Velocity-force characteristics of an interface driven through a periodic potential

TL;DR

This paper investigates the creep dynamics of a 2D interface in a periodic potential, revealing different transport behaviors depending on temperature relative to the roughening transition, with detailed velocity-force characteristics.

Contribution

The study applies dynamical renormalization group methods to characterize the nonlinear velocity-force behavior across the roughening transition, highlighting new scaling laws and crossover phenomena.

Findings

Above T_c, velocity-force is Ohmic with a discontinuity in mobility.

Below T_c, transport is nonlinear with power-law and exponential behaviors.

Near T_c, velocity scales as F^σ with σ-1 proportional to (T_c - T).

Abstract

We study the creep dynamics of a two-dimensional interface driven through a periodic potential using dynamical renormalization group methods. We find that the nature of weak-drive transport depends qualitatively on whether the temperature $T$ is above or below the equilibrium roughening transition temperature $T_c$. Above $T_c$, the velocity-force characteristics is Ohmic, with linear mobility exhibiting a jump discontinuity across the transition. For $T \le T_c$, the transport is highly nonlinear, exhibiting an interesting crossover in temperature and weak external force $F$. For intermediate drive, $F>F_*$, we find near $T_c^{-}$ a power-law velocity-force characteristics $v(F)\sim F^\sigma$, with $\sigma-1\propto \tilde{t}$, and well-below $T_c$, $v(F)\sim e^{-(F_*/F)^{2\tilde{t}}}$, with $\tilde{t}=(1-T/T_c)$. In the limit of vanishing drive ($F\ll F_*$) the velocity-force characteristics crosses over to $v(F)\sim e^{-(F_0/F)}$, and is controlled by soliton nucleation.