Non-Hermitian Stealthy Hyperuniformity.

Symmetry-driven wave physics in open systems, exemplified by parity-time (PT) symmetry, has extended the landscape of crystalline phases in materials science to include gain-loss media. Given the growing interest in engineering disorder for wave manipulation, such non-Hermitian crystals motivate the extension of non-Hermitian frameworks into the realm of correlated disorder. Here, we propose hyperuniformity and stealthiness in non-Hermitian systems as a generalization of PT-symmetric crystals to correlated disorder in the weak-scattering limit. We extend the scattering-microstructure correspondence to open systems, formulating non-Hermitian hyperuniformity and stealthiness that encompass their Hermitian counterparts. This approach-incorporating a statistical crystallography framework for non-Hermitian materials-demonstrates that real-imaginary cross-correlations of the material potential are irrelevant for achieving hyperuniformity but essential for characterizing stealthiness, revealing unidirectional scattering phases that are inaccessible in both Hermitian materials and non-Hermitian crystals. Our non-Hermitian extension also reveals unique band coalescence in the strong scattering regime, suggesting stochastic exceptional-point dynamics. By analyzing the microstructural statistics of the resulting materials, our results-building on non-Hermitian wave physics-establish a connection to materials science, encompassing conventional descriptors of correlated disorder.