2024/06/10 by Kai Zhang, C. Shu, Zhang, Kai +3 · 9 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Optics (physics.optics) #Quantum Gases (cond-mat.quant-gas) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2406.06682
openalex publication_date 2024/06/10 · openalex created_date 2024/06/13 · openalex updated_date 2026/07/28
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.