Conductivity of a quasiperiodic system in two and three dimensions

TL;DR

This paper introduces a generalized quasiperiodic model in 2D and 3D, analyzing its conductivity and density of states, revealing precursor signs of an Anderson transition without a mobility edge.

Contribution

It presents an exactly solvable quasiperiodic model with hopping terms, extending the Aubry-Andre model to higher dimensions and analyzing its transport properties.

Findings

No mobility edge observed in the model

Regular ac-conductivity indicates transition precursors

Reduced Drude weight suggests approaching Anderson transition

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.