Probing Quantum Hall edge states with sub-nanometer resolution

量子霍尔效应的核心成分是本体局域-离域跃迁和伴随的边缘态携带的霍尔电导的完美量子化。包括局域化天空的出现在内的局域化-非局域化过渡已经被广泛地探索到原子尺度。相比之下，边缘状态的探测及其预测重建只能在横向分辨率下绘制，无法详细观察重建，或者在边缘处绘制，其中电位的陡峭度抑制了任何类型的重建。最近，我们已经证明双门控石墨烯可以通过扫描隧道显微镜来探测横向扩展的边缘状态。因此，我们开发了一种方法，通过适当选择栅极电压来避免尖端诱导量子点在界面区域的干扰影响[A1]。在这里，我们想将这个原理验证实验扩展到研究各种填充因子之间的界面，以便在静态和动态条件下（即无电流和有电流）直接观察边缘状态重建。在相同的装置和栅极结构下，用扫描隧道电位法或开尔文探针力显微镜直接探测局部电位将支持这些研究。

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.