Disorder effects in the two-dimensional Lieb lattice and its extensions

Abstract

We study the localization properties of the two-dimensional Lieb lattice and its extensions in the presence of disorder using transfer matrix method and finite-size scaling. We find that all states in the Lieb lattice and its extensions are localized for $W\ge 1$. Clear differences in the localization properties between disordered flat band and disordered dispersive bands are identified. Our results complement previous experimental studies of clean photonic Lieb lattices and provide information about their stability with respect to disorder.

7 pages, 20 figures, 1 table

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• Flat-band solutions in $D$-dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem
• Tailoring flat bands and topological phases in a multi-strand Creutz network
• Localization properties in Lieb lattices and their extensions
• Persistent homology analysis of a generalized Aubry-André-Harper model
• Unconventional delocalization in a family of 3D Lieb lattices
• Compact localised states in magnonic Lieb lattices
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions
• Complete escape from localization on a hierarchical lattice: A Koch fractal with all states extended
• Quantum engineering for compactly localized states in disordered Lieb lattices
• Optical trimer: A theoretical physics approach to waveguide couplers
• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping
• RKKY couplings in the Lieb lattice: flat-band induced frustration