Probing Quantum Hall edge states with sub-nanometer resolution

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The central ingredients of the Quantum Hall effect are a bulk localization-delocalization transi-tion and an accompanying perfect quantization of the Hall conductance carried by edge states. The localization-delocalization transition including the appearance of localized skyrmions has been probed extensively down to the atomic scale. In contrast, the probing of the edge states and its predicted reconstructions have only been mapped either at a lateral resolution that does not enable to observe reconstructions in detail or at edges where the steepness of the potential inhibits any type of reconstruction. Recently, we have shown that double-gated graphene can be used to probe laterally extended edge states by scanning tunnelling microscopy. Therefore, we developed a method to avoid the disturbing influence of the tip induced quantum dot in the interface region by adequate choice of the gate voltages [A1]. Here, we want to extend this proof-of-principle experiment to study interfaces between various filling factors heading for the direct observation of edge state reconstructions under both static and dynamic conditions, i.e. without and with current flow. The investigations will be backed up by direct probing of the local potential with scanning tunnelling potentiometry or Kelvin probe force microscopy at the same device and gate configurations.