Hofstadter butterflies of bilayer graphene

Abstract

We calculate the electronic spectrum of bilayer graphene in perpendicular magnetic fields nonperturbatively. To accommodate arbitrary displacements between the two layers, we apply a periodic gauge based on singular flux vortices of phase $2\pi$. The resulting Hofstadter-like butterfly plots show a reduced symmetry, depending on the relative position of the two layers against each other. The split of the zero-energy relativistic Landau level differs by one order of magnitude between Bernal and non-Bernal stacking.

updated to refereed and edited version

References in corpus (10)

• Two Dimensional Atomic Crystals
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Unconventional Integer Quantum Hall effect in graphene
• Asymmetry gap in the electronic band structure of bilayer graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Electronic states and Landau levels in graphene stacks
• Dependence of band structures on stacking and field in layered graphene
• Quantum Hall effect and the topological number in graphene
• Hofstadter butterflies of carbon nanotubes: Pseudofractality of the magnetoelectronic spectrum
• Supersymmetry in carbon nanotubes in a transverse magnetic field

Cited by in corpus (12)

• Tuning of energy levels and optical properties of graphene quantum dots
• Charge Transport in Disordered Graphene-Based Low Dimensional Materials
• Landau Levels as a Probe for Band Topology in Graphene Moiré Superlattices
• Revealing Hofstadter Spectrum for Graphene in a Periodic Potential
• Convenient Peierls phase choice for periodic atomistic systems under magnetic field
• Recursive Green's functions optimized for atomistic modelling of large superlattice-based devices
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Electron trapping in graphene quantum dots with magnetic flux
• Direct observation of locally modified excitonic effect within a moiré unit cell in twisted bilayer graphene
• Dots and Boxes Algorithm for Peierls Substitution: Application to Multidomain Topological Insulators
• The selection rule of graphene in a composite magnetic field
• Hofstadter Butterfly in Graphene