Criticality of two-dimensional disordered Dirac fermions in the unitary class and universality of the integer quantum Hall transition
arXiv:2008.09025 · doi:10.1103/PhysRevLett.126.076801
Abstract
Two-dimensional (2D) Dirac fermions are a central paradigm of modern condensed matter physics, describing low-energy excitations in graphene, in certain classes of superconductors, and on surfaces of 3D topological insulators. At zero energy E=0, Dirac fermions with mass m are band insulators, with the Chern number jumping by unity at m=0. This observation lead Ludwig et al [Phys. Rev. B 50, 7526 (1994)] to conjecture that the transition in 2D disordered Dirac fermions (DDF) and the integer quantum Hall transition (IQHT) are controlled by the same fixed point and possess the same universal critical properties. Given the far-reaching implications for the emerging field of the quantum anomalous Hall effect, modern condensed matter physics and our general understanding of disordered critical points, it is surprising that this conjecture has never been tested numerically. Here, we report the results of extensive numerics on the phase diagram and criticality of 2D-DDF in the unitary class. We find a critical line at m=0, with energy-dependent localization length exponent. At large energies, our results for the DDF are consistent with state-of-the-art numerical results ν_IQH = 2.56 - 2.62 from models of the IQHT. At E=0 however, we obtain ν_0 =2.30-2.36 incompatible with ν_IQH. This result challenges conjectured relations between different models of the IQHT, and several interpretations are discussed.
arXiv commentclose to published version
References in corpus (44)
- Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Anderson Transitions
- Intrinsic quantized anomalous Hall effect in a moiré heterostructure
- Kwant: a software package for quantum transport
- Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
- Quantum-limited shot noise in graphene
- Scaling Theory of the Integer Quantum Hall Effect
- Riemannian symmetric superspaces and their origin in random matrix theory
- Demonstration of one-parameter scaling at the Dirac point in graphene
- Random Network Models and Quantum Phase Transitions in Two Dimensions
- Quantum criticality and minimal conductivity in graphene with long-range disorder
- Critical exponent for the quantum Hall transition
- Models for the integer quantum Hall effect: the network model, the Dirac equation, and a tight-binding Hamiltonian
- Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
- Quantum Hall effect in a one-dimensional dynamical system
- Ballistic transport in disordered graphene
- Toward a theory of the integer quantum Hall transition: continuum limit of the Chalker-Coddington model
- Observation of the quantum-anomalous-Hall insulator to Anderson insulator quantum phase transition and its scaling behavior
- Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
- Point-Contact Conductances at the Quantum Hall Transition
- Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions
- Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect
- Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field
- Boundary multifractality at the integer quantum Hall plateau transition: implications for the critical theory
- Critical Conductance and Its Fluctuations at Integer Hall Plateau Transitions
- The integer quantum Hall plateau transition is a current algebra after all
- Classification and symmetry properties of scaling dimensions at Anderson transitions
- Topological quantum number and critical exponent from conductance fluctuations at the quantum Hall plateau transition
- Universal Conductance and Conductivity at Critical Points in Integer Quantum Hall Systems
- Integer quantum Hall transition on a tight-binding lattice
- Finite Size Scaling of the Chalker-Coddington Model
- Localization length exponent in two models of quantum Hall plateau transitions
- Gaussian free fields at the integer quantum Hall plateau transition
- Point-Contact Conductances from Density Correlations
- Conductance Correlations Near Integer Quantum Hall Transitions
- Random network models with variable disorder of geometry
- Localization length index in a Chalker-Coddington model: a numerical study
- Pure scaling operators at the integer quantum Hall plateau transition
- Numerical evidence for marginal scaling at the integer quantum Hall transition
- Integer quantum Hall transition in a of a Landau level
- Spectrum-wide quantum criticality at the surface of class AIII topological phases: An "energy stack" of integer quantum Hall plateau transitions
- Current scaling of the topological quantum phase transition between a quantum anomalous Hall insulator and a trivial insulator
- Strong disorder in nodal semimetals: Schwinger-Dyson--Ward approach
Cited by in corpus (23)
- The general approach to the critical phase with coupled quasiperiodic chains
- Modular Commutators in Conformal Field Theory
- Fractional Chern insulators with a non-Landau level continuum limit
- Disorder in dissipation-induced topological states: Evidence for a different type of localization transition
- Turbulence Hierarchy and Multifractality in the Integer Quantum Hall Transition
- Scaling collapse of longitudinal conductance near the integer quantum Hall transition
- Numerical evidence for marginal scaling at the integer quantum Hall transition
- Field theory of non-Hermitian disordered systems
- Marginal CFT perturbations at the integer quantum Hall transition
- A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system
- Green's functions on a renormalized lattice: An improved method for the integer quantum Hall transition
- Composite Fermion Nonlinear Sigma Models
- The integer quantum Hall transition: an -matrix approach to random networks
- Localization renormalization and quantum Hall systems
- Interaction effects in graphene in a weak magnetic field
- Quantum Hall criticality in an amorphous Chern insulator
- How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
- Born approximation study of the strong disorder in magnetized surface states of topological insulator
- Coexistent multifractal mesoscopic fluctuations in Integer Quantum Hall Transition and in Orbital Hall Transition
- Emergent fractals in dirty topological crystals
- Genuine topological Anderson insulator from impurity induced chirality reversal
- Random Magnetic Field and the Dirac Fermi Surface
- Effect of Uncorrelated On-site Scalar Potential and Mass Disorder on Transport of Two-Dimensional Dirac Fermions