Interplay of Flat-band and Anderson localizations in disordered moire superlattices

TL;DR

This study investigates how flat-band and Anderson localizations interact in disordered moire superlattices, revealing complex behaviors and guiding principles for device engineering.

Contribution

It introduces a combined framework to map localization transitions and uncovers distinct localization behaviors in disordered moire lattices.

Findings

Flat bands within the interband gap remain strongly localized despite disorder.

Low-frequency flat bands exhibit an inverse Anderson transition.

High-frequency flat bands show coexistence of flat-band and Anderson localization at high disorder.

Abstract

Disorder in moire superlattices simultaneously degrades flat-band localization and induces Anderson localization, yet how these two regimes interact has remained unclear. Here, we introduce a combined framework linking localization-length scaling with differential probability density analysis to map localization transitions in partially disordered one-dimensional silicon moire lattices. It is found that flat bands confined within the interband gap keep their strong localization even as disorder grows. In contrast, flat bands intersecting dispersive bands exhibit rich behaviors: the low-frequency branch undergoes an inverse Anderson transition, while the high-frequency branch supports coexisting flat-band and Anderson localization at strong disorder. Our results deliver the direct evidence of competing localization mechanisms in disordered moire systems and offer guiding principles for engineering robust, nonideal moire photonic devices.