Mapping quantum Hall edge states in graphene by scanning tunneling microscopy

Abstract

Quantum Hall edge states are the paradigmatic example of the bulk-boundary correspondence. They are prone to intricate reconstructions calling for their detailed investigation at high spatial resolution. Here, we map quantum Hall edge states of monolayer graphene at a magnetic field of 7 T with scanning tunneling microscopy. The graphene sample features a gate-tunable lateral interface between areas of different filling factor. We compare the results with detailed tight-binding calculations quantitatively accounting for the perturbation by the tip-induced quantum dot. We find that the edge state pattern is mapped with little perturbation by adequate choice of gate voltage. We observe extended compressible regions, the antinodal structure of edge states and their meandering along the lateral interface.

23 pages, 23 figures

References in corpus (41)

• The electronic properties of graphene
• Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering
• Electronic Properties of Graphene Encapsulated with Different Two-Dimensional Atomic Crystals
• Raman spectroscopy as probe of nanometer-scale strain variations in graphene
• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
• Bulk-edge correspondence for two-dimensional topological insulators
• Observation of neutral modes in the fractional quantum Hall regime
• Random strain fluctuations as dominant disorder source for high-quality on-substrate graphene devices
• The Quantum Hall Transition in Real Space: From Localized to Extended States
• Analytic Model for the Energy Spectrum of a Graphene Quantum Dot in a Perpendicular Magnetic Field
• Evolution of Microscopic Localization in Graphene in a Magnetic Field from Scattering Resonances to Quantum Dots
• Local Thermometry of Neutral Modes on the Quantum Hall Edge
• Tuning the pseudospin polarization of graphene by a pseudo-magnetic field
• Scanned Potential Microscopy of Edge and Bulk Currents in the Quantum Hall Regime
• Electrostatically confined monolayer graphene quantum dots with orbital and valley splittings
• Quantized Landau level spectrum and its density dependence
• Scalable Tight-Binding Model for Graphene
• Edge reconstruction in the fractional quantum Hall regime
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene
• A New Paradigm for Edge Reconstruction in Fractional Quantum Hall States
• Imaging of the Coulomb driven quantum Hall edge states
• Imaging work and dissipation in the quantum Hall state in graphene
• Large tunable valley splitting in edge-free graphene quantum dots on boron nitride
• Evolution of Landau Levels into Edge States at an Atomically Sharp Edge in Graphene
• Interaction Driven Quantum Hall Wedding cake-like Structures in Graphene Quantum Dots
• Melting of interference in the fractional quantum Hall effect: Appearance of neutral modes
• Imaging two-component nature of Dirac-Landau levels in the topological surface state of Bi2Se3
• Edge Channels of Broken-Symmetry Quantum Hall States in Graphene probed by Atomic Force Microscopy
• Real-space imaging of quantum Hall effect edge strips
• Imaging the Conductance of Integer and Fractional Quantum Hall Edge States
• Imaging fractional incompressible stripes in integer quantum Hall systems
• Scanning Tunneling Microscopy and Spectroscopy of Graphene on Insulating Substrates
• Fractional Edge Reconstruction in Integer Quantum Hall Phases
• Upstream modes and antidots poison graphene quantum Hall effect
• Manifestation of many-body interactions in the integer quantum Hall effect regime
• Exchange-mediated dynamic screening in the integer quantum Hall regime
• Edge State Wave Functions from Momentum-Conserving Tunneling Spectroscopy
• Probing the nodal structure of Landau level wave functions in real space
• Quantum Monte Carlo at the Graphene Quantum Hall Edge

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• Electronic band structure from quasiparticle interference and Landau quantization in WTe${}_2$
• Distributed Current Injection into a One-Dimensional Ballistic Edge Channel