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We show that the direction of coherent electron transport across a cyclicsystem of quantum dots or a cyclic molecule can be modulated by an externalmagnetic field if the cycle has an odd number of hopping sites, but thetransport becomes completely symmetric if the number is even. These contrastingbehaviors, which remain in the case of interacting electrons, are a consequenceof the absence or presence of alternance symmetry in the system. These findingsare relevant for the design of nanocircuits based on coupled quantum dots ormolecular junctions.

The Role of Alternance Symmetry in Magnetoconductance