Localization properties of a two-channel 3D Anderson model

TL;DR

This paper investigates how interlattice hopping influences localization and delocalization in a coupled 3D Anderson model, revealing shifts in critical disorder and the emergence of mobility edges, with implications for disorder-free channels.

Contribution

It introduces a study of two coupled 3D lattices with different disorder properties, analyzing how hopping modifies localization transitions and the emergence of mobility edges.

Findings

Moderate hopping lowers the critical disorder for localization in the disordered channel.

Ordered channel develops effective disorder and mobility edges due to interlattice coupling.

Certain correlations can produce a disorder-free, decoupled channel.

Abstract

We study two coupled 3D lattices, one of them featuring uncorrelated on-site disorder and the other one being fully ordered, and analyze how the interlattice hopping affects the localization-delocalization transition of the former and how the latter responds to it. We find that moderate hopping pushes down the critical disorder strength for the disordered channel throughout the entire spectrum compared to the usual phase diagram for the 3D Anderson model. In that case, the ordered channel begins to feature an effective disorder also leading to the emergence of mobility edges but with higher associated critical disorder values. Both channels become pretty much alike as their hopping strength is further increased, as expected. We also consider the case of two disordered components and show that in the presence of certain correlations among the parameters of both lattices, one obtains a disorder-free channel decoupled from the rest of the system.