A New Interpretation of Flux Quantization

We study the effect of Aharonov-Bohm flux on the superconducting state in metallic cylinders. Although Byers and Yang attributed flux quantization to the flux-dependent minimum of kinetic energies of the Cooper pairs, it is shown that kinetic energies do not produce any discernible oscillations in the free energy of the superconducting state (relative to that of normal state) as a function of the flux. This result is indeed anticipated by the observation of persistent current in normal metal rings at low temperature. Instead, we have found that pairing interaction depends on the flux, leading to flux quantization. When the flux $(\Phi$) is given by $\Phi=n\times hc/2e$ (with integer n), the pairing interaction and the free energy become unchanged (even n) or almost unchanged (odd n), due to degenerate-state pairing resulting from the energy level crossing. As a result, flux quantization and Little-Parks oscillations follow.