Quantum Hall plateau transition in the lowest Landau level of disordered graphene

Abstract

We investigate, analytically and numerically, the effects of disorder on the density of states and on the localization properties of the relativistic two dimensional fermions in the lowest Landau level. Employing a supersymmetric technique, we calculate the exact density of states for the Cauchy (Lorentzian) distribution for various types of disorders. We use a numerical technique to establish the localization-delocalization (LD) transition in the lowest Landau level. For some types of disorder the LD transition is shown to belong to a different universality class, as compared to the corresponding nonrelativistic problem. The results are relevant to the integer quantum Hall plateau transitions observed in graphene.

arXiv comment18 pages and 11 figures

References in corpus (35)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Chiral tunneling and the Klein paradox in graphene
• Electronic Properties of Disordered Two-Dimensional Carbon
• Unconventional Integer Quantum Hall effect in graphene
• Strong suppression of weak (anti)localization in graphene
• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Scaling Theory of the Integer Quantum Hall Effect
• Graphene: new bridge between condensed matter physics and quantum electrodynamics
• Interactions and phase transitions on graphene's honeycomb lattice
• Transport of Dirac quasiparticles in graphene: Hall and optical conductivities
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• Intervalley scattering, long-range disorder, and effective time reversal symmetry breaking in graphene
• Ghost excitonic insulator transition in layered graphite
• Edge States and the Quantized Hall Effect in Graphene
• Magnetic field-induced insulating behavior in highly oriented pyrolitic graphite
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Dynamical Flavor Symmetry Breaking by a Magnetic Field in $2+1$ Dimensions
• Disorder Effects in Two-Dimensional d-wave Superconductors
• Electron interactions in graphene in a strong magnetic field
• Excitonic gap, phase transition, and quantum Hall effect in graphene
• Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors
• Quantum Hall Effect of Dirac Fermions in Graphene: Disorder Effect and Phase Diagram
• On electron (anti)localization in graphene
• A Unified Model for Two Localisation Problems: Electron States in Spin-Degenerate Landau Levels, and in a Random Magnetic Field
• Gaussian field theories, random Cantor sets and multifractality
• Density of states for the $\pi$-flux state with bipartite real random hopping only: A weak disorder approach
• Corrections to Scaling in the Integer Quantum Hall Effect
• Universal Scaling of Strong-Field Localization in an Integer Quantum Hall Liquid
• Composite Dirac fermions in graphene
• Landau level mixing and spin degeneracy in the quantum Hall effect
• Effect of spin degeneracy on scaling in the quantum Hall regime
• Long-range-correlated disorder in graphene

Cited by in corpus (13)

• The electronic properties of graphene
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Theory of Anomalous Quantum Hall Effects in Graphene
• Entanglement entropy and multifractality at localization transitions
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Dissipation and criticality in the lowest Landau level of graphene
• Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps
• Unconventional Features in the Quantum Hall Regime of Disordered Graphene: Percolating Impurity States and Hall Conductance Quantization
• High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
• Edge states in graphene in magnetic fields -- a speciality of the edge mode embedded in the n=0 Landau band
• Scaling of von Neumann entropy at the Anderson transition
• Diffusive transport in the lowest Landau level of disordered 2d semimetals: the mean-square-displacement approach
• Shape of the zeroth Landau level in graphene with non-diagonal disorder