The Quantum Hall Effect in Graphene: Emergent Modular Symmetry and the Semi-circle Law
arXiv:cond-mat/0612269 · doi:10.1103/PhysRevB.76.113406
Abstract
Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed quantum Hall effect in graphene as a test of these ideas, and identify to this end a class of predictions for graphene which would follow from the same modular arguments. We are led to a suite of predictions for high mobility samples that differs from those obtained for the conventional quantum Hall effect in semiconductors, including: predictions for the locations of the quantum Hall plateaux; predictions for the positions of critical points on transitions between plateaux; a selection rule for which plateaux can be connected by low-temperature transitions; and a semi-circle law for conductivities traversed during these transitions. Many of these predictions appear to provide a good description of graphene measurements performed with intermediate-strength magnetic fields.
arXiv comment4 pages, 2 figures
References in corpus (19)
- Two-Dimensional Gas of Massless Dirac Fermions in Graphene
- Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
- Unconventional Integer Quantum Hall effect in graphene
- Landau Level Splitting in Graphene in High Magnetic Fields
- Fractional Quantum Hall Effect in Graphene
- Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems
- Evidence for charge-flux duality near the quantum Hall liquid to insulator transition
- A different view of the quantum Hall plateau-to-plateau transitions
- Derivation of the Semi-circle Law from the Law of Corresponding States
- Modular invariance, universality and crossover in the quantum Hall effect
- One-Dimensional Flows in the Quantum Hall System
- Universal flow diagram for the magnetoconductance in disordered GaAs layers
- Duality in the Quantum Hall Effect - the Role of Electron Spin
- Duality and the Modular Group in the Quantum Hall Effect
- Duality and Non-linear Response for Quantum Hall Systems
- Scaling flow diagram in the fractional quantum Hall regime of GaAs/AlGaAs heterostructures
- On the Implications of Discrete Symmetries for the Beta Function of Quantum Hall Systems
- An experimental study on (2) modular symmetry in the quantum Hall system with a small spin-splitting
- N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect
Cited by in corpus (20)
- Conformal Invariance and Shape-Dependent Conductance of Graphene Samples
- Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
- Metal to insulator transition on the N = 0 Landau level in graphene
- Dual Gravitons in AdS4/CFT3 and the Holographic Cotton Tensor
- Holographic anyonic superfluidity
- AdS/QHE: Towards a Holographic Description of Quantum Hall Experiments
- Holographic pinning
- Electric-magnetic Duality and Deformations of Three-Dimensional CFT's
- Anomalous Quantum Hall Effect on Sphere
- A Holographic Quantum Hall Ferromagnet
- Probing semiclassical magneto-oscillations in the low-field quantum Hall effect
- Duality, the Semi-Circle Law and Quantum Hall Bilayers
- Non-commutative massive unquenched ABJM
- Holographic fundamental matter in multilayered media
- Striped anyonic fluids
- Holomorphic and anti-holomorphic conductivity flows in the quantum Hall effect
- Flowing holographic anyonic superfluid
- An RG potential for the quantum Hall effects
- Elliptic mirror of the quantum Hall effect
- Quantum Hall conductance of two-terminal graphene devices