Flat band states: disorder and nonlinearity

TL;DR

This paper investigates how disorder and nonlinearity affect flat band states and Anderson localization in a quasi-one-dimensional lattice, revealing unique scaling laws and diverse wave dynamics.

Contribution

It uncovers the distinct scaling behavior of flat band states under disorder and explores the impact of nonlinearity on wave spreading regimes.

Findings

Flat band localization length scales as W^{-1.3}

Dispersive bands scale as W^{-2}

Nonlinearity induces various wave spreading regimes

Abstract

We study the critical behaviour of Anderson localized modes near intersecting flat and dispersive bands in the quasi-one-dimensional diamond ladder with weak diagonal disorder $W$. The localization length $\xi$ of the flat band states scales with disorder as $\xi \sim W^{-\gamma}$, with $\gamma \approx 1.3$, in contrast to the dispersive bands with $\gamma =2$. A small fraction of dispersive modes mixed with the flat band states is responsible for the unusual scaling. Anderson localization is therefore controlled by two different length scales. Nonlinearity can produce qualitatively different wave spreading regimes, from enhanced expansion to resonant tunneling and self-trapping.