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arXiv · 2008.05501

Impurity induced scale-free localization

Linhu Li·Ching Hua Lee·Jiangbin Gong
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Abstract

This work develops a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with PBCs, OBCs and even their interpolations being special cases across a whole range of boundary impurity strengths. As the impurity strength is tuned, the localization of steady states can assume very rich behavior, including the expected non-Hermitian skin effect, Bloch-like states albeit broken translational invariance, and surprisingly, scale-free accumulation along or even against the direction of non-reciprocity. We further uncover the possibility of the co-existence of non-Hermitian skin effect and scale-free localization, where qualitative aspects of the system's spectrum can be extremely sensitive to impurity strength. We have also proposed specific circuit setups for experimental detection of the scale-free accumulation, with simulation results confirming our main findings.

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Linhu Li, Ching Hua Lee, Jiangbin Gong. 2020-08-12. Impurity induced scale-free localization. https://doi.org/10.1038/s42005-021-00547-x

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