Quantum Hall plateau transition in graphene with spatially correlated random hopping

Abstract

We investigate how the criticality of the quantum Hall plateau transition in disordered graphene differs from those in the ordinary quantum Hall systems, based on the honeycomb lattice with ripples modeled as random hoppings. The criticality of the graphene-specific n=0 Landau level is found to change dramatically to an anomalous, almost exact fixed point as soon as we make the random hopping spatially correlated over a few bond lengths. We attribute this to the preserved chiral symmetry and suppressed scattering between K and K' points in the Brillouin zone. The results suggest that a fixed point for random Dirac fermions with chiral symmetry can be realized in free-standing, clean graphene with ripples.

5 pages, 4 figures, changes in figure 2

References in corpus (9)

• The electronic properties of graphene
• The structure of suspended graphene sheets
• Gauge field induced by ripples in graphene
• Theory of Anomalous Quantum Hall Effects in Graphene
• Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field
• Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields
• Unconventional conductance plateau transitions in quantum Hall wires with spatially correlated disorder
• Levitation and percolation in quantum Hall systems with correlated disorder
• Conductance plateau transitions in quantum Hall wires with spatially correlated random magnetic fields

Cited by in corpus (32)

• Properties of Graphene: A Theoretical Perspective
• Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
• Generalized Chiral Symmetry and Stability of Zero Modes for Tilted Dirac Cones
• Impact of graphene quantum capacitance on transport spectroscopy
• Topological aspect of graphene physics
• Chiral symmetry and its manifestation in optical responses in graphene: interaction and multi-layers
• Interacting electrons in graphene nanoribbons in the lowest Landau level
• Quantum transport in chemically functionalized graphene at high magnetic field: Defect-Induced Critical States and Breakdown of Electron-Hole Symmetry
• Chiral condensate with topological degeneracy in graphene and its manifestation in edge states
• Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime
• Correlated random hopping disorder in graphene at high magnetic fields: Landau level broadening and localization properties
• Survival of sharp $n=0$ Landau levels in massive tilted Dirac fermions: Protection by generalized chiral operator
• Electron traversal times in disordered graphene nanoribbons
• Splitting of critical energies in the $n$=0 Landau level of graphene
• Narrow depression in the density of states at the Dirac point in disordered graphene
• Lattice realization of the generalized chiral symmetry in two dimensions
• Topologically protected Landau levels in bilayer graphene in finite electric fields
• Anomalous criticality in the quantum Hall transition at $n=0$ Landau level of graphene with chiral-symmetric disorders
• Plateau transitions of spin pump and bulk-edge correspondence
• Landau level broadening in graphene with long-range disorder -- Robustness of the n=0 level
• Topological Transition of Graphene from Quantum Hall Metal to Quantum Hall Insulator at $\nu =0$
• Topologically protected flatness in chiral moiré heterostructures
• Shape of the zeroth Landau level in graphene with non-diagonal disorder
• Stability of zero-mode Landau levels in bilayer graphene against disorder in the presence of the trigonal warping
• Spin-resoloved chiral condensate as a spin-unpolarized ν=0 quantum Hall state in graphene
• Narrow Zero Mode in Organic Massless Dirac Electron System $\alpha$-(BEDT-TTF)${}_2$I${}_3$
• High-field magnetoresistance revealing scattering mechanisms in graphene
• Robust quantized thermal conductance of Majorana floating edge bands in d-wave superconductors
• Chiral Symmetry and Many-Body Effect in Multilayer Graphene
• Chiral Symmetry and Electron-Electron Interaction in Many-Body Gap Formation in Graphene
• Robust Zero Modes in Disordered Two-Dimensional Honeycomb Lattice with Kekulé Bond Ordering
• Periodic Behavior of Topology in Graphene with Nanohole Array