Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy

Sungmin Kim,Kenji Watanabe,Joseph A Stroscio,Daniel Walkup,Cory R Dean,Julian Berwanger,Marlou R Slot,Takashi Taniguchi,Johannes Schwenk,Franz J Giessibl,Yihang Zeng,Son T Le,Fereshte Ghahari,Steven R Blankenship,Nikolai B Zhitenev

doi:10.1038/s41467-021-22886-7

Abstract

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 {{nu }}={{0}},pm {{1}} 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.

Highlights

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
Nontrivial topology is often related to electronic systems with highly degenerate ground states[1], the most famous recent example being twisted bilayer graphene displaying the enormous richness of physical phenomena[2,3,4]
More recent intriguing progress in imaging quantum Hall edge states has been made using SQUID-on-tip measurements of graphene[18], the authors were not successful in imaging any broken-symmetry states inside the graphene zero energy Landau level (zLL) as the technique is limited to a moderate magnetic field range

Summary

Introduction

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. Extensive theoretical studies of the ground state of the zLL have shown the existence of many competing phases with distinct symmetry-breaking properties[21,22,23,24,25,26,27]. Transitions between different ground states may be induced by changing the contribution of the Zeeman energy by tilting the magnetic field with respect to the graphene sheet[26], and through other microscopic variables which break sublattice symmetry, the prominent example being the moiré-induced superlattice[27]. Recent experimental observations of a metal–insulator transition observed in transport measurements as a function of tilted magnetic field[26] have been interpreted as the evidence of the CAF ground state in accordance with theoretical predictions[28]. Imaging the spatial properties of these broken-symmetry states can shed light on revealing the competing interactions and make a direct connection with theoretical models

Methods

Results

Conclusion