# Methodology to Construct Large Realizations of Perfectly Hyperuniform Disordered Packings

## TL;DR

This paper introduces a general theoretical method to construct perfectly hyperuniform disordered packings in any dimension, overcoming previous limitations and enabling the design of materials with exotic physical properties.

## Contribution

The authors develop a novel methodology to generate perfectly hyperuniform packings from arbitrary tessellations, independent of particle shape or placement, applicable in multiple dimensions.

## Key findings

- Successfully converts large nonhyperuniform packings into hyperuniform ones in 2D and 3D.
- Proves hyperuniformity of Hashin-Shtrikman coated-spheres structures.
- Demonstrates tunability and potential for discovering new hyperuniform materials.

## Abstract

Disordered hyperuniform packings are unusual amorphous states of two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large hyperuniform samples due to practical limitations of conventional methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in $d$-dimensional Euclidean space. Specifically, beginning with an initial general tessellation of space that meets a "bounded-cell" condition, hard particles are placed inside each cell such that the packing fraction within the cell becomes identical to the global packing fraction. We prove that the constructed packings are perfectly hyperuniform in the infinite-sample-size limit and their hyperuniformity is independent of particle shapes, positions, and numbers per cell. We employ two distinct types of initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in $\mathbb{R}^2$ and $\mathbb{R}^3$. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures that possess optimal effective transport and elastic properties. In addition, the tunability of our methodology offers promise for discovery of novel disordered hyperuniform two-phase materials.