Non-Hermitian stealthy hyperuniformity

TL;DR

This paper extends the concepts of hyperuniformity and stealthiness to non-Hermitian systems, revealing new wave manipulation properties and unidirectional scattering phases in open, gain-loss media, broadening the understanding of correlated disorder.

Contribution

It introduces a framework for non-Hermitian hyperuniformity and stealthiness, generalizing PT-symmetric crystals to include correlated disorder in open systems, and develops a statistical crystallography approach for these materials.

Findings

Real-imaginary cross-correlations are irrelevant for hyperuniformity.

Cross-correlations are essential for stealthiness characterization.

Unidirectional scattering phases are identified in non-Hermitian materials.

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. 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 are essential for characterizing stealthiness, revealing unidirectional scattering phases that are inaccessible in Hermitian materials and in non-Hermitian crystals. By analysing 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.