Non‐Hermitian Stealthy Hyperuniformity

ABSTRACT

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.