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 Ityp is enhanced 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.