Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one-dimension

We report local roughness exponents, $\alpha_{\text{loc}}$, for three interface growth models in one dimension which are believed to belong the non-linear molecular-beam-epitaxy (nMBE) universality class represented by the Villain-Lais-Das Sarma (VLDS) stochastic equation. We applied an optimum detrended fluctuation analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801 (2017)] and compared the outcomes with standard detrending methods. We observe in all investigated models that ODFA outperforms the standard methods providing exponents in the narrow interval $\alpha_{\text{loc}}\in[0.96,0.98]$ consistent with renormalization group predictions for the VLDS equation. In particular, these exponent values are calculated for the Clarke-Vvdensky and Das Sarma-Tamborenea models characterized by very strong corrections to the scaling, for which large deviations of these values had been reported. Our results strongly support the absence of anomalous scaling in the nMBE universality class and the existence of corrections in the form $\alpha_{\text{loc}}=1-\epsilon$ of the one-loop renormalization group analysis of the VLDS equation

Optimal detrended fluctuation analysis as a tool for the determination of the roughness exponent of the mounded surfaces

We present an optimal detrended fluctuation analysis (DFA) and applied it to evaluate the local roughness exponent in non-equilibrium surface growth models with mounded morphology. Our method consists in analyzing the height fluctuations computing the shortest distance of each point of the profile to a detrending curved that fits the surface within the investigated interval. We compare the optimal DFA (ODFA) with both the standard DFA and nondetrended analysis. We validate the ODFA method considering a one-dimensional model in the Kardar-Parisi-Zhang universality class starting from a mounded initial condition. We applied the methods to the Clarke-Vvdensky (CV) model in 2 + 1 dimensions with thermally activated surface diffusion and absence of step barriers. It is expected that this model belongs to the nonlinear Molecular Beam Epitaxy (nMBE) universality class. However, an explicit observation of the roughness exponent in agreement with the nMBE class was still missing. The effective roughness exponent obtained with ODFA agrees with the value expected for nMBE class whereas using the other methods it does not. We also characterized the transient anomalous scaling of the CV model and obtained that the corresponding exponent is in agreement with the value reported for other nMBE models with weaker corrections to the scaling