Hofstadter butterfly and the quantum Hall effect in twisted double bilayer graphenes

Abstract

We study the energy spectrum and quantum Hall effects of the twisted double bilayer graphene in uniform magnetic field. We investigate two different arrangements, AB-AB and AB-BA, which differ in the relative orientation but have very similar band structures in the absence of a magnetic field. For each system, we calculate the energy spectrum and quantized Hall conductivities at each spectral gap by using a continuum Hamiltonian that satisfies the magneto-translation condition. We show that the Hofstadter butterfly spectra of AB-AB and AB-BA stackings differ significantly, even though their zero magnetic field band structures closely resemble; the spectrum of AB-AB has valley degeneracy, which can be lifted by applying interlayer potential asymmetry, while the spectrum of AB-BA has no such degeneracy in any case. We explain the origin of the difference from the perspectives of lattice symmetry and band topology.

10 pages, 4 figures

References in corpus (5)

• The electronic properties of bilayer graphene
• Continuum Model of the Twisted Bilayer
• Flatbands in twisted double bilayer graphene
• Band structure and topological property of twisted double bilayer graphenes
• Interlayer interaction in general incommensurate atomic layers

Cited by in corpus (11)

• Tunable moiré materials for probing Berry physics and topology
• Tailoring the band structure of twisted double bilayer graphene with pressure
• Magnetic Bloch Theorem and Reentrant Flat Bands in Twisted Bilayer Graphene at $2\pi$ Flux
• Perpendicular electric field drives Chern transitions and layer polarization changes in Hofstadter bands
• Recursive Green's functions optimized for atomistic modelling of large superlattice-based devices
• Ferroelectricity in twisted double bilayer graphene
• Moiré Landau levels of a $C_4$-symmetric twisted bilayer system in the absence of a magnetic field
• Hofstadter-Moiré Butterfly in Twisted Trilayer Graphene
• Analogue of atomic collapse for adatoms on rhombohedral multilayer graphene
• Shift current response in twisted double bilayer graphenes
• Hofstadter Butterfly in Graphene