Localization of weakly disordered flat band states

TL;DR

This paper investigates how weak disorder affects the localization of flat band states in various lattice models, revealing both robustness and destruction depending on the class of flat band.

Contribution

It provides a systematic analysis of the stability of flat band localization under disorder across different lattice classes in one and two dimensions.

Findings

Flat band states can be either robust or fragile under disorder.

Localization lengths can diverge with unconventional exponents.

The behavior depends on the specific flat band class.

Abstract

Certain tight binding lattices host macroscopically degenerate flat spectral bands. Their origin is rooted in local symmetries of the lattice, with destructive interference leading to the existence of compact localized eigenstates. We study the robustness of this localization to disorder in different classes of flat band lattices in one and two dimensions. Depending on the flat band class, the flat band states can either be robust, preserving their strong localization for weak disorder W, or they are destroyed and acquire large localization lengths $\xi$ that diverge with a variety of unconventional exponents $\nu$, $\xi \sim 1/W^{\nu}$.