Fast Hyperuniform Structure Generation with Tunable k-space Features

Hyperuniform materials, characterized by the suppression of density fluctuations at large length scales or, equivalently, a structure factor decaying to zero at low wavevectors, are of great interest in the study of functional (e.g., optical bandgap) materials. We introduce a quasilinear-time structural optimization algorithm capable of generating large (N > 200,000) two- and three-dimensional hyperuniform structures significantly faster than previous approaches. Our method allows for high control of the structure factor in k-space and can jointly minimize other loss functions, such as pairwise repulsive interactions to generate sphere packings with desired spectral characteristics. As a result, we can inversely designmaterial structures exhibiting a variety of k-space features including anisotropy, n-fold symmetry, and disordered hyperuniformity, including stealthiness on specific length scales. Thus, systems approaching experimentally verifiable sizes can now be generated, and the relationship between 2-body statistics and emergent physical properties can be studied systematically at scale.