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

We study creep dynamics of a two-dimensional interface driven through a periodic potential using dynamic 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 Tc. Above Tc, the velocity-force characteristics are Ohmic, with linear mobility exhibiting a jump discontinuity across the transition. For T<~Tc, the transport is highly nonlinear, exhibiting an interesting crossover in temperature and weak external force F. For intermediate drive, F>F*, we find near Tc^- a power-law velocity-force characteristics v(F)~F^σ, with σ-1∝ ̃ \~t, and well below Tc, v(F)~e^-(F*/F)^2 ̃ \~t, with ̃ \~t=(1-T/Tc). In the limit of vanishing drive (FF*), the velocity-force characteristics cross over to v(F)~e^-(F₀/F), and are controlled by soliton nucleation.