Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices

TL;DR

This paper introduces a generalized class of mosaic lattices with disorder, deriving expressions for mobility edges and localization lengths, and demonstrating how gaps in the lattice protect against Anderson localization.

Contribution

It generalizes previous results on mosaic lattices by deriving new formulas for mobility edges and localization lengths with incommensurate disorder, and shows how lattice gaps protect against localization.

Findings

Extended states persist at resonance frequencies despite strong disorder.

Mobility edges are analytically derived for incommensurate sinusoidal disorder.

Gaps in the disorder-free lattice protect against Anderson localization.

Abstract

Mosaic lattice models have been recently introduced as a special class of disordered systems displaying resonance energies, multiple mobility edges and anomalous transport properties. In such systems on-site potential disorder, either uncorrelated or incommensurate, is introduced solely at every equally-spaced sites within the lattice, with a spacing $M \geq 2$. A remarkable property of disordered mosaic lattices is the persistence of extended states at some resonance frequencies that prevent complete Anderson localization, even in the strong disorder regime. Here we introduce a broader class of mosaic lattices and derive general expressions of mobility edges and localization length for incommensurate sinusoidal disorder, which generalize previous results [Y. Wang {\it et al.}, Phys. Rev. Lett. {\bf 125}, 196604 (2020)]. For both incommensurate and uncorrelated disorder, we prove that Anderson localization is protected by the open gaps of the disorder-free lattice, and derive some general criteria for complete Anderson localization. The results are illustrated by considering a few models, such as the mosaic Su-Schrieffer-Heeger (SSH) model and the trimer mosaic lattice.