Fate of Dirac Points in a Vortex Superlattice

Abstract

We consider noninteracting fermions on the honeycomb lattice in the presence of a magnetic vortex superlattice. It is shown that depending on the superlattice periodicity, a gap may open at zero energy. We derive an expression of the gap in the small-flux limit but the main qualitative features are found to be valid for arbitrary fluxes. This study provides an original example of a metal-insulator transition induced by a strongly modulated magnetic field in graphene. At the same time our results directly apply to Kitaev's honeycomb model in a vortex superlattice.

5 pages, 3 figures, published version

References in corpus (8)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Optical Flux Lattices for Ultracold Atomic Gases
• Designing Dirac points in two-dimensional lattices
• Band structure and gaps of triangular graphene superlattices
• Optical Flux Lattices for Two-Photon Dressed States
• Zero modes, energy gap, and edge states of anisotropic honeycomb lattice in a magnetic field

Cited by in corpus (12)

• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Perturbed vortex lattices and the stability of nucleated topological phases
• Flat bands and long range Coulomb interactions: conducting or insulating?
• Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way
• Majorana correlations in the Kitaev model with ordered-flux structures
• Gap opening of single-layer graphene under the continuum model
• Dirac fermions in graphene and analogues: magnetic field and topological properties
• Hierarchy of gaps and magnetic minibands in graphene in the presence of the Abrikosov vortex lattice
• Topological Mid-gap States of Topological Insulators with Flux-Superlattice
• Effective models for dense vortex lattices in the Kitaev honeycomb model
• Majorana Gap Formation in the Anisotropic Kitaev Model with Ordered Flux Configuration
• Landau levels of a Dirac electron in graphene from non-uniform magnetic fields