Hyperuniform disordered solids with crystal-like stability

Hyperuniform disordered solids, characterised by unusually suppressed density fluctuations at low wavenumbers (q), are of great interest due to their potentially distinct properties as a unique glass state. From the jamming perspective, there is ongoing debate about the relationship between hyperuniformity and the jamming transition, as well as whether hyperuniformity persists above the jamming point. Here, we successfully generate over-jammed disordered solids exhibiting the strongest class of hyperuniformity, characterised by a power-law density spectrum (q^α with α = 4). By decompressing both hyperuniform and conventional over-jammed packings to their respective marginally jammed states, we identify protocol-independent exponents: α ≈ 0.25 for density hyperuniformity and α ≈ 2 for contact-number hyperuniformity, both associated with the jamming transition. Although both marginally jammed and conventional over-jammed packings exhibit marginal stability, we demonstrate that hyperuniform over-jammed packings possess exceptional stability across vibrational, kinetic, thermodynamic, and mechanical properties-similar to crystals. These findings suggest that hyperuniform over-jammed packings offer crucial insights into the ideal disordered solid state and stand out as promising candidates for disordered metamaterials, uniquely combining hyperuniformity with ultrastability.