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

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 moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.

References in corpus (12)

• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• Electronic transport and quantum Hall effect in bipolar graphene p-n-p junction
• Flavour Hund's Coupling, Correlated Chern Gaps, and Diffusivity in Moiré Flat Bands
• Edge-State Velocity and Coherence in a Quantum Hall Fabry-Perot Interferometer
• Edge excitations of the canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in graphene: a simplified analysis
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• Experimental determination of the energy per particle in partially filled Landau levels
• High quality electrostatically defined hall bars in monolayer graphene
• Skyrmion zoo in graphene at charge neutrality in a strong magnetic field

Cited by in corpus (19)

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• Absence of edge reconstruction for quantum Hall edge channels in graphene devices
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Theory of the microwave impedance microscopy of Chern insulators
• Mapping quantum Hall edge states in graphene by scanning tunneling microscopy
• Optical flux pump in the quantum Hall regime
• Stacking-induced Chern insulator
• Chiral transport of hot carriers in graphene in the quantum Hall regime
• Contacts and upstream modes explain the electron-hole asymmetry in the graphene quantum Hall regime
• Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet
• Simultaneous symmetry breaking in spontaneous Floquet states: temporal Floquet-Nambu-Goldstone modes, Floquet thermodynamics, and the time operator
• Spin waves in doped graphene: a time-dependent spin-density-functional approach to collective excitations in paramagnetic two-dimensional Dirac fermion gases
• Quantum Monte Carlo at the Graphene Quantum Hall Edge
• Peculiarities of the Landau level collapse in graphene ribbons in crossed magnetic and in-plane electric fields
• Assembly of High-Performance van der Waals Devices Using Commercial Polyvinyl Chloride Films
• Zigzag edge states in graphene in the presence of in-plane electric field
• Quantum Hall Transport Measurements of Lateral p-n Junctions Formed via Precise Spatial Photodoping of Graphene/hBN Heterostructures
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors