Escape-Induced Temporally Correlated Noise Driven Universality Crossover

TL;DR

The paper addresses the experimental realization of a universality crossover between conserved KPZ ($cKPZ$) and temporally correlated noise KPZ ($TCN$-$KPZ$) in nonequilibrium interface growth. Using atomically resolved STM, scaling analyses, AES, structure-factor measurements, and MD simulations of Sn growth on MBST (30% Sb-doped MnBi2Te4), the authors identify a crossover at deposition time $t_c \approx 5.4$ min from early $cKPZ$-like scaling with $\beta_1 = 0.21 \pm 0.03$, $\alpha_{loc1} = 0.71 \pm 0.03$, $1/z_1 = 0.31 \pm 0.07$ to late-time $TCN$-$KPZ$ scaling with $\beta_2 = 0.66 \pm 0.13$, $\alpha_{loc2} = 0.87 \pm 0.07$, $1/z_2 = 0.74 \pm 0.05$, and a noise-correlation exponent $\theta \approx 0.45$. MD simulations reveal the microscopic origin: adatom escape generates temporally correlated noise with short-time power-law and long-time exponential decay, consistent with the measured $\theta$ and with AES showing a Sn/Te intensity-slope drop from $\sim 0.7$ to $\sim 0.23$ at the crossover. The work establishes a direct link between atomistic kinetics and emergent universality in $(2+1)$D, offering a framework to control non-equilibrium morphologies through noise correlations and validating theoretical predictions that temporal correlations can drive universality-class changes.

Abstract

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 MnBi$_2$Te$_4$, revealing a sharp dynamical crossover between two fundamentally different regimes. Early stage growth follows conserved KPZ scaling, forming two-dimensional islands and stanene layers. Beyond a critical deposition time, temporally correlated noise dominates, driving the nucleation of $α$ -Sn clusters, their evolution into faceted grains, and coexistence with faceted $β$-Sn. Molecular dynamics simulation and Auger electron spectroscopy show adatom escape as the microscopic origin of temporally correlated noise, providing a microscopic mechanism for the universality crossover. These findings establish, for the first time, that temporal noise correlations can fundamentally alter the scaling class of a growing interface, linking atomistic kinetics to emergent universal behavior.

Figures (17)

• Figure 1: Universality crossover in interface growth. (A-D) STM topographies showing the sequence of growth morphologies with increasing deposition time: (A) early-stage alloyed and few-layer stanene islands, (B) abrupt onset of clustering at $t = 5.4$ min, (C) coalesced mound-like structures, and (D) faceted grains at later stages.(E–H) Atomically resolved STM images revealing (E) buckled stanene, (F) single-phase $\alpha$-Sn grain with (111) facets, and (G–H) coexistence of $\alpha$-Sn grain with (100) and $\beta$-Sn grain with (111) facets at late times. (I–L) height profiles along the marked arrows in (A-D) and 3D view of topographies (M–O) emphasize the morphological transition from 2D islands to 3D faceted grains. (P) Root-mean-square surface roughness, $\omega(t)$, extracted from STM height maps, exhibits two distinct power-law regimes (transition marked by arrow).
• Figure 2: Conserved KPZ and temporally correlated noise KPZ classes and their scaling(A, B) Two-dimensional height–height correlation functions $H(\mathbf{r},t)$ from early (island) and late (mound/faceted) regimes. (C, D) Power-law fits of angularly averaged $\langle H(r,t)\rangle_\theta$ yield local roughness exponents $\alpha_{\mathrm{loc1}}$ and $\alpha_{\mathrm{loc2}}$. (E) Temporal evolution of $\alpha_{\mathrm{loc}}$ exhibits a sharp crossover at $t = 5.4$ min. (F) 2D autocorrelation function and definition of lateral correlation length. (G) Lateral correlation length $\xi(t) \sim t^{1/z}$ yields $1/z_{1}$ and $1/z_{2}$. (H, I) Rescaled $H(\mathbf{r},t)$ collapses onto universal curves for each regime. (J) AES intensity ratio Sn/Te versus growth time shows a reduction in Sn sticking probability from $t = 5.4$ min.
• Figure 3: Spectral scaling and emergence of faceted growth driven by temporally correlated noise.(A, B) Two-dimensional structure factors $S(\mathbf{k},t)$ for island-dominated ($t = 3.0$ min) and mound/faceted ($t = 150$ min) regimes. (C, D) Angularly averaged $\langle S(k,t)\rangle_{\theta}$ exhibit power-law scaling with spectral roughness exponents $\alpha_{s1}$ and $\alpha_{s2}$. (E) Temporal evolution of $\alpha_{s}$. (F, G) Data collapse of rescaled $S(k,t)$.
• Figure 4: Escape-induced noise and microscopic origin of temporally correlated noise.(A–C) Simulated Sn surface morphologies showing the transition from island nucleation to mounded and faceted growth. (D–F) 3D renderings corresponding to (A–C) and (G–I) height profiles along the arrows marked in (A-C). (J) Temporal evolution of the rms roughness $\omega(t)$ exhibits two distinct power-law regimes. (K–M) Local roughness and dynamic exponents $\alpha_{\mathrm{loc}}$ and $z$ show a crossover at $t = 5.4$ min. (N) Particle-tracking analysis during deposition showing that up to $t = 5.4$ min all deposited atoms are incorporated into growth (top), whereas at later times a significant fraction escape the surface (bottom), generating temporally correlated noise. (O) Temporal correlations of the escape-induced noise exhibit a hybrid form - power-law at short lags and exponential decay at longer times. (P) The average over the fitted correlation exponents $\theta_\mathrm{avg} = 0.48 \pm 0.01$ agrees with theory ( $\theta \approx 0.45$ ), confirming that escape events generate temporally correlated noise.
• Figure S1: (A–N) Wide-area ($500~\mathrm{nm} \times 500~\mathrm{nm}$) STM topographies at successive growth times showing the morphological evolution of Sn films from initial island nucleation to clustered mounds and faceted grains.