Magnetic Bloch bands and Weiss oscillations in Dirac mass superlattices

Abstract

We study two-dimensional Dirac fermions in a one-dimensional mass superlattice under a perpendicular magnetic field. Using exact solutions for isolated and finite arrays of domain walls, we demonstrate the persistence of Jackiw-Rebbi modes with a field-dependent renormalized velocity. For the periodic case, we adopt a gauge-invariant projection method onto magnetic Bloch states, valid for arbitrary fields and mass profiles, which yields dispersive Landau levels, and confirm its accuracy by comparison with finite arrays spectra. From the miniband spectra we predict modified quantum Hall plateaus and Weiss-like magnetoconductivity oscillations, characterized by a strongly reduced amplitude and a $\pi /2$ phase shift compared to electrostatic superlattices.

17 pages, 11 figures, updated references

References in corpus (26)

• The electronic properties of graphene
• Unconventional Integer Quantum Hall effect in graphene
• Anisotropic behaviors of massless Dirac fermions in graphene under periodic potential
• New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
• Novel electric field effects on Landau levels in Graphene
• Electron Beam Supercollimation in Graphene Superlattices
• Landau Levels and Quantum Hall Effect in Graphene Superlattices
• Topological and stacked flat bands in bilayer graphene with a superlattice potential
• Transport in superlattices on single layer graphene
• Quantum Spin-Valley Hall Kink States: From Concept to Materials Design
• Engineering high quality graphene superlattices via ion milled ultra-thin etching masks
• Brown-Zak and Weiss oscillations in a gate-tunable graphene superlattice: A unified picture of miniband conductivity
• Magnetic Bloch Theorem and Reentrant Flat Bands in Twisted Bilayer Graphene at $2\pi$ Flux
• Electron supercollimation in graphene and Dirac fermion materials using one-dimensional disorder potentials
• Multilayer graphene with a superlattice potential
• Proximity screening greatly enhances electronic quality of graphene
• Gate-tunable topological phases in superlattice modulated bilayer graphene
• Signature of Correlated Insulator in Electric Field Controlled Superlattice
• Moiré Landau fans and magic zeros
• Designing topology and fractionalization in narrow gap semiconductor films via electrostatic engineering
• Transport Anisotropy in One-dimensional Graphene Superlattice in the High Kronig-Penney Potential Limit
• Two-dimensional Dirac fermions in a mass superlattice
• Weiss oscillations in the electronic structure of modulated graphene
• Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices
• Designer spin-orbit superlattices: symmetry-protected Dirac cones and spin Berry curvature in two-dimensional van der Waals metamaterials
• Designing (higher) Hall crystals