Time-space height correlations of thermally fluctuating 2-d systems. Application to vicinal surfaces and analysis of STM images of Cu(115)

TL;DR

This paper develops a 2D Langevin model to analyze surface height fluctuations, revealing how correlations behave in different regimes and applying the theory to interpret STM images of Cu(115) surfaces.

Contribution

It introduces a Langevin formalism for 2D surface fluctuations, including anisotropic effects, and applies it to real STM data of vicinal Cu(115) surfaces.

Findings

Correlation functions diverge logarithmically in the rough phase

Time correlations exhibit power-law crossover behaviors

Application to STM images of Cu(115) demonstrates model relevance

Abstract

For thermally fluctuating 2-d systems, like solid surfaces, time and space correlation of the local surface height diverge logarithmically in the rough phase, whereas saturation is obtained below the roughening transition. A 2-d Langevin formalism, allowing to recover for long times and/or large distances these asymptotic behaviors, is presented. An overall expression for correlation functions that are related to atom hopping rates and surface stiffnesses is given. Considering anisotropic systems allows describing vicinal surfaces. At finite times, time correlations cross over to power laws alpha*t^(1/n) (n = 1, 2 or 4), within limited time ranges as it was observed for isolated fluctuating steps. Limits of time ranges are related to stiffnesses and diffusion anisotropies. Application to the analysis of STM images of Cu(115) below the roughening transition is given.