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

• An electron accumulates a phase on each transition, leading to the period halving.
• A maximal diamagnetic even-harmonic is analytically derived for the tricky experiment.
• A variation of 1–2 orders in PC is induced only by a quantum size effect.
• Higher harmonic is observed to rapidly decay, which is different from previous theory.

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.