Quantum Hall effect transition in scanning gate experiments

We present systematic scanning gate studies on a two-dimensional electron gas in the regime of the quantum Hall effect (QHE). We observe the macroscopic Hall bar response as a function of the local variation of the potential landscape in order to investigate the QHE transition. At even integer filling factors, no changes can be introduced by the local perturbation, consistent with the robustness of the QHE. Between two QHE plateaus such local changes induce sharp features in the Hall resistance images. We observe two distinct $1∕B$-periodic patterns, one in the low-field part and one in the high-field part of the transition. The crossover between the patterns is smooth, with both coexisting at a characteristic filling factor. We distinguish experimentally different Hall bar responses to the perturbations, for example, in the nonlocal Hall resistance. Based on our experimental findings we draw an intuitive picture of the QHE transition as a percolation transition of edge states and their coupling at saddle points of the local potential.