Single-electron effects in a coupled dot-ring system

Aharonov-Bohm oscillations are studied in the magnetoconductance of a micron-sized open quantum ring coupled capacitively to a Coulomb-blockaded quantum dot. As the plunger gate of the dot is modulated and tuned through a conductance resonance, the amplitude of the Aharonov-Bohm oscillations in the transconductance of the ring displays a minimum. We demonstrate that the effect is due to a single-electron screening effect, rather than to dephasing. Aharonov-Bohm oscillations in a quantum ring can thus be used for the detection of single charges.

Figure 1

(a) Scanning force microscope image of the quantum ring coupled to a quantum dot. The structure was written by AFM lithography. (b) Coulomb-blockade oscillations in the conduction through the quantum dot as a function of the plunger-gate voltage. (c) Aharonov-Bohm oscillations in the dc conductance of the ring. The AB period as expected from the ring area is marked by the horizontal arrows. The bias voltage was $40\mu \mathrm{V}$, the top-gate voltage $136\mathrm{mV}$. (d) Aharonov-Bohm oscillations in the transconductance of the ring. The ac voltage on the plunger gate was modulated at $89\mathrm{Hz}$ with an amplitude of $1.8\mathrm{mV}$.

Figure 2

(a) AB oscillations in the transconductance $G_{\text{ring}}^{\text{trans}}$ for two different gate voltages $V_{\mathrm{pg}}^{\mathrm{dc}}=37$ and $39\mathrm{mV}$, respectively [indicated in (b) by the vertical lines]. (b) AB oscillation amplitude $G_1^{\text{trans}}$ (full line) obtained from the magnetic field range shown in (a), and dot conductance (dashed line) as a function of plunger-gate voltage. The AB amplitude is reduced by about $30\%$ when the dot shows a conductance peak. (c) Dot conductance peak (dashed line) and ring transconductance $G_{\text{ring}}^{\text{trans}}\left(V_{\mathrm{pg}}^{\mathrm{dc}},\mathrm{B}=4\mathrm{mT}\right)$ (full line). The data are taken at a fixed magnetic field of $4\mathrm{mT}$ where the effect is largest [see (a)]. The straight line represents the expected behavior if there was no conductance peak in the dot at this gate voltage. (d) Integrated transconductance signal from (c) (full line), and dot conductance (dashed line). The straight line is again the extrapolation without charging effects. $G_{\text{ring}}^{\mathrm{dc}}\left(V_{\mathrm{pg}}^{\mathrm{dc}}\right)$ is expected to exhibit a step-like behavior caused by the conductance peak in the dot. (e) An accurate dc measurement (precision ${10}^{-4}$) reveals the step in $G_{\text{ring}}^{\mathrm{dc}}\left(V_{\mathrm{pg}}^{\mathrm{dc}}\right)$. The global evolution of $G_{\text{ring}}^{\mathrm{dc}}$ differs from the estimated value in (d) because of a major charge rearrangement between the two measurements. Measurements were performed at $B=4\mathrm{mT}$ on an AB extremum.

Figure 3

Dot current and ring transconductance for a dot bias from $V_{\text{dot}}^{\text{bias}}=-110\mu \mathrm{V}$ to $V_{\text{dot}}^{\text{bias}}=+110\mu \mathrm{V}$ (thin lines). A higher dot bias voltage increases the current through the dot. For small bias voltages, the dot $I\text{−}V$ characteristic is linear (on a conductance peak). At higher bias voltages $V_{\text{dot}}^{\text{bias}}=130,180,230,280,330\mu \mathrm{V}$ (bold and dashed line), new dot levels become available for transport. The dip in the transconductance $G_{\text{ring}}^{\text{trans}}$ measured at fixed magnetic field does not change, except for the highest bias voltage (dashed line), where a second dip appears (see vertical arrow). Inset: Electrostatic model for the coupling of the dot to the ring. The notation is described in the text.