Correlated random hopping disorder in graphene at high magnetic fields: Landau level broadening and localization properties

Abstract

We study the density of states and localization properties of the lowest Landau levels of graphene at high magnetic fields. We focus on the effects caused by correlated long-range hopping disorder, which, in exfoliated graphene, is induced by static ripples. We find that the broadening of the lowest Landau level shrinks exponentially with increasing disorder correlation length. At the same time, the broadening grows linearly with magnetic field and with disorder amplitudes. The lowest Landau level peak shows a robust splitting, whose origin we identify as the breaking of the sublattice (valley) degeneracy.

9 pages, 8 figures - 1 Figure (Fig.5) and a few new references added

References in corpus (14)

• The electronic properties of graphene
• Room-Temperature Quantum Hall Effect in Graphene
• Landau level spectroscopy of ultrathin graphite layers
• Infrared spectroscopy of Landau levels in graphene
• Scanning Tunneling Spectroscopy of Graphene on Graphite
• Midgap states and charge inhomogeneities in corrugated graphene
• Cyclotron Resonance study of the electron and hole velocity in graphene monolayers
• Disorder and Electronic Transport in Graphene
• Theory of Anomalous Quantum Hall Effects in Graphene
• Quantum-Hall activation gaps in graphene
• Order from Disorder in Graphene Quantum Hall Ferromagnet
• The shape of disorder broadened Landau subbands in graphene
• Valley polarization effects on the localization in graphene Landau levels
• Splitting of critical energies in the $n$=0 Landau level of graphene

Cited by in corpus (7)

• High-energy Landau levels in graphene beyond nearest-neighbor hopping processes: Corrections to the effective Dirac Hamiltonian
• Polarization of graphene in a strong magnetic field beyond the Dirac cone approximation
• Two-phonon scattering in graphene in the quantum Hall regime
• Shape of the zeroth Landau level in graphene with non-diagonal disorder
• Effective tunnel conductance and effective ac conductivity of randomly strained graphene
• Zero energy mode for an electron in graphene in a perpendicular magnetic field with constant asymptotics
• Boundary-condition-assisted chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice