Extended-localized transition for a tight-binding model with mass position dependence

Abstract This work reports results for a tight-binding model with mass position dependence, for which localized-extended wave function transitions can be identified. We show that it is possible to control the density of localized and extended states by tuning the transition-related parameter for a continuous range of energy values. Mathematically exact results for extended or localized states are derived in two extreme conditions of this parameter, as well as an exact energy value for a mobility edge transition in the intermediate regime.