Landau level splitting due to graphene superlattices

Abstract

The Landau level spectrum of graphene superlattices is studied using a tight-binding approach. We consider non-interacting particles moving on a hexagonal lattice with an additional one-dimensional superlattice made up of periodic square potential barriers, which are oriented along the zig-zag or along the arm-chair directions of graphene. In the presence of a perpendicular magnetic field, such systems can be described by a set of one-dimensional tight-binding equations, the Harper equations. The qualitative behavior of the energy spectrum with respect to the strength of the superlattice potential depends on the relation between the superlattice period and the magnetic length. When the potential barriers are oriented along the arm-chair direction of graphene, we find for strong magnetic fields that the zeroth Landau level of graphene splits into two well separated sublevels, if the width of the barriers is smaller than the magnetic length. In this situation, which persists even in the presence of disorder, a plateau with zero Hall conductivity can be observed around the Dirac point. This Landau level splitting is a true lattice effect that cannot be obtained from the generally used continuum Dirac-fermion model.

12 pages, 9 figures

References in corpus (26)

• The electronic properties of graphene
• Substrate-induced band gap opening in epitaxial graphene
• Ripple Texturing of Suspended Graphene Atomic Membranes
• Quantum interference and Klein tunneling in graphene heterojunctions
• Evidence of Klein tunneling in graphene p-n junctions
• Anisotropic behaviors of massless Dirac fermions in graphene under periodic potential
• Transport measurements across a tunable potential barrier in graphene
• Periodically rippled graphene: growth and spatially resolved electronic structure
• Dirac Cones and Minigaps for Graphene on Ir(111)
• New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
• Midgap states and charge inhomogeneities in corrugated graphene
• The zero-energy state in graphene in a high magnetic field
• Edge States and the Quantized Hall Effect in Graphene
• Unit cell of graphene on Ru(0001): a 25 x 25 supercell with 1250 carbon atoms
• Multiple magnetic barriers in graphene
• Landau Levels and Quantum Hall Effect in Graphene Superlattices
• Divergent resistance at the Dirac point in graphene: Evidence for a transition in a high magnetic field
• Electron optics with magnetic vector potential barriers in graphene
• Electronic superlattices in corrugated graphene
• Transport in superlattices on single layer graphene
• Semimetalic graphene in a modulated electric potential
• Band structure and gaps of triangular graphene superlattices
• Electronic and magnetic properties of superlattices of graphene/graphane nanoribbons with different edge hydrogenation
• Exchange induced charge inhomogeneities in rippled neutral graphene
• Dirac-Kronig-Penney model for strain-engineered graphene
• Effective Magnetic Fields in Graphene Superlattices