Hyperuniformity Order Metric of Barlow Packings

TL;DR

This paper introduces a hyperuniformity order metric to analyze Barlow packings, revealing how local stacking geometry influences large-scale density fluctuations and hyperuniformity properties.

Contribution

It applies the hyperuniformity order metric to Barlow packings, demonstrating its dependence on local cluster geometry and providing bounds on stealthy hyperuniformity.

Findings

The order metric is approximately linear in the fraction of fcc-like clusters.

All Barlow packings are stealthy hyperuniform with a common wavevector suppression.

The order metric varies between hcp and fcc packings based on local structure.

Abstract

The concept of hyperuniformity has been a useful tool in the study of large-scale density fluctuations in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric $\bar{\Lambda}$. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The "stealthy stacking" theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity which involves the suppression of scattering up to a wavevector $K$. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on $K$ for all Barlow packings. We compute $\bar{\Lambda}$ for the aforementioned three classes of Barlow packings and find that to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the $\bar{\Lambda}$ of all Barlow packings is primarily controlled by the local cluster geometry. These results indicate the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.