Asymmetric Roughness of Elastic Interfaces at the Depinning Threshold

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.