Depinning of an anisotropic interface in random media: The tilt effect

Abstract

We study the tilt dependence of the pinning-depinning transition for an interface described by the anisotropic quenched Kardar-Parisi-Zhang equation in 2+1 dimensions, where the two signs of the nonlinear terms are different from each other. When the substrate is tilted by m along the positive sign direction, the critical force F_c(m) depends on m as F_c(m)-F_c(0) \sim -|m|^{1.9(1)}. The interface velocity v near the critical force follows the scaling form v \sim |f|^θΨ_{\pm}(m^2 /|f|^{θ+ϕ}) with θ= 0.9(1) and ϕ= 0.2(1), where f \equiv F-F_c(0) and F is the driving force.