Kinetic roughening of a terrace ledge

We study the motion of an isolated terrace ledge on a crystalline surface within the framework of the terrace-ledge-kink model. We argue that for length scales larger than the diffusion length the step roughness is governed by the Kardar-Parisi-Zhang (KPZ) equation that predicts a broadening as ${\mathit{t}}^{1/3}$. For smaller length scales a variety of possibilities are explored. Their occurrence depends sensitively on the rates for the adsorption and desorption processes both on the terraces and at the ledge. The ledge could be unstable, developing a fractal, dendritic type of structure. If the ledge is stable, we obtain a crossover from a ${\mathit{t}}^{1/6}$ (conserved dynamics, model B) to a ${\mathit{t}}^{1/4}$ (nonconserved dynamics, model A) and a ${\mathit{t}}^{1/3}$ (KPZ) broadening.