The Fano regime of one-dot Aharonov-Bohm interferometers

We use the Landauer-B\"{u}ttiker formalism to study the mesoscopic Fano effect in Aharonov-Bohm rings with an embedded two-dimensional noninteracting dot. The magnetic field dependence of the dot levels leads to a global shift of the Fano lines which becomes important for small ring/dot area ratios. As the magnetic field is varied the Fano dips move periodically from one side of the peak to the other, as reported by Kobayashi {\it et al.} [Phys. Rev. Lett. {\bf 88}, 256806 (2002)]. We show that this effect appears due to a specific magnetic control of the difference between the phase of the single nonresonant path via the free arm of the ring and the global phase of all trajectories involving resonant tunnelings through the dot.