Fano-Kondo resonance versus Kondo plateau in an Aharonov-Bohm ring with an embedded quantum dot

We theoretically examine the transport through an Aharonov-Bohm ring with an embedded quantum dot (QD), the so-called QD interferometer, to address two controversial issues regarding the shape of the Coulomb peaks and measurement of the transmission phase shift through a QD. We extend a previous model [B. R. Bulka and P. Stefa\ifmmode \acute{n}\else \'{n}\fi{}ski, Phys. Rev. Lett. 86, 5128 (2001); W. Hofstetter, J. K\"onig, and H. Schoeller, ibid. 87, 156803 (2001)] to consider multiple conduction channels in two external leads, $L$ and $R$. We introduce a parameter ${p}_{\ensuremath{\alpha}}$ ($|{p}_{\ensuremath{\alpha}}|\ensuremath{\le}1$) to characterize a connection between the two arms of the ring through lead $\ensuremath{\alpha}$ ($=L$, $R$), which is the overlap integral between the conduction modes coupled to the two arms. First, we study the shape of a conductance peak as a function of energy level in the QD, in the absence of electron-electron interaction $U$. We show an asymmetric Fano resonance for $|{p}_L,R|=1$ in the case of single conduction channel in the leads and an almost symmetric Breit-Wigner resonance for $|{p}_L,R|<0.5$ in the case of multiple channels. Second, the Kondo effect is taken into account by the Bethe ansatz exact solution in the presence of $U$. We precisely evaluate the conductance at temperature $T=0$ and show a crossover from an asymmetric Fano-Kondo resonance to the Kondo plateau with changing ${p}_L,R$. Our model is also applicable to the multiterminal geometry of the QD interferometer. We discuss the measurement of the transmission phase shift through the QD in a three-terminal geometry by a ``double-slit experiment.'' We derive an analytical expression for the relation between the measured value and the intrinsic value of the phase shift.