The ballistic transport through a one-dimensional two-lead ring at zero magnetic field is studied. We have focused on the case in which the potential in the ring does not define closed cavities or dots. Even in the absence of well-defined quasibound states, we find Fano profiles in the transmission probability. Those Fano profiles appear at energies corresponding to the standing-wave states in the ring, but their occurrence depends sensitively on the commensurability of the system parameters. When the system parameters are commensurate, the widths of the profiles at some energies are infinitesimally small. These findings suggest that the conventional understanding of the Fano profiles as a result of the interference effect of the transition through resonant states and nonresonant continuum of states, might not account for all the Fano profiles seen in the transport measurements. Moreover, the sensitivity and tunability of the resonance with respect to the system parameters may be usable in the fabrication of electrical nanodevices.

• Received 15 March 2005

DOI:https://doi.org/10.1103/PhysRevB.72.165307