Asymmetric Roughness of Elastic Interfaces at the Depinning Threshold

TL;DR

This paper reveals that at the depinning threshold, elastic interfaces exhibit asymmetric roughness due to symmetry breaking, characterized by skewed height distributions and a spectrum of local scaling exponents.

Contribution

It demonstrates the existence of asymmetric roughness in elastic interfaces at depinning, quantified by local scaling exponents and skewed height distributions, due to symmetry breaking.

Findings

Asymmetric roughness characterized by skewed height distributions.

Local scaling exponents depend linearly on height differences.

Symmetry breaking causes the observed asymmetry at depinning.

Abstract

Roughness of driven elastic interfaces in random media is typically understood to be characterized by a single roughness exponent $\zeta$. We show that at the depinning threshold, due to symmetry breaking caused by the direction of the driving force, elastic interfaces with local, long-range and mean-field elasticity exhibit asymmetric roughness. It is manifested as a skewed distribution of the local interface heights, and can be quantified by using detrended fluctuation analysis to compute a spectrum of local, segment-level scaling exponents. The asymmetry is observed as approximately linear dependence of the local scaling exponents on the difference of the segment height from the mean interface height.