Disordered stealthy hyperuniform (SHU) packings are an emerging class of
exotic amorphous two-phase materials endowed with novel physical properties.
Such packings of identical spheres have been created from SHU point patterns
via a modified collective-coordinate optimization scheme that includes a
soft-core repulsion, besides the standard `stealthy’ pair potential. Using the
distributions of minimum pair distances and nearest-neighbor distances, we find
that when the stealthiness parameter $\chi$ is lower than 0.5, the maximal
values of $\phi$, denoted by $\phi_{\max}$, decrease to zero on average as the
particle number $N$ increases if there are no soft-core repulsions. By
contrast, the inclusion of soft-core repulsions results in very large
$\phi_{\max}$ independent of $N$, reaching up to $\phi_{\max}=1.0, 0.86, 0.63$
in the zero-$\chi$ limit and decreasing to $\phi_{\max}=1.0, 0.67, 0.47$ at
$\chi=0.45$ for $d=1,2,3$, respectively. We obtain explicit formulas for
$\phi_{\max}$ as functions of $\chi$ and $N$ for a given $d$. For $d=2,3$, our
soft-core SHU packings for small $\chi$ become configurationally very close to
the jammed hard-particle packings created by fast compression algorithms, as
measured by the pair statistics. As $\chi$ increases beyond $0.20$, the
packings form fewer contacts and linear polymer-like chains. The resulting
structure factors $S(k)$ and pair correlation functions $g_2(r)$ reveal that
soft-core repulsions significantly alter the short- and intermediate-range
correlations in the SHU ground states. We also compute the spectral density
$\tilde{\chi}_{_V}(k)$, which can be used to estimate various physical
properties (e.g., electromagnetic properties, fluid permeability, and mean
survival time) of SHU two-phase dispersions. Our results offer a new route for
discovering novel disordered hyperuniform two-phase materials with
unprecedentedly high density.

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