SUPERCURRENT DETERMINED FROM THE AHARONOV-BOHM EFFECT IN MESOSCOPIC SUPERCONDUCTING RINGS

We have solved the Bogoliubov-de Gennes equation for a clean, one-dime nsional mesoscopic superconducting ring threaded by a magnetic flux PH I. We show that the superfluid velocity is driven directly by PHI whil e the relative motion of the pair of electrons is independent of PHI. Meanwhile, the fluxoid quantization is obtained straightforwardly. Mor e importantly, we have also calculated the supercurrent numerically an d self-consistently and find it is periodic in PHI with the period PHI (s) = hc/2e for PHI(s) less-than-or-equal-to PHI(d) = (mupsilon(d)L/hB AR pi)PHI(s) and with the period PHI0 = hc/e for PHI(d) < PHI(s), whic h arises from mesoscopic effects.