Zero-energy modes and valley asymmetry in the Hofstadter spectrum of bilayer graphene van der Waals heterostructures with hBN

Abstract

We investigate the magnetic minibands of a heterostructure consisting of bilayer graphene (BLG) and hexagonal boron nitride (hBN) by numerically diagonalizing a two-band Hamiltonian that describes electrons in BLG in the presence of a moire potential. Due to inversion-symmetry breaking characteristic for the moire potential, the valley symmetry of the spectrum is broken, but despite this, the zero-energy Landau level in BLG survives, albeit with reduced degeneracy. In addition, we derive effective models for the low-energy features in the magnetic minibands and demonstrate the appearance of secondary Dirac points in the valence band, which we confirm by numerical simulations. Then, we analyze how single-particle gaps in the fractal energy spectrum produce a sequence of incompressible states observable under a variation of carrier density and magnetic field.

8 pages, 4 figures

References in corpus (5)

• STM Spectroscopy of ultra-flat graphene on hexagonal boron nitride
• Cyclotron Resonance study of the electron and hole velocity in graphene monolayers
• Electronic properties of graphene hexagonal boron nitride moiré superlattice
• Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
• Graphene quantum dot on boron nitride: Dirac cone replica and Hofstadter butterfly

Cited by in corpus (9)

• Observation of fractional Chern insulators in a van der Waals heterostructure
• High-order fractal states in graphene superlattices
• Magnetic ratchet effect in bilayer graphene
• Cyclotron resonance of the magnetic ratchet effect and second harmonic generation in bilayer graphene
• Umklapp electron-electron scattering in bilayer graphene moiré superlattice
• High-mobility compensated semimetals, orbital magnetization, and umklapp scattering in bilayer graphene moire superlattices
• Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene
• Semimetallic and semiconducting graphene-hBN multilayers with parallel or reverse stacking
• Coexisting Massive and Massless Dirac Fermions in Moire'-Reconstructed Bilayer Graphene