Odd-Integer Quantum Hall Effect in Graphene: Interaction and Disorder Effects

Abstract

We study the competition between the long-range Coulomb interaction, disorder scattering, and lattice effects in the integer quantum Hall effect (IQHE) in graphene. By direct transport calculations, both $\nu =1$ and $\nu =3$ IQHE states are revealed in the lowest two Dirac Landau levels. However, the critical disorder strength above which the $\nu =3$ IQHE is destroyed is much smaller than that for the $\nu =1$ IQHE, which may explain the absence of a $\nu =3$ plateau in recent experiments. While the excitation spectrum in the IQHE phase is gapless within numerical finite-size analysis, we do find and determine a mobility gap, which characterizes the energy scale of the stability of the IQHE. Furthermore, we demonstrate that the $\nu =1$ IQHE state is a Dirac valley and sublattice polarized Ising pseudospin ferromagnet, while the $\nu =3$ state is an $xy$ plane polarized pseudospin ferromagnet.

5 pages, 5 figures

References in corpus (19)

• 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
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Electronic Properties of Disordered Two-Dimensional Carbon
• Unconventional Integer Quantum Hall effect in graphene
• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Fabrication and Electric Field Dependent Transport Measurements of Mesoscopic Graphite Devices
• Electric Field Modulation of Galvanomagnetic Properties of Mesoscopic Graphite
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Electron interactions in graphene in a strong magnetic field
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Excitonic gap, phase transition, and quantum Hall effect in graphene
• Quantum Hall Effect of Dirac Fermions in Graphene: Disorder Effect and Phase Diagram
• Collapse of Spin-Splitting in the Quantum Hall Effect
• Disorder driven collapse of the mobility gap and transition to an insulator in fractional quantum Hall effect
• Phase Diagram for Quantum Hall Bilayers at $\nu =1$
• Mobility gap in fractional quantum Hall liquids: Effects of disorder and layer thickness

Cited by in corpus (55)

• The electronic properties of graphene
• Electronic transport in two dimensional graphene
• Properties of Graphene: A Theoretical Perspective
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Spin and valley quantum Hall ferromagnetism in graphene
• Theory of Anomalous Quantum Hall Effects in Graphene
• Field-induced Kosterlitz-Thouless transition in the N=0 Landau level of graphene
• Theory of the Magnetic-Field-Induced Insulator in Neutral Graphene
• Fractional topological phases and broken time reversal symmetry in strained graphene
• Coulomb interaction in graphene: Relaxation rates and transport
• Selective equilibration of spin and valley polarized quantum Hall edge states in graphene
• STM Study of Quantum Hall Isospin Ferromagnetic States of Zero Landau Level in Graphene Monolayer
• The nature of localization in graphene under quantum Hall conditions
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• Approaching Three-Dimensional Quantum Hall effect in Bulk HfTe5
• Transition to Landau Levels in Graphene Quantum Dots
• Many-body localization and mobility edge in a disordered Heisenberg spin ladder
• Dynamics and phase diagram of the $\nu =0$ quantum Hall state in bilayer graphene
• Fractional Quantum Hall Effects in Graphene and Its Bilayer
• Spin Superfluidity in the $\nu =0$ Quantum Hall State of Graphene
• Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps
• Broken-symmetry $\nu =0$ quantum Hall states in bilayer graphene: Landau level mixing and dynamical screening
• Twistronics in graphene-based van der Waals structures
• Quantum transport in disordered systems under magnetic fields: A study based on operator algebras
• Broken-symmetry states and phase diagram of the lowest Landau level in bilayer graphene
• Odd integer quantum Hall effect in graphene
• Coupled charge and valley excitations in graphene quantum Hall ferromagnets
• Toward theory of quantum Hall effect in graphene
• Noncollinear magnetic phases and edge states in graphene quantum Hall bars
• Skyrmion zoo in graphene at charge neutrality in a strong magnetic field
• Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene
• Tomonaga-Luttinger liquid parameters of magnetic waveguides in graphene
• Weak momentum scattering and the conductivity of graphene
• Valley polarization effects on the localization in graphene Landau levels
• The spin-polarized $\nu =0$ state of graphene: a spin superconductor
• Quantum Hall ferromagnetism in graphene: a SU(4) bosonization approach
• Quantum Spin Hall Effect in Twisted Bilayer Graphene
• Lifting of the Landau level degeneracy in graphene devices in a tilted magnetic field
• SU(4) spin waves in the $\nu =\pm 1$ quantum Hall ferromagnet in graphene
• Chiral condensate with topological degeneracy in graphene and its manifestation in edge states
• On the electron-polaron--electron-polaron scattering and Landau levels in pristine graphene-like quantum electrodynamics
• Quantum Hall Skyrmions at $\nu =0,\pm 1$ in monolayer graphene
• Hierarchy of Spin and Valley Symmetry Breaking in Quantum Hall Single Layer Graphene
• Gap generation and phase diagram in strained graphene in a magnetic field
• Spectrum of edge states in the $\nu =0$ quantum Hall phases in graphene
• Electronic zero modes of vortices in Hall states of gapped graphene
• Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene
• Integer quantum Hall effect and topological phase transitions in silicene
• Integer Quantum Hall Effect of Interacting Electrons in Graphene
• Landau Level Splitting in Rotationally Faulted Multilayer Graphene
• Spin-resoloved chiral condensate as a spin-unpolarized ν=0 quantum Hall state in graphene
• Graphene in the Quantum Hall Regime: Effects of Vacancies, Sublattice Polarization and Disorder
• Chiral Symmetry and Many-Body Effect in Multilayer Graphene