Hyperuniformity near jamming transition over a wide range of bidispersity

We numerically investigate hyperuniformity in two-dimensional frictionless jammed packings of bidisperse systems. Hyperuniformity is characterized by the suppression of density fluctuations at large length scales, and the structure factor asymptotically vanishes in the small-wavenumber limit as S(q) ∝ q^α, where $α> 0$. It is well known that jammed configurations exhibit hyperuniformity over a wide range of wavenumbers windows, down to q^σ≈ 0.2, where $σ$ is the particle diameter. In two dimensions, we find that the exponent $α$ is approximately 0.6--0.7. This contrasts with the reported value of $α= 1$ for three-dimensional systems. We employ an advanced method recently introduced by Rissone et al. {https://link.aps.org/doi/10.1103/PhysRevLett.127.038001}{[Phys. Rev. Lett. { 127}, 038001 (2021)]}, originally developed for monodisperse and three-dimensional systems, to determine $α$ with high precision. This exponent is found to be unchanged for all size ratios between small and large particles, except in the monodisperse case, where the system crystallizes.