Figure 1

Schematic drawing of the key idea behind our experiment: The SGM tip is used to actively control the edge trajectories to obtain a continuously tunable interaction region length $d$. This allows a spatially resolved analysis of the equilibration process.Reuse & Permissions

Figure 2

Scheme of the experimental setup. Three Schottky gates are used to independently contact two co-propagating edge channels and to define a 6-$\mu$m-long and 1-$\mu$m-wide constriction. Using the SGM tip it is possible to selectively reflect the inner channel and define a variable interedge relaxation region length $d$.Reuse & Permissions

Figure 3

(a) Topography scan of device S1. (b) Calibration scan: The SGM map refers to the differential conductance signal measured at contact B when contact 2 is floating. $V_{\mathrm{tip}}=-10$ V. (c) Conductance profiles measured along the green (left panel) and the blue (right panel) line in (b). (d) Imaging of the interchannel equilibration (contact 2 grounded). (e) SGM measurement at zero magnetic field, with dc source bias $V=100$ $\mu$V. (f) Finite bias equilibration signal measured along the trajectory determined by means of the calibration scan. There is a clear correlation between the steps in the equilibration curves and the position of scattering centers in the SGM scan at zero magnetic field. Furthermore, we observe an enhancement of the equilibration steps with increasing bias.Reuse & Permissions

Figure 4

Results of the tight-binding simulations for the zero-bias case: the inter-channel, zero-temperature differential conductance (solid line) compared with experimental data from device S2 (filled dots). From the exponential fit (dashed line) we deduce an equilibration length ${\ell }_{\mathrm{eq}}=15$ $\mu$m. The position of strong scattering centers in the simulation is indicated by red arrows. Comparison of the curves in Figs. 3 and 4 demonstrates that the position of the jumps changes from sample to sample and critically depends on the specific distribution of the scattering centers in each sample, which is the main finding of our paper.Reuse & Permissions