Persistent currents in multichannel interacting systems

Persistent currents in disordered multichannel mesoscopic rings threaded by a magnetic flux are calculated using exact diagonalizations and self-consistent Hartree-Fock treatments of two-dimensional tori and cylinders of spinless interacting fermions. The validity of the Hartree-Fock approximation is controlled by a direct comparison with the exact results on small 4×4 clusters. The existence of a crossover value for the disorder parameter ${\mathit{W}}_{\mathit{c}}$ (depending on the electronic density and the system size) separating two different regimes is established. Decomposing the current I(φ) in terms of its fundamental harmonics, we find that, while the first harmonic is always enhanced by the interaction, the second harmonic is enhanced for W<${\mathit{W}}_{\mathit{c}}$ and strongly suppressed otherwise. This effect is stronger as we increase the disorder.