Researchers from institutions including Penn State University, Nanjing University, and Fudan University have developed an experimental framework to map complex band structures in non-Hermitian systems, according to a study published in Nature Communications.
Periodic Hermitian systems rely on real-valued band structures, but non-Hermitian systems produce complex band structures where both energy and momentum contain imaginary parts. Mapping these complex relationships and measuring their corresponding eigenstates has historically presented significant experimental difficulties.
To resolve the issue, the research team created a non-Bloch supercell framework that uses non-Bloch Fermi points as primary observables. These points serve as non-Hermitian counterparts to standard Fermi surfaces, providing measurable markers for point-gap topology and open-boundary behaviors while separating the real and imaginary components of momentum.
The experimental setup combined an exponent-flattening protocol with twisted boundary conditions. This configuration gave the researchers system-size-independent control over imaginary momentum and preserved high-resolution sampling across real momentum coordinates.
The authors deployed the technique in programmable one-dimensional and two-dimensional acoustic crystals. By conducting Green’s function measurements, they extracted momentum-resolved complex energy surfaces and biorthogonal eigenstates. The measured band structures, which included distributions of complex momentum, complex energy, and Berry curvature, accurately predicted open-boundary spectra and eigenstates during separate open-geometry validation experiments.
Lead authors Jia-Xin Zhong and Jing Lin contributed equally to the paper alongside co-authors Kai Chen, Jing Lu, Kun Ding, and Yun Jing. The work received support from Penn State University startup funding, the National Key R&D Program of China, the National Natural Science Foundation of China, the Shanghai Science and Technology Innovation Action Plan, and the AI & AI for Science Project of Nanjing University.
