  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. Stefanski, Phys. Rev. Lett. 86, 5128 (2001); W. Hofstetter, J.
Konig, and H. Schoeller, ibid. 87, 156803 (2001)] to consider multiple
conduction channels in two external leads, L and R. We introduce a parameter
p_{\alpha} (|p_{\alpha}| \le 1) to characterize a connection between the two
arms of the ring through lead \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 multi-terminal 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.
