Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes

Abstract

Superlattices (SLs) in monolayer and bilayer graphene, formed by spatially periodic potential variations, lead to a modified bandstructure with extra finite-energy and zero-energy Dirac fermions with tunable anisotropic velocities. We theoretically show that transport in a weak perpendicular (orbital) magnetic field allows one to not only probe the number of emergent Dirac points but also yields further information about their dispersion. or monolayer graphene, we find that a moderate magnetic field can lead to a strong reversal of the transport anisotropy imposed by the SL potential, an effect which arises due to the SL induced dispersion of the zero energy Landau levels. This effect may find useful applications in switching or other devices. For bilayer graphene, we discuss the structure of Landau level wave functions and local density of states in the presence of a uniform bias, as well as in the presence of a kink in the bias which leads to topologically bound `edge states'. We consider implications of these results for scanning tunneling spectroscopy measurements, valley filtering, and impurity induced breakdown of the quantum Hall effect in bilayer graphene.

Published version, selected as an Editors' Suggestion; 14 Figures

References in corpus (22)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Room-Temperature Quantum Hall Effect in Graphene
• Biased bilayer graphene: semiconductor with a gap tunable by electric field effect
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Valley filter and valley valve in graphene
• Asymmetry gap in the electronic band structure of bilayer graphene
• Giant Faraday rotation in single- and multilayer graphene
• Dirac Cones and Minigaps for Graphene on Ir(111)
• Topological confinement in bilayer graphene
• Graphene valley filter using a line defect
• New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
• Electron Beam Supercollimation in Graphene Superlattices
• Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice
• Electronic Highways in Bilayer Graphene
• Valley-Hall Kink and Edge States in Multilayer Graphene
• Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids
• Landau Levels and Quantum Hall Effect in Graphene Superlattices
• Bilayer graphene with single and multiple electrostatic barriers: band structure and transmission
• Transport in superlattices on single layer graphene
• Chiral states in bilayer graphene: magnetic field dependence and gap opening
• Quantum Hall effect in bilayer and multilayer graphenes with finite gate voltage

Cited by in corpus (29)

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• Large Landau level splitting with tunable one-dimensional graphene superlattice probed by magneto capacitance measurements
• Beating oscillation and Fano resonance in the laser assisted electron transmission through graphene δ- function magnetic barriers
• Piezoelectric Electrostatic Superlattices in Monolayer MoS${}_2$
• Collective Edge Modes of a Quantum Hall Ferromagnet in Graphene
• Helical quantum Hall Edge modes in bilayer graphene: a realization of quantum spin-ladders
• Edge states in bilayer graphene in a magnetic field