Edge Channels of Broken-Symmetry Quantum Hall States in Graphene probed by Atomic Force Microscopy

TL;DR

This study uses atomic force microscopy to spatially map and analyze the edge states of broken-symmetry quantum Hall states in graphene, revealing the interplay of moiré potentials and symmetry-breaking effects.

Contribution

First direct spatial mapping of broken-symmetry quantum Hall edge states in graphene using AFM, highlighting the effects of moiré superlattice and electron interactions.

Findings

Resolved energies of the four-fold degenerate zero energy Landau level.

Demonstrated the influence of moiré superlattice on edge states.

Showed the interplay of spin/valley symmetry-breaking effects at high magnetic fields.

Abstract

The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded and brought into focus the concept of topological order in physics. The topologically protected quantum Hall edge states are of crucial importance to the QH effect but have been measured with limited success. The QH edge states in graphene take on an even richer role as 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 but has eluded spatial measurements. In this report, we 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 atomic force microscopy (AFM). 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 moir\'e superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.