Discontinuity in the phase evolution of electron transport in a quantum channel with attached quantum dots

In a recent phase experiment by Schuster et al. [Nature 385, 417 (1997)], an abrupt phase drop of π was observed when the electron transmission through a quantum dot embedded in a quantum channel vanished. We show, both analytically and numerically, that this phase discontinuity is an intrinsic property of single electron transport: It arises from interference, known as Fano resonance, between two different transmission channels belonging to a localized state in the dot and a continuous state of the quantum channel. This phase behavior should also be seen in the same type of scattering resonances in other physical systems.