Displacement profile of charge density waves and domain walls at critical depinning

The influence of a strong surface potential on the critical depinning of an elastic system driven in a random medium is considered. If the surface potential prevents depinning completely the curvature C of the displacement profile exhibits at zero temperature a pronounced rhombic hysteresis curve of width 2f(c) with the bulk depinning threshold f(c). The hysteresis disappears at nonzero temperatures if the driving force is changed adiabatically. If the surface depins by the applied force or thermal creep, C is reduced with increasing velocity. The results apply, e.g., to driven magnetic domain walls, fluxline lattices, and charge-density waves.