Growth of structural lengthscale in Kob-Andersen binary mixtures: Role of medium range order

A central and extensively debated question in glass physics concerns whether a single, growing lengthscale fundamentally controls glassy dynamics, particularly in systems lacking obvious structural motifs such as the Kob-Andersen binary Lennard-Jones (KALJ) model. In this work, we investigate structural and dynamical lengthscales in supercooled liquids using the KALJ model in two compositions: 80:20 and 60:40. We compute the dynamical lengthscale from displacement-displacement correlation functions and observe a consistent growth as temperature decreases. To explore the static counterpart, we use a structural order parameter (SOP) based on the mean field caging potential. While this SOP is known to predict short time dynamics effectively, its bare correlation function reveals minimal spatial growth. Motivated by recent findings that long time dynamics reflect collective rearrangements, we perform spatial coarse-graining of the SOP and identify an optimal lengthscale Lmax that maximizes structure-dynamics correlation. We show that the structural correlation length derived from SOP coarse-grained over Lmax exhibits clear growth with cooling and closely tracks the dynamical lengthscale, especially for A particles in the 80:20 mixture and for both A and B particles in the 60:40 system. Our results reconcile the previously observed absence of static length growth in the KALJ model by highlighting the necessity of intermediate range structural descriptors. Furthermore, we find that the particles with larger structural length growth also correspond to species with latent crystallization tendencies, suggesting a possible link between structural order, dynamics, and incipient crystallization.