New localization in a quasiperiodic system

Abstract

We present a new type of localization phenomenon in a one-dimensional tight-binding model with a quasiperiodic potential ${\mathit{V}}_{\mathit{n}}$=tanh[Acos(2\ensuremath{\pi}\ensuremath{\omega}n)]/tanhA, where \ensuremath{\omega} is an irrational number. When A is small, the localization starts from the center of the spectrum at a value of \ensuremath{\lambda}; then the mobility edges move towards the edges of the spectrum with increasing \ensuremath{\lambda}; finally all the states become localized. This behavior is in contrast to the Anderson localization in three-dimensional random systems. When A is large, a more complicated behavior is found.