Persistent current in finite-width ring with surface disorder

We explore the surface disorder effect on the persistent current in a finite-width ring. In the strong disorder regime, the persistent current increases with surface disorder strength, while it decreases in the weak disorder regime. The result is at variance with the observation in bulk-disordered ring. Also, it is shown that the disorder-induced changes in the persistent current strongly depend on both the ring width and radius, which show up a singular quantum size effect.