Figure 2: Scanning gate microscopy.

Base temperature is 20 mK. (a,b) SGM maps of the QPC conductance G versus tip position in the (X,Y) horizontal plane for gate voltages V_gate=−1 V (a) and −0.95 V (b) corresponding, respectively, to points α and β as defined in Fig. 1b (gate voltages are shifted by 35 mV in presence of the tip). Concentric rings are only visible at α, and interference fringes are more contrasted at β. Additional data are presented in Supplementary Fig. 2. (c) Schematic view of the SGM experiment showing the tip scanning above the 2DEG near the QPC gates and three SGM maps. The horizontal map is the same as in a, but the data have been differentiated with respect to the Y-coordinate to highlight details. The two vertical maps are recorded in planes perpendicular to the surface along the purple line 1 (size 500 × 200 nm, gate voltage α) and the green line 2 (size 250 × 40 nm, gate voltage β) as indicated on the right image (identical to a). The two vertical maps have been differentiated with respect to their horizontal coordinate to highlight details (raw data are shown in Supplementary Fig. 3). The vertical map along line 1 reveals that the concentric rings visible in a form also rings in the vertical plane, whereas the vertical map along line 2 shows that interference fringes disappear rapidly with the tip-to-surface distance.