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arXiv · 2607.22976

Spectral Topology and Non-Bloch Band Theory for Domain-Wall Systems

Mingtao Xu·Rui Wang·Tian-Shu Deng·Wei Yi
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Abstract

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.

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Mingtao Xu, Rui Wang, Tian-Shu Deng, Wei Yi. 2026-07-25. Spectral Topology and Non-Bloch Band Theory for Domain-Wall Systems. https://arxiv.org/abs/2607.22976

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