Boundary-dependent self-dualities, winding numbers, and asymmetrical localization in non-Hermitian aperiodic one-dimensional models

Xiaoming Cai
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引用次数: 28

Abstract

We study a non-Hermitian Aubry-Andr\'e-Harper model with both nonreciprocal hoppings and complex quasiperiodical potentials, which is a typical non-Hermitian quasicrystal. We introduce boundary-dependent self-dualities in this model and obtain analytical results to describe its Asymmetrical Anderson localization and topological phase transitions. We find that the Anderson localization is not necessarily in accordance with the topological phase transitions, which are characteristics of localization of states and topology of energy spectrum respectively. Furthermore, in the localized phase, single-particle states are asymmetrically localized due to non-Hermitian skin effect and have energy-independent localization lengths. We also discuss possible experimental detections of our results in electric circuits.
非厄米非周期一维模型的边界相关自对偶性、圈数和不对称局域化
研究了一个具有非互易跳跃和复准周期势的非厄米Aubry-Andr\'e-Harper模型,它是一个典型的非厄米准晶体。我们在该模型中引入了边界相关的自对偶,并得到了描述其不对称Anderson局域化和拓扑相变的解析结果。我们发现Anderson局域化不一定符合拓扑相变,而拓扑相变分别是态局域化和能谱拓扑化的特征。此外,在局域相中,单粒子态由于非厄米集肤效应而非对称局域化,并且具有与能量无关的局域化长度。我们还讨论了我们的结果在电路中可能的实验检测。
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