Kondo effect in a one-electron double quantum dot: Oscillations of the Kondo current in a weak magnetic field

We present transport measurements of the Kondo effect in a double quantum dot charged with only one or two electrons, respectively. For the one-electron case, we observe a surprising quasiperiodic oscillation of the Kondo conductance as a function of a small perpendicular magnetic field $\mid B_{\perp }\mid \lesssim 50\mathrm{mT}$. We discuss possible explanations of this effect and interpret it by means of a fine tuning of the energy mismatch of the single dot levels of the two quantum dots. The observed degree of control implies important consequences for applications in quantum information processing.

Figure 1

(Color online) (a) Stability diagram of the DQD. Plotted is the transconductance $\mathrm{d}{I}_{\mathrm{QPC}}∕\mathrm{d}{U}_{g_{\mathrm{L}}}$ (color scale) of the DQD as a function of the side gate voltages $U_{g_{\mathrm{L}}}$ and $U_{g_{\mathrm{R}}}$. The measurement was done by using a nearby QPC. A background is subtracted for clarity. Numerals denote the number of electrons charging the (left/right) QD. (b) SEM micrograph of the top gates on the sample surface. Arrows mark possible current paths through the DQD and the nearby QPC. The estimated DQD geometry is sketched in white. (c) Differential conductance $\mathrm{d}I∕\mathrm{d}{U}_{\mathrm{SD}}$ of the symmetrically charged DQD as a function of bias voltage $U_{\mathrm{SD}}$ and center gate voltage $U_{g_{\mathrm{C}}}$. The variation of $U_{g_{\mathrm{C}}}$ corresponds approximately to the path in the stability diagram indicated by an arrow in (a). Numerals indicate the number of electrons charging the DQD.

Figure 2

Kondo effect differential conductance in a one- (two-) electron DQD. The inset displays exemplary raw data curves of the KDC of the DQD at $N=2$ as a function of the bias voltage for different magnetic fields but constant gate voltages. All raw data curves are measured within CB regions as sketched by the vertical white lines in Fig. 1. Black $(N=1)$ and gray $(N=2)$ circles in the main figure display the KDC in a logarithmic scale at $U_{\mathrm{SD}}\simeq 0$ (local maxima of raw data curves) as a function of a perpendicular magnetic field. Lines are model curves explained in the main text.

Figure 3

Nonmonotonic magnetic-field dependence of the Kondo effect in a one-electron DQD. Measurements of the KDC as shown in Fig. 2 but for the small magnetic-field limit. The inset and the main figure plot data for $N=2$ and 1, respectively. One data set (open circles) is vertically shifted for clarity. The dashed curve describes the limit $B_{\perp }⪡B_{\mathrm{K}}$ for $N=1$ and identical parameters as the corresponding model curve in Fig. 2. Vertical lines mark local minima of the $N=1$ KDC. Both datasets are taken at very similar conditions. Nevertheless, in these as in all our measurements we observe slight differences in the oscillation amplitude.