Kim Sungmin, Schwenk Johannes, Walkup Daniel, Zeng Yihang, Ghahari Fereshte, Le Son T, Slot Marlou R, Berwanger Julian, Blankenship Steven R, Watanabe Kenji, Taniguchi Takashi, Giessibl Franz J, Zhitenev Nikolai B, Dean Cory R, Stroscio Joseph A
Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA.
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD, USA.
Nat Commun. 2021 May 14;12(1):2852. doi: 10.1038/s41467-021-22886-7.
The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the "bulk" topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of [Formula: see text] across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.
量子霍尔（QH）效应是一种拓扑非平凡量子相，它扩展了物理学中的拓扑序概念，使“体”拓扑与边缘态之间的紧密关系成为焦点。石墨烯中的量子霍尔效应以其四重简并零能朗道能级（zLL）为特征，在晶格尺度势之上，电子相互作用打破了这种对称性。然而，破缺对称性的边缘态一直无法进行空间测量。在本文中，我们使用高分辨率原子力显微镜（AFM）在量子霍尔边缘边界上对包含石墨烯zLL的量子霍尔破缺对称性边缘态进行了空间映射，展示了从体到量子霍尔边缘边界的带隙基态。化学势的测量解析了四重简并zLL的能量作为磁场的函数，并展示了石墨烯/氮化硼系统的莫尔超晶格势与大磁场中自旋/谷对称性破缺效应之间的相互作用。
