Ultradense sphere packings derived from disordered stealthy hyperuniform ground states

Disordered stealthy hyperuniform (SHU) packings are an emerging class of exotic amorphous two-phase materials endowed with novel optical, transport, chemical, and mechanical properties. Such packings of identical spheres have been created from SHU ground-state point patterns via a modified collective-coordinate optimization scheme that includes a soft-core repulsion, in addition to the standard "stealthy" pair potential. To explore the maximal ranges of the packing fraction ϕ, we investigate the distributions of minimum pair distances as well as nearest-neighbor distances of ensembles of SHU point patterns without and with soft-core repulsions in the first three space dimensions as a function of the stealthiness parameter χ and number of particles N within a hypercubic simulation box under periodic boundary conditions. Within the disordered regime (χ < 0.5), we find that the maximal values of ϕ, denoted by ϕmax(χ, d), decrease to zero on average as N increases if there are no soft-core repulsions. By contrast, the inclusion of soft-core repulsions results in very large ϕmax(χ, d) independent of N, reaching up to ϕmax(χ, d) = 1.0, 0.86, 0.63 in the zero-χ limit and decreasing to ϕmax(χ, d) = 1.0, 0.67, 0.47 at χ = 0.45 for d = 1, 2, 3, respectively. We obtain explicit formulas for ϕmax(χ, d) as functions of χ and N for a given value of d in both cases with and without soft-core repulsions. In two and three dimensions, our soft-core SHU ground-state packings for small χ become configurationally very close to the corresponding jammed hard-particle packings created by fast compression algorithms, as measured by their pair statistics. As χ increases beyond 0.20, the particles in this family of disordered packings form fewer contacts and linear polymer-like chains as χ tends to 1/2. The resulting structure factors Sk and pair correlation functions g2r reveal that soft-core repulsions significantly alter the short- and intermediate-range correlations in the SHU ground states. We show that the degree of large-scale order of the soft-core SHU ground states increases as χ increases from 0 to 0.45 for d = 2, 3. We also compute the spectral density χ̃Vk, which can be used to estimate various physical properties, including electromagnetic properties, fluid permeability, and mean survival time of SHU two-phase dispersions. Our results offer a new route for the discovery of novel disordered hyperuniform two-phase materials with unprecedentedly high density.