Recovery of the persistent current induced by the electron-electron interaction in mesoscopic metallic rings

Persistent currents in mesoscopic metallic rings induced by static magnetic fields are investigated by means of a Hamiltonian which incorporates diagonal disorder and the electron-electron interaction through a Hubbard term ($U$). Correlations are included up to second order perturbation theory which is shown to work accurately for $U$ of the order of the hopping integral. If disorder is not very strong, interactions increase the current up to near its value for a clean metal. Averaging over ring lengths eliminates the first Fourier component of the current and reduces its value, which remains low after interactions are included.