Magnetic response of mesoscopic rings: a quantum size effect

We analytically study the magnetic response of persistent current (PC) in normally non-interacting mesoscopic rings of bimodal potential with nearest neighboring interactions (t) and alternating site energies. It is shown that a ring of perimeter (N) and width (M) generally shows weak diamagnetic, breaking the even-odd rule of electron filling. Especially, a maximal paramagnetic current in primary F0/2 period is predicted at N=(2p+1)(M+1) with odd M and integer p, while a maximal diamagnetic F0/2- current obtained at N=(2p+1)(M+1)+/-1 with even M. The current amplitudes depend strongly on both N and M, varied by at least 1~2 orders of magnitude, exhibiting a remarkable quantum size effect. A current limit of paramagnetic harmonics is expected at N=2p(M+1), independent of the sizes of N and M, in favor of experiment observation. A new mechanism of magnetic response is proposed that an electron circling the ring shall pass successively each channel within one flux quantum, accumulating an additional phase on each inter-channel transition, which leads to the paramagnetic-diamagnetic transition and period halving. The results unify and unveil the contradictions in PC between theory and experiments, validating quantum mechanics at mesoscopic scale.