Discrete charging of traps visualized by scanning gate experiments on a quantum point contact

A quantum point contact (QPC) patterned on a two-dimensional electron gas is investigated with a scanning gate setup operated at a temperature of $300\mathrm{mK}$. The conductance of the point contact is recorded while the local potential is modified by scanning the tip. Discrete charging of traps induced by the local potential is observed as a stepwise conductance change of the constriction. By selectively changing the state of some of these traps, it is possible to observe changes in the transmission of the QPC. The lateral position of such traps is determined, and their density is estimated to be below $50\text{per}\mu {\mathrm{m}}^2$, corresponding to less than 1% of the doping concentration.

Figure 1

(a) Topography image of the sample taken at a temperature of $300\mathrm{mK}$. The QPC used for the measurements is visible in the center of the image. (b) Conductance through the QPC as a function of the voltage applied on the gate region labeled with gate 1. The dashed line indicates a line scan along which Fig. 2 was taken.

Figure 2

(Color online) Determination of the contact potential difference. The image shows the conductance through the QPC for different positions of the tip and tip bias voltages. The tip was scanned along the dotted line in Fig. 1a. The contact potential difference is assumed to be zero, when the conductance of the QPC for a certain tip voltage and position corresponds to the conductance in the absence of the tip. The values 200 and $1700\mathrm{mV}$ labeling the vertical arrows are the estimated tip voltages that compensate the contact potential differences of the two apparent tips (see text for details). The labels (1) and (2) denote sections of contour lines emphasized by the black curves and primarily caused by tip1 or tip2 of the double tip.

Figure 3

(Color online) (a) Conductance trace of the QPC with the tip placed over the constriction. The voltage applied on gate 1 for the measurement in (c) is marked by the dashed line. (b) Simulation of the gating effect obtained by using the conductance trace and a model for the tip-induced potential (explained in the text) with the same parameters as used for the experiment. (c) Measured scanning gate image showing very similar features as the simulated image. The transmission modulations match almost exactly the experimentally observed ones. The position of the QPC is drawn in the image.

Figure 4

(Color online) Scanning gate image of the area surrounding the constriction (drawn in the image). The inset shows a detail of the region (gradient of the measured data), where charging events are present.

Figure 5

(Color online) Wavelet analysis of the linescans used to determine the influence of the tip on local charge trapping sites. (a) Position of the different line scans and (b) a set of line scans for different gate voltages. A single conductance trace as a function of gate voltage before (c) and after (d) the wavelet analysis. The local maxima of (d) are marked in the trace (e), which is identical to (a) otherwise. The markers are then plotted in conductance grayscale, showing the evolution of local maxima with tip position (see Fig. 6 on the left).

Figure 6

(Color online) Demonstration that charging events can be observed as different slopes $d{V}_{\text{gate}1}∕dX$ of conductance maxima positions. The left image shows the position of local maxima as a function of tip position and gate voltage [see Fig. 5b] for the raw data. The line scan was done on line (i) of Fig. 5a. The curves labeled 1–4 mark the position of single local maxima; while curves 1 and 2 are parallel to the conductance onset (left dashed line) and curve 3 displays a larger change in voltage for different tip positions. Figures A–E on the right are conductance traces obtained from the raw data, and show the position of the local maxima 1–4 for the tip positions denoted in the left figure.

Figure 7

(Color online) Conductance features can be made to disappear, if the tip is placed over the position of certain localized charges. (a) Position of local maxima after a wavelet analysis [the line scan was done on line (iii) of Fig. 5a]. The regions marked with (i) and (ii) lack a maximum. (b) Position of the line scans with respect to the QPC. The lack of local maxima can be observed on all line scans at the positions marked (i) and (ii), thus a scatterer can be expected to be positioned at those locations.

Figure 8

(Color online) Transconductance measurement of the area close to the constriction (b) compared to the dc transport data differentiate mathematically in scanning direction (a) of the inset of Fig. 4, taken on a different region of the sample. A profile taken through the scanning gate image (c) clearly shows the large current resolution and current peaks corresponding to positive and negative current through the QPC. The lines marked with A–C are discussed in Fig. 9. The circles mark the crossing points between charging events and lines A–C.

Figure 9

Evolution of the lines corresponding to charging events with tip bias, if the tip is scanned along the lines A–C of Fig. 8. The numbers give the $d{V}_{\text{tip}}∕dX$ of the tip normalized to $d{V}_{\text{tip}}∕dX$ measured from the gating effect. The circle in A highlights a set of charging events which can be either related to sequential charging of the same site, or to a coupling between two different sites.