Persistent currents in mesoscopic cavities with surface roughness

We consider a bidimensional discrete annular cavity with surface roughness (SR) threaded by a magnetic flux. In the ballistic regime and at half filling, localized border-states show up. These border states contribute coherentely to the persistent current and the magnitude of the typical current $I_{typ}$ is enhaced with respect to their value in the absence of confinement. This result is robust with respect to changes in the relevant lengths of the sample.