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

We have solved the Bogoliubov-de Gennes equation for a clean, one-dimensional mesoscopic superconducting ring threaded by a magnetic flux PHI. We show that the superfluid velocity is driven directly by PHI while the relative motion of the pair of electrons is independent of PHI. Meanwhile, the fluxoid quantization is obtained straightforwardly. More importantly, we have also calculated the supercurrent numerically and 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/hBAR pi)PHI(s) and with the period PHI0 = hc/e for PHI(d) < PHI(s), which arises from mesoscopic effects.