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 $S(q)\propto q^{\alpha }$, where $\alpha >0$. It is well known that jammed configurations exhibit hyperuniformity over a wide range of wavenumbers windows, down to $q^{\ast }\sigma \approx 0.2$, where $\sigma$ is the particle diameter. In two dimensions, we find that the exponent $\alpha$ is approximately $0.6\text{–}0.7$. This contrasts with the reported value of $\alpha =1$ for three-dimensional systems. We employ an advanced method recently introduced by Rissone $\mathit{\text{et}}\mathit{\text{al.}}$ \href{https://link.aps.org/doi/10.1103/PhysRevLett.127.038001}{[Phys. Rev. Lett. {\bf 127}, 038001 (2021)]}, originally developed for monodisperse and three-dimensional systems, to determine $\alpha$ 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.