Multiple skin transitions in two-band non-Hermitian systems with long-range nonreciprocal hopping

Ye-Wei-Yi Li, Xiao-Feng Nie, Wen-Xue Cui, Hong-Fu Wang
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Abstract

Non-Hermitian skin effect is a prominent feature in non-Hermitian physics, leading to novel topological properties and expanding the traditional energy band theories. In this paper, we investigate a two-band non-Hermitian system in which multiple skin transitions are induced by long-range nonreciprocal hopping. The spectral winding number under periodic boundary conditions reveals the localization directions of skin states. Further, we present the analytical solution of transition points by tracing the self-intersecting points on the complex plane. Interestingly, the current system exhibits the abundant non-Hermitian skin effects, including the normal, W-shaped, and bipolar localization properties, which the eigenstate distributions and the generalized Brillouin zone can clearly illustrate. We also provide a phase diagram to represent the skin transition properties of the system comprehensively. Further, we demonstrate that the multimer non-Hermitian lattices also present the anomalous skin effect and multiple transitions, which occur in the region of the bulk band touching, the same as the two-band lattice. Moreover, a feasible scheme is proposed to realize the current non-Hermitian system with long-range nonreciprocal hopping by a topoelectrical circuit. This work further supplies the content of skin transitions and may help us explore more plentiful localization features in the two-band non-Hermitian systems.
具有长程非互易跳变的双波段非赫米提系统中的多重皮层转换
非ermitian 趋肤效应是非ermitian 物理学的一个突出特征,它带来了新的拓扑特性,并扩展了传统的能带理论。在本文中,我们研究了一个双能带非赫米提系统,在该系统中,长程非互易跳变诱发了多重趋肤转换。周期性边界条件下的谱绕组数揭示了趋肤态的局域化方向。此外,我们还通过追踪复平面上的自交点,给出了过渡点的解析解。有趣的是,当前系统表现出丰富的非赫米提趋肤效应,包括法线、W 形和双极局域化特性,特征态分布和广义布里渊区可以清楚地说明这一点。我们还提供了一个相图,以全面表示该系统的集肤转变特性。此外,我们还证明了多聚非赫米提晶格也存在反常趋肤效应和多重跃迁,其发生区域与双带晶格相同,都在体带接触区域。此外,还提出了一种可行的方案,通过拓扑电路来实现具有长程非互易跳变的当前非赫米提系统。这项工作进一步丰富了集肤跃迁的内容,有助于我们探索双带非ermitian 系统中更丰富的局域化特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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