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We study transport of non-interacting electrons through two quantum dotmolecules embedded in an Aharonov-Bohm interferometer. The system inequilibrium exhibits bound states in the continuum (BIC) and total suppressionof transmission. It also shows a magnetic flux-dependent effective levelattraction and lines of perfect transmission when the intramolecular couplingis weak. Out of equilibrium, the current displays two kind of negativedifferential conductance (NDC) regions, which have different origins. One isgenerated by the usual mechanism of the NDC arising in a double quantum dotsystem. The other is induced by the magnetic flux, and it occurs at smallvoltages and for a well definite range of the intramolecular couplings. Weexplain this effect in terms of the level attraction displayed by the system.

Effective level attraction and magnetic flux-induced negative  differential conductance in two double quantum dot molecules embedded in an  Aharonov-Bohm ring