Conductivity of a quasiperiodic system in two and three dimensions

Abstract

A generalization of the Aubry-Andre model in two and three dimensions is introduced which allows for quasiperiodic hopping terms in addition to the quasiperiodic site potentials. This corresponds to an array of interstitial impurities within the periodic host crystal. The resulting model is exactly solvable and I compute the density of states and the ac-conductivity. There is no mobility edge as in completely disordered systems but the regular ac-conductivity and the strongly reduced Drude weight indicate a precursor of the Anderson transition as the Fermi energy goes from the center to the band edges.