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.

中文翻译：

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带有嵌入式量子点的Aharonov-Bohm环中的Fano-Kondo共振与Kondo高原

从理论上讲，我们研究了通过带有嵌入式量子点（QD）的Aharonov-Bohm环的传输，即所谓的QD干涉仪，以解决有关库仑峰形状和通过QD测量传输相移的两个有争议的问题。我们扩展了以前的模型[BR Bulka和P.Stefański，Phys。牧师 86，5128（2001）; W. Hofstetter，J。König和H. Schoeller，同上。 87，156803（2001）]，以考虑在两条外部引线多个传导通道，$\mathrm{大号}$ 和 $\mathrm{[R}$。我们介绍一个参数$p_{\alpha }$ （$|p_{\alpha }|\le \mathrm{1个}$）表征通过引线的环的两个臂之间的连接 $\alpha$ （$=\mathrm{大号}$， $\mathrm{[R}$），这是耦合到两个臂的传导模式之间的重叠积分。首先，我们研究在没有电子-电子相互作用的情况下，电导峰的形状与量子点中能级的关系$ü$。我们显示出不对称的Fano共振$|p_{\mathrm{大号}，\mathrm{[R}}|=\mathrm{1个}$ 如果导线中有单个传导通道，并且几乎对称的Breit-Wigner共振 $|p_{\mathrm{大号}，\mathrm{[R}}|<0.5$在多个渠道的情况下。其次，Bethe ansatz精确解在存在以下情况的情况下考虑了近藤效应$ü$。我们精确评估温度下的电导$Ť=0$ 并显示了从非对称Fano-Kondo共振到Kondo高原的交叉变化 $p_{\mathrm{大号}，\mathrm{[R}}$。我们的模型也适用于QD干涉仪的多端子几何形状。我们通过“双缝实验”讨论了在三端子几何结构中通过QD的传输相移的测量。我们得出了一个测量值和相移固有值之间关系的解析表达式。