Probing Quantum Hall edge states with sub-nanometer resolution

量子霍尔效应的核心成分是体定域-离域跃迁和伴随的边缘态霍尔电导的完全量子化。定域-离域跃迁包括定域skyrmion的出现已经被广泛地探测到原子尺度。相比之下，边缘状态的探测及其预测的重建仅在横向分辨率下被映射，该横向分辨率不能详细观察重建，或者在边缘处，其中电势的陡度抑制任何类型的重建。最近，我们已经表明，双栅石墨烯可以用来探测横向扩展的边缘状态的扫描隧道显微镜。因此，我们开发了一种通过适当选择栅极电压来避免界面区域中尖端诱导量子点的干扰影响的方法[A1]。在这里，我们希望扩展这个原理验证实验，以研究各种填充因子之间的接口，用于在静态和动态条件下直接观察边缘状态重建，即没有和有电流。研究将通过在相同的器件和栅极配置下使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来支持。

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.