Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions

• URL: http://arxiv.org/abs/2406.06682v2
• Date: Sat, 09 Aug 2025 14:41:29 GMT
• Title: Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Authors: Kai Zhang, Chang Shu, Kai Sun,
• Abstract summary: The non-Hermitian skin effect is characterized by a proliferation of exponentially localized edge modes in open-boundary systems.<n>We report a distinct phenomenon--the algebraic non-Hermitian skin effect--which arises generically in non-Hermitian systems with two or more spatial dimensions.
• Score: 8.053285346330739
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The non-Hermitian skin effect, characterized by a proliferation of exponentially localized edge modes in open-boundary systems, has led to the discovery of numerous novel physical phenomena that challenge the limits of conventional band theory. In sharp contrast to this familiar exponential localization, we report a distinct phenomenon--the algebraic non-Hermitian skin effect--which arises generically in non-Hermitian systems with two or more spatial dimensions. In such cases, the amplitude of skin modes typically decays from the boundary following a power law, rather than an exponential form--a behavior not captured by existing theoretical frameworks. To bridge this gap and describe the transition in localization from one to higher dimensions, we develop a generalized Fermi surface framework applicable to open-boundary systems in arbitrary dimensions. This framework not only reproduces known results for the exponential skin effect in 1D, but also predicts a new class of skin effects with algebraic decay in 2D and above. We demonstrate this framework in both tight-binding and continuum models in two and three dimensions. This investigation not only unveils a novel category of the non-Hermitian skin effect but also offers a comprehensive theoretical structure that describes skin effects in any non-Hermitian system, irrespective of its spatial dimensionality.

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