Escape-induced temporally correlated noise driven crossover in growth kinetics and universality class

Universal behavior in far-from-equilibrium systems is driven by interactions between transport processes and noise structure. The Kardar-Parisi-Zhang (KPZ) framework predicts that extensions incorporating conserved currents or temporally correlated noise give rise to distinct growth morphologies and universality classes, yet direct experimental realization has remained elusive. Here, we report atomically resolved Sn thin-film growth on Sb-doped MnBi₂Te₄, revealing a sharp dynamical crossover between two fundamentally different regimes. Early-stage growth follows Villain-Lai-Das Sarma (VLDS) scaling, forming two-dimensional islands and stanene layers. Beyond a critical deposition time, temporally correlated noise becomes the dominant factor, driving the nucleation of α-Sn clusters, their development into faceted grains, and the coexistence of faceted β-Sn. Molecular dynamics simulations and Auger electron spectroscopy reveal that adatom escape serves as the microscopic origin of this temporally correlated noise, offering a mechanism for the observed universality crossover. These findings establish that temporal noise correlations can fundamentally alter the universality class of a growing interface, linking atomistic kinetics to emergent universal behavior.