Noninvasive detection of charge rearrangement in a quantum dot in high magnetic fields

We demonstrate electron redistribution caused by magnetic field on a single quantum dot measured by means of a quantum point contact as noninvasive detector. Our device, which is fabricated by local anodic oxidation, allows us to control independently the quantum point contact and all tunneling barriers of the quantum dot. Thus we are able to measure both the change of the quantum dot charge and also changes of the electron configuration at constant number of electrons on the quantum dot. We use these features to exploit the quantum dot in a high magnetic field where transport through the quantum dot displays the effects of Landau shells and spin blockade. We confirm the internal rearrangement of electrons as function of the magnetic field for a fixed number of electrons on the quantum dot.

Figure 1

(Color online) Operating principle of the device containing a QD and a QPC. Conductivity of QD (dashed line, right axis) and QPC (solid line, left axis) are shown as a function of gate voltage applied to G2. The inset shows a three-dimensional AFM image of the device.

Figure 2

(Color online) (a) Conductance $g_{\mathrm{QD}}$ of the QD and (b) $d{g}_{\mathrm{QPC}}$ and $d{U}_{\mathrm{G}2}$ of the QPC as a function of the gate voltage and magnetic field, where light-colored means zero conductance and dark-colored means finite conductance. Several Coulomb peaks can be seen, changing position with increasing magnetic field. Even for vanishing transport through the QD, the QPC signal clearly traces the addition of further electrons to the QD. The filling factor $\nu =2$ in the QD is marked in both plots. The hatched boxes represent the measurement range shown in Fig. 3.

Figure 3

(Color online) (a) Conductance of the QD as a function of gate voltage and magnetic field in more detail. The Coulomb peaks show a typical zigzag pattern as a function of magnetic field. (b) Same range of $B$ for $d{g}_{QPC}∕dB$. Vertical dashed lines drawn are guides to the eye. Between the Coulomb peaks vertical lines can be seen, when the electrons rearrange due to the magnetic field. (c) Trace along a Coulomb peak in the QD conductance [dashed line in (a)]. The conductance oscillates over a wide magnetic field range as demonstrated in the inset. (d) $\Delta q$ detected by the QPC as a function of the magnetic field along the dashed line in (b). For each of the light vertical lines a distinct step in $\Delta q$ occurs.

Figure 4

(Color online) Simple model for the charge redistribution. The spheres depict the inner and outer Landau shell and the two highest electron states on the QD for the different configurations. Below, the idealized QPC signal is shown. The conductance of the QPC slowly decreases due to the rising magnetic field. At each electron transition from the inner to the outer shell a step occurs. Below this the measured charge is shown, as it can be calculated from the QPC signal.

Figure 5

(Color online) $d{g}_{\mathrm{QPC}}∕dB$ as a function of magnetic field and gate voltage. Same type of measurement as presented in Fig. 3b, but for a symmetric coupling to source and drain and in a range, where the current though the QD is too low for direct measurement. Again, lines can be seen when an electron changes to the outer shell, white dashed lines are drawn as a guide to the eye. Additional bright areas with an inverse slope occur between this lines.