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 (9)

• Electric Field Effect in Atomically Thin Carbon Films
• Unconventional Integer Quantum Hall effect in graphene
• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• 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

Cited by in corpus (18)

• The electronic properties of graphene
• 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
• Theory of Anomalous Quantum Hall Effects in Graphene
• Coulomb interaction in graphene: Relaxation rates and transport
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• Transition to Landau Levels in Graphene Quantum Dots
• Dynamics and phase diagram of the $\nu =0$ quantum Hall state in bilayer graphene
• Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps
• Coupled charge and valley excitations in graphene quantum Hall ferromagnets
• Noncollinear magnetic phases and edge states in graphene quantum Hall bars
• Toward theory of quantum Hall effect in graphene
• Weak momentum scattering and the conductivity of graphene
• Tomonaga-Luttinger liquid parameters of magnetic waveguides in graphene
• Valley polarization effects on the localization in graphene Landau levels
• Quantum Hall ferromagnetism in graphene: a SU(4) bosonization approach
• Spectrum of edge states in the $\nu =0$ quantum Hall phases in graphene