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When a circular ring suffers a special topological transformation, it becomesa two-layer ring. Due to the special topology of the two-layer ring, orbitalangular momenta are allowed to be a half-integer, this would affect thetraditional Aharonov-Bohm oscillation (ABO). In this paper the fractional ABOof the ground state energy, persistent current, and dipole transition of atwo-layer ring with two electrons has been studied. Collective and internalcoordinates $\theta_{C}$ and $\phi $ have been introduced. Based on them a verysimple formula for the current has been obtained, the symmetry constraintimposed on the dipole transition has been clarified, a strict relation betweenthe photon energies of the dipole radiation and the persistent current of theground state has been found. Comparing with the one-layer rings, the period ofthe fractional ABO of the two-layer rings becomes much shorter.

Fractional Aharonov-Bohm oscillation of a two-layer ring with two electrons