Anomalous minimum and scaling behavior of localization length near an isolated flat band

Abstract

Using one-dimensional tight-binding lattices and an analytical expression based on the Green's matrix, we show that anomalous minimum of the localization length near an isolated flat band, previously found for evanescent waves in a defect-free photonic crystal waveguide, is a generic feature and exists in the Anderson regime as well, i.e., in the presence of disorder. Our finding reveals a scaling behavior of the localization length in terms of the disorder strength, as well as a summation rule of the inverse localization length in terms of the density of states in different bands. Most interesting, the latter indicates the possibility of having two localization minima inside a band gap, if this band gap is formed by two flat bands such as in a double-sided Lieb lattice.

arXiv comment8 pages, 10 figures

Cited by in corpus (9)

• Artificial flat band systems: from lattice models to experiments
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Defect states emerging from a non-Hermitian flat band of photonic zero modes
• Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling
• Flat band in two-dimensional non-Hermitian optical lattices
• Lifetime of flatband states
• Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity
• Dynamical transitions in aperiodically kicked tight-binding models
• Scaling laws for weakly disordered 1D flat bands