Recently, Assistant Professor Jia-Xin Zhong and Professor Jing Lu from the School of Physics at Nanjing University, together with collaborators at Fudan University and The Pennsylvania State University, introduced a non-Bloch supercell framework for experimentally mapping complex non-Hermitian band structures. Unlike the real-valued bands of Hermitian systems, non-Hermitian bands involve complex energy and momentum, and the imaginary part of momentum controls spatial amplification and attenuation. This information is essential for describing skin effects and other boundary-sensitive phenomena but is difficult to measure directly. The new method combines twisted boundary conditions with an exponent-flattening protocol, allowing the real and imaginary parts of momentum to be tuned independently. Implemented in programmable one- and two-dimensional acoustic crystals, it reconstructs complex energy surfaces and biorthogonal eigenstates from full Green's function measurements. The measured non-Bloch bands accurately predict open-boundary spectra and eigenstates, generalized Brillouin zones, spectral singularities, and boundary-selected interference patterns. The team further reconstructed biorthogonal Berry curvature and the Chern number in a non-Hermitian Chern insulator. The work establishes a scalable, dimension-independent toolkit for exploring non-Hermitian band geometry and topology across programmable wave platforms.

The work was accepted for publication in Nature Communications under the title "Unveiling non-Hermitian band structures with non-Bloch supercells." Jia-Xin Zhong of Nanjing University and Jing Lin of Fudan University are co-first authors. Jing Lin, Jing Lu, Kun Ding, and Yun Jing are the corresponding authors, and Kai Chen also contributed to the work.

Figure 1. From conventional Hermitian bands and Fermi surfaces to non-Hermitian complex bands and non-Bloch Fermi points. The latter connect complex momentum and energy to open-boundary spectra and eigenstates.

Publication link:  https://doi.org/10.1038/s41467-026-77152-5