Existence of Nonequilibrium Glasses in the Degenerate Stealthy Hyperuniform Ground-State Manifold

Stealthy interactions are an emerging class of nontrivial, bounded long-ranged oscillatory pair potentials with classical ground states that can be disordered, hyperuniform, and infinitely degenerate. Their hybrid crystal-liquid nature endows them with novel physical properties with advantages over their crystalline counterparts. Here, we show the existence of nonequilibrium hard-sphere glasses within this unusual ground-state manifold as the stealthiness parameter $\chi$ tends to zero that are remarkably configurationally extremely close to hyperuniform 3D maximally random jammed (MRJ) sphere packings. The latter are prototypical glasses since they are maximally disordered, perfectly rigid, and perfectly nonergodic. Our optimization procedure, which leverages the maximum cardinality of the infinite ground-state set, not only guarantees that our packings are hyperuniform with the same structure-factor scaling exponent as the MRJ state, but they share other salient structural attributes, including a packing fraction of $0.638$, a mean contact number per particle of 6, gap exponent of $0.44(1)$, and pair correlation functions $g_2(r)$ and structures factors $S(k)$ that are virtually identical to one another for all $r$ and $k$, respectively. Moreover, we demonstrate that stealthy hyperuniform packings can be created within the disordered regime ($0 < \chi <1/2$) with heretofore unattained maximal packing fractions. As $\chi$ increases from zero, they always form interparticle contacts, albeit with sparser contact networks as $\chi$ increases from zero, resulting in linear polymer-like chains of contacting particles with increasingly shorter chain lengths. The capacity to generate ultradense stealthy hyperuniform packings for all $\chi$ opens up new materials applications in optics and acoustics.