Unveiling non-Hermitian band structures with non-Bloch supercells

• URL: http://arxiv.org/abs/2510.20160v1
• Date: Thu, 23 Oct 2025 03:18:23 GMT
• Title: Unveiling non-Hermitian band structures with non-Bloch supercells
• Authors: Jia-Xin Zhong, Jing Lin, Kai Chen, Jing Lu, Kun Ding, Yun Jing,
• Abstract summary: Non-Hermitian systems exhibit complex band structures where both energy and momentum have imaginary parts.<n>We introduce a non-Bloch supercell framework designed to overcome this challenge by decoupling Bloch phase control from the imaginary part of momentum.
• Score: 23.45255537572689
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Real-valued band structures are foundational to analyzing periodic systems within the Hermitian description and have been experimentally well-established over recent decades. In contrast, non-Hermitian systems exhibit complex band structures where both energy and momentum have imaginary parts, underpinning phenomena like the non-Hermitian skin effect and anomalous bulk-boundary correspondence that defy conventional Bloch theory. Experimentally mapping these complex bands-relating complex momentum to complex energy-and identifying their associated eigenstates is crucial for understanding these systems but remains a significant challenge. Here, we introduce a non-Bloch supercell framework designed to overcome this challenge by decoupling Bloch phase control from the imaginary part of momentum. Our method combines an exponent-flattening protocol with twisted boundary conditions, enabling system-size-independent control of imaginary momentum while preserving high-resolution Bloch phase sampling. Implemented in programmable one- and two-dimensional acoustic crystals, our approach acquires momentum-resolved complex energy surfaces and biorthogonal eigenmodes by Green's function measurements.Data obtained using this framework accurately predict open-boundary spectra and eigenstates, findings we verify through separate open-geometry experiments. Our work provides a broadly applicable experimental toolkit for exploring non-Hermitian band geometry and topology in diverse engineered classical and quantum platforms.

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