Coupling symmetry of quantum dot states

With noninvasive methods, we investigate ground and excited states of a lateral quantum dot. Charge detection via a quantum point contact is used to map the dot dynamics in a regime where the current through the dot is too low for transport measurements. In this way we investigate and compare the tunneling rates from the dot to source and drain. We find a symmetry line on which the tunneling rates to both leads are equal. In this situation ground states as well as excited states influence the mean charge of the dot. A detailed study in this regime reveals that the coupling symmetry depends on the number of states contributing to transport and on the spatial distribution of individual states.

Figure 1

(Color online) (a) differential QD conductance $G$, QPC current $I_{QPC}$, and dot charge as a function of $V_{G1}$. $G$ shows Coulomb blockade peaks typical for single quantum dots. At each peak a step in $I_{QPC}$ is visible due to capacitive coupling. This still holds when the Coulomb peaks vanish. Inset: AFM image of the device. (b) Charge diagram for $G$. Bright means high differential conductance, dark means low. (c) Derivative $d{I}_{QPC}∕d{V}_G$ of QPC current corresponding to (b). Dark means charging event, bright means constant charge. The color encoding is used throughout this work.

Figure 2

(Color online) Nonlinear measurements along line A and line B (compare Fig. 1). Along line A, full diamonds are visible in the differential QD conductance (a) but only lines with negative slopes in the QPC current (b) due to asymmetric tunneling rates. Along line B, a transition from lines with positive slopes to lines with negative slopes appears in the QPC current (c). In the middle, a symmetric configuration is found where both slopes and excited states are visible. The sketches indicate the configurations of the tunneling barriers.

Figure 3

(Color online) Derivative of QPC current for a charge diagram similar to Fig. 1 but with $V_{SD}=1\mathrm{mV}$ and $B=3.7\mathrm{T}$. On the left and right single lines are visible which correspond to ground-state transitions. The lines on the left appear at higher voltages (higher $V_{\perp }$) than those on the right. Thus on the left (right) the drain (source) barrier is more opaque (see sketches). In the middle a symmetry line is observed (marked dotted) where both lines appear along with excited states.

Figure 4

(Color online) (a) 3D plot of the QD charge for the region marked in Fig. 3. The large steps correspond to the addition of electrons. Several smaller steps marked by white lines reflect resonances of ground and excited states near the symmetric configuration. The charging for these resonances and for those at $N\to N+1$ is studied in detail in (b) as a function of $V_{\Vert }$.