# Anomalous Minimum and Scaling Behavior of Localization Length Near an Isolated Flat Band

@article{Ge2015AnomalousMA, title={Anomalous Minimum and Scaling Behavior of Localization Length Near an Isolated Flat Band}, author={Li Ge}, journal={Annalen der Physik}, year={2015}, volume={529} }

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…

## 13 Citations

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- Physics
- 2018

In this work, we first discuss systematically three general approaches to construct a non-Hermitian flat band, defined by its dispersionless real part. These approaches resort to, respectively,…

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- 2019

A flat band is nondispersive and formed under destructive interference. Although flat bands are found in various Hermitian systems, to realize a flat band in non-Hermitian systems is an interesting…

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- PhysicsPhysical Review A
- 2019

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- PhysicsPhysical Review B
- 2021

If a localized quantum state in a tight-binding model with structural aperiodicity is subject to noisy evolution, then it is generally expected to result in diffusion and delocalization. In this…

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- 2019

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- 2019

Asymmetric coupling amplitudes effectively create an imaginary gauge field, which induces a non-Hermitian Aharonov-Bohm (AB) effect. Nonzero imaginary magnetic flux invalidates the bulk-boundary…

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- 2020

This paper proposes a non-Hermitian asymmetric rhombic lattice which supports fully flat spectrum and Aharonov-Bohm caging formed by the oppositely oriented unidirectional couplings at the…

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