Observation of the Fano-Kondo Antiresonance in a Quantum Wire with a Side-Coupled Quantum Dot

We have observed the Fano-Kondo antiresonance in a quantum wire with a side-coupled quantum dot. In a weak coupling regime, dips due to the Fano effect appeared. As the coupling strength increased, conductance in the regions between the dips decreased alternately. From the temperature dependence and the response to the magnetic field, we conclude that the conductance reduction is due to the Fano-Kondo antiresonance. At a Kondo valley with the Fano parameter $q\approx 0$, the phase shift is locked to $\pi /2$ against the gate voltage when the system is close to the unitary limit in agreement with theoretical predictions by Gerland et al. [Phys. Rev. Lett. 84, 3710 (2000)].

Figure 1

(a) Schematic diagram of a stub resonator. (b) Scanning electron micrograph of the device. The white areas are metallic gates made of $\mathrm{Au}/\mathrm{Ti}$. The dot and the wire are indicated by dotted lines. Conduction between Source1 and Drain is used to measure the direct transport through the dot, while that between Source and Drain gives the main results of this Letter. (c) Conductance of the wire measured at several coupling strengths tuned by $V_{\mathrm{m}}$. The base temperature is 30 mK. The step in $V_{\mathrm{m}}$ is 6 mV, and the data are offset by $0.3e^2/h$ for clarity. The broken line shows the data at $V_{\mathrm{m}}=-0.846\mathrm{V}$ shown in Fig. 2.

Figure 2

Upper: Zero-bias conductance of the quantum wire at three different temperatures as a function of the gate voltage $V_{\mathrm{g}}$ at $V_{\mathrm{m}}=-0.846\mathrm{V}$. The bars indicate the positions of Coulomb dips and A–D indicate the Coulomb valleys where the Kondo effect emerges. Lower: Color scale plot of the conductance on the $V_{\mathrm{g}}\mathrm{\text{−}}{V}_{\mathrm{sd}}$ plane at 30 mK. Both the upper and the lower panels use the same $V_{\mathrm{g}}$ axis.

Figure 3

(a) Upper: Conductance at temperatures from 750 to 50 mK with the step of 50 mK at $V_{\mathrm{m}}=-0.814\mathrm{V}$. Lower: Kondo temperatures $T_{\mathrm{K}}$ obtained from the temperature dependence. (b) Examples of the fitting to obtain $T_{\mathrm{K}}$. The gate voltages adopted here are indicated by arrows in (a). (c) Schematic diagram of a simple quantum circuit model of the system. The factor 2 of $\Delta \theta$ in $a_2$ is due to the reflection. (d) Phase shift of the QD obtained for the data in (a) at $V_{\mathrm{m}}=-0.814\mathrm{V}$ and 50 mK (thick line), 750 mK (thin line), and for the data in Fig. 1c at $V_{\mathrm{m}}=-0.832$, $-0.838$, $-0.844$, and $-0.850\mathrm{V}$ (dotted lines), based on the model shown in (c). The data folding at $\pi /2$ is due to taking plus of the double sign in (4).

Figure 4

(a) Conductance versus $V_{\mathrm{sd}}$ at Kondo valley A under various magnetic fields up to 6 T. The arrows indicate the positions of the conductance dips, which are determined by fitting two Gaussian curves. The broken lines are eye guides to show the baselines. (b) Distance between two dip positions versus the magnetic field. The data were taken at Kondo valleys A (open circles) and C (crosses) in Fig. 2. The line corresponds to $|g|=0.33$.