Diamagnetic current of period halving in mesoscopic ring by quantum size effect

A consistently diamagnetic persistent current (PC) of period halving (Φ0/2-current) observed in mesoscopic rings is in apparent contradiction with the theoretical prediction of barely exclusively paramagnetism. By developing a super-cell method, we analytically and numerically study the magnetic response mechanics of non-interacting mesoscopic rings in both the absence and presence of random disorder. A maximal paramagnetic and/or diamagnetic PC is obtained in primary Φ0- and/or Φ0/2-period, exhibiting a remarkable quantum size effect. It is shown that for lower free energy, an electron circling the ring accumulates an additional phase on each inter-channel transition induced by magnetic flux, leading to the period halving and the paramagnetic–diamagnetic transition. Our results can well mediate the disputes between the experiments and theory.