Flat Bands Under Correlated Perturbations

TL;DR

This paper investigates how correlated perturbations affect flat band networks, revealing phenomena like state expulsion, localization length vanishing, and divergence in density of states, supported by analytical and numerical analysis.

Contribution

It provides a detailed analytical and numerical study of the effects of correlated disorder on flat band systems, highlighting new spectral and localization phenomena.

Findings

States are expelled from the flat band energy $E_{FB}$

Localization length vanishes as $ ightarrow 1 / ext{ln}(E - E_{FB})$

Density of states diverges logarithmically or algebraically depending on symmetry

Abstract

Flat band networks are characterized by coexistence of dispersive and flat bands. Flat bands (FB) are generated by compact localized eigenstates (CLS) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLS without additional renormalization, yet with surprising consequencies: (i) states are expelled from the FB energy $E_{FB}$, (ii) the localization length of eigenstates vanishes as $\xi \sim 1 / \ln (E- E_{FB})$, (iii) the density of states diverges logarithmically (particle-hole symmetry) and algebraically (no particle-hole symmetry), (iv) mobility edge curves show algebraic singularities at $E_{FB}$. Our analytical results are based on perturbative expansions of the CLS, and supported by numerical data in one and two lattice dimensions.