develop a mobility gap—a band of localized states—at the Van Hove singularity in the density of states. This reentrant localization behavior should be experimentally observable and may explain some recent experimental results.