Distinctive Fluctuations of Facet Edges

Spurred by theoretical predictions of distinctive static scaling of the step bounding a facet,\footnote{P.L.~Ferrari et al., Phys.~Rev.~E {\bf 69} (2004) 035102(R) } we extend the results to dynamic scaling, also rederiving the static results heuristically\footnote{A.~Pimpinelli et al., Surf.~Sci.~Lett.~{\bf 598} (2005) L355 } and we measure this behavior using STM line scans.\footnote{M. Degawa et al., Phys.~Rev.~Lett.~{\bf 97}, 080601 (2006)} The correlation functions go as $t^{0.15 \pm 0.03}$ decidedly different from the $t^{0.26 \pm 0.02}$ behavior for fluctuations of isolated steps. From the exponents, we categorize the universality, confirming the prediction that the non-linear term of the KPZ equation, long known to play a central role in non-equilibrium phenomena, can also arise from the curvature or potential-asymmetry contribution to the step free energy. We study a simple model with Monte Carlo simulations to illustrate the novel scaling of fluctuations in an asymmetric potential.