Extended and localized phonons, free electrons, and diffusive states in disordered lattice models

TL;DR

This paper demonstrates that phonons and diffusive electrons in disordered lattice models exhibit a different type of localization behavior than bonded electrons, with extended states persisting in two dimensions and unique properties at mobility edges.

Contribution

It introduces a new class of localization phenomena for phonons and diffusive electrons, distinct from traditional electronic models, supported by numerical evidence.

Findings

Extended states exist in two-dimensional disordered models.

Correlation length does not diverge at mobility edges in three dimensions.

Participation ratio of extended states approaches zero at the mobility edge.

Abstract

In this paper we propose that phonons, free diffusive electrons, and diffusion in two-and three--dimensional disordered lattice problems belong to a different class of localization than bonded electrons. This is manifested by three effects that can be observed numerically. First, there are extended states even at two dimensions, whereas there are no extended states in the usual electronic models. Second, the correlation length does not diverge at the mobility edges in three dimensions, and finally, the participation ratio of the extended states, decays to zero at this edge. This indicates zero electronic conductivity, in the extended region near the mobility edge. We show that low energy modes for these models can either have diverging localization lengths or are extended.