Dynamical localization of electrons in an aperiodic superlattice

Abstract

We derive the analytical form of the time-dependent wave function for a single-band tight-binding model of independent conduction electrons within an aperiodic semiconductor superlattice, created by modification in the composition of a single layer of an otherwise periodic superlattice. While the was function for long times in known to feature both diffusive and localized behavior, the latter originating in the superlattice aperiodicity, we provide quantitative results for these features for all values of the time.