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. Stefański, Phys. Rev. Lett. 86, 5128 (2001); W. Hofstetter, J. König, 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 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.

• Received 10 September 2020
• Revised 4 November 2020
• Accepted 5 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.245402

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