Landau levels in twisted bilayer graphene and semiclassical orbits

Abstract

Twisted bilayer graphene has been argued theoretically to host exceptionally flat bands when the angle between the two layers falls within a magic range near 1.1${}^{\circ }$. This is now strongly supported by experiment, which furthermore reveals dramatic correlation effects in the magic range due to the relative dominance of interactions when the bandwidth is suppressed. Experimentally, quantum oscillations exhibit different Landau level degeneracies when the angles fall in or outside the magic range; these observations can contain crucial information about the low energy physics. In this paper, we report a thorough theoretical study of the Landau level structure of the non-interacting continuum model for twisted bilayer graphene as the magnetic field and the twist angle are tuned. We first show that a discernible difference exists in the butterfly spectra when twist angle falls in and outside the magic range. Next, we carry out semiclassical analysis in detail, which quantitatively determines the origin of the low energy Landau levels from the zero field band structure. We find that the Landau level degeneracy predicted in the above analyses is capable of partially explaining features of the quantum oscillation experiments in a natural way. Finally, topological aspects, validity, and other subtle points of the model are discussed.

References in corpus (3)

• Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene
• Topological delocalization of two-dimensional massless Dirac fermions
• The Colored Hofstadter Butterfly for the Honeycomb Lattice

Cited by in corpus (6)

• Topological Flat Bands and Correlated States in Twisted Monolayer-Bilayer Graphene
• TSTG II: Projected Hartree-Fock Study of Twisted Symmetric Trilayer Graphene
• Current Switching of Valley Polarization in Twisted Bilayer Graphene
• Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene
• Tracing out Correlated Chern Insulators in Magic Angle Twisted Bilayer Graphene
• Moiré Landau levels of a $C_4$-symmetric twisted bilayer system in the absence of a magnetic field