A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system

TL;DR

This paper investigates how amorphous disorder in 2D photonic-inspired models leads to coexistence of Anderson localization and flat-band phenomena, revealing unique localization behaviors not seen in crystalline or disordered systems.

Contribution

It introduces a family of amorphous kagomé-like models with exact results, demonstrating coexistence of flat bands and Anderson localization, and shows how amorphousness can induce novel localization effects.

Findings

Flat-band degeneracy persists without on-site disorder in amorphous systems.

Localized states emerge at specific fields, different from crystalline kagomé lattices.

Evidence of a localization-delocalization transition near certain states.

Abstract

Emerging experimental platforms use amorphousness, a constrained form of disorder, to tailor meta-material properties. We study localization under this type of disorder in a family of 2D models generalizing recent experiments on photonic systems. Models in this family reside on amorphous analogs of kagom\'{e} lattices with fixed coordination number, vary by a tunable synthetic field, and remarkabaly, permit exact results. We observe two kinds of localization that emerge in these models: Anderson localization by amorphous disorder, and the existence of compact, macroscopically degenerate localized states as in many crystalline flat bands. The flat-band-like degeneracy innate to kagom\'{e} lattices survives under amorphousness without on-site disorder. This phenomenon arises from the cooperation between the structure of the compact localized states and the geometry of the amorphous graph. More surprisingly, for particular values of the field, such states emerge in the amorphous system that were not present on the kagom\'{e} lattice in the same field. Outside the flat band, constrained amorphous graph geometry necessitates the existence of a fully delocalized state, near which we observe evidence of a localization-delocalization transition. Our platform serves as a demonstration of how the qualitative behavior of a disordered system can be tuned at fixed graph topology and lead to localization phenomena unique to amorphous systems that are not observed in their generically disordered counterparts.