AI 中文总结
研究处于畴壁构型的一维非厄米模型谱拓扑，通过扩展朗金函数形式得到复动量空间中广义布里渊区条件，发现两种趋肤模式，其分布和GBZ条件不同，行波状模式有有限通量谱缠绕数，对边界敏感。
AI 中文摘要
我们研究了处于畴壁构型的一维非厄米模型的谱拓扑，其中不同畴以环形几何排列。虽然在非厄米趋肤效应下本征态可局域在界面附近，但我们表明本征态的局域源于两个相邻畴相对于相应本征能量的谱缠绕数差异。然后，通过将朗金函数形式扩展到畴壁构型，我们得到了复动量空间中广义布里渊区（GBZ）的条件。除了在开放边界条件下对应于单个畴上驻波的传统趋肤模式外，还出现了一种独特的行波状趋肤模式，其构建涉及所有畴。这两种模式不仅空间分布不同，而且遵循不同的GBZ条件，在GBZ上可区分。有趣的是，行波状模式还携带有限通量谱缠绕数，表明它们对边界敏感。
英文摘要
We study the spectral topology of one-dimensional non-Hermitian models in a domain-wall configuration, where different domains are arranged in a ring geometry. While eigenstates can localize near an interface under the non-Hermitian skin effect, we show that the localization of an eigenstate originates from the difference in the spectral winding numbers, with respect to the corresponding eigenenergy, between the two adjacent domains. We then obtain the conditions for the generalized Brillouin zone (GBZ) in the complex momentum space, by extending the Ronkin-function formalism to the domain-wall configuration. In addition to the conventional skin modes that correspond to standing waves on individual domains under the open boundary condition, a unique type of traveling-wave-like skin modes emerges, whose construction involves all domains. Besides their difference in the spatial profiles, these two types of modes obey distinct GBZ conditions, making them differentiable on the GBZ. Interestingly, the traveling-wave-like modes further carry a finite flux spectral winding number, indicating their boundary sensitivity.
Comments27 pages, 6 figures
