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By considering a nanoscale Aharonov-Bohm (AB) interferometer containing aparrallel-coupled double dot coupled to the source and drain electrodes, weinvestigate the AB phase oscillations of transport current via the bonding andantibonding state channels. The results we obtained justify the experimentalanalysis given in [Phys. Rev. Lett. \textbf{106}, 076801 (2011)] that bondingstate currents in different energy configurations are almost the same. On theother hand, we extend the analysis to the transient transport currentcomponents flowing through different channels, to explore the effect of theparity of bonding and antibonding states on the AB phase dependence of thecorresponding current components in the transient regime. The relations of theAB phase dependence between the quantum states and the associated currentcomponents are analyzed in details, which provides useful information for thereconstruction of quantum states through the measurement of the transportcurrent in such systems. With the coherent properties in the quantum dot statesas well as in the transport currents, we also provide a way to manipulate thebonding and antibonding states by the AB magnetic flux.

Quantum coherence of the molecular states and their corresponding currents in nanoscale Aharonov-Bohm interferometers