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

TL;DR

This paper theoretically investigates electron transport in an Aharonov-Bohm ring with an embedded quantum dot, analyzing Fano and Kondo resonances, and explores how lead coupling affects conductance and phase measurements.

Contribution

It extends existing models to include multiple conduction channels and derives analytical relations for phase shift measurements in a multi-terminal quantum dot interferometer.

Findings

Asymmetric Fano resonance observed for single-channel leads.

Transition from Fano-Kondo resonance to Kondo plateau with lead coupling.

Analytical expression relating measured and intrinsic phase shifts.

Abstract

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.