Flat Bands Under Correlated Perturbations

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.

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• Bose condensation in flat bands
• Electronic Transport in DNA
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Cited by in corpus (4)

• Observation of a localized flat-band state in a photonic Lieb lattice
• Observation of bound states in Lieb photonic lattices
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Flat band analogues and flux driven extended electronic states in a class of geometrically frustrated fractal networks