Angle Dependence of Landau Level Spectrum in Twisted Bilayer Graphene

Abstract

In the context of the low energy effective theory, the exact Landau level spectrum of quasiparticles in twisted bilayer graphene with small twist angle is analytically obtained by spheroidal eigenvalues. We analyze the dependence of the Landau levels on the twist angle to find the points, where the two-fold degeneracy for twist angles is lifted in the nonzero modes and below/above which massive/massless fermion pictures become valid. In the perpendicular magnetic field of 10\,T, the degeneracy is removed at ${\theta }_{\mathrm{deg}}\sim 3^{\circ }$ %angles around 3 degrees for a few low levels, specifically, ${\theta }_{\mathrm{deg}}\simeq 2.56^{\circ }$ for the first pair of nonzero levels and ${\theta }_{\mathrm{deg}}\simeq 3.50^{\circ }$ for the next pair. Massive quasiparticle appears at $\theta <{\theta }_{\mathrm{c}}\simeq 1.17^{\circ }$ in 10\,T, %angles less than 1.17 degrees. which match perfectly with the recent experimental results. Since our analysis is applicable to the cases of arbitrary constant magnetic fields, we make predictions for the same experiment performed in arbitrary constant magnetic fields, e.g., for B=40\,T we get ${\theta }_{\mathrm{c}}\simeq 2.34^{\circ }$ and the sequence of angles ${\theta }_{\mathrm{deg}}=5.11,7.01,8.42,...$ for the pairs of nonzero energy levels. The symmetry restoration mechanism behind the massive/massless transition is conjectured to be a tunneling (instanton) in momentum space.

8 pages, 7 figures, version to appear in PRB

References in corpus (8)

• Moire bands in twisted double-layer graphene
• Observation of Van Hove singularities in twisted graphene layers
• Flat Bands in Slightly Twisted Bilayer Graphene
• Single Layer Behavior and Its Breakdown in Twisted Graphene Layers
• Landau level spectroscopy of ultrathin graphite layers
• Commensuration and Interlayer Coherence in Twisted Bilayer Graphene
• Topologically Protected Zero Modes in Twisted Bilayer Graphene
• Energy spectrum of graphene multilayers in a parallel magnetic field

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• Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization not Mott Insulation
• Band Symmetries and Singularities in Twisted Multilayer Graphene
• Observation of Helical Edge States and Fractional Quantum Hall Effect in a Graphene Electron-hole Bilayer
• Optical Conductivity of Twisted Bilayer Graphene
• Superlattice structures in twisted bilayers of folded graphene
• Chiral Tunnelling in Twisted Graphene Bilayer
• Interlayer coupling in rotationally faulted multilayer graphenes
• Transport across twist angle domains in moiré graphene
• Spin-polarized tunneling current through a thin film of topological insulator in a parallel magnetic field
• Berry Phase Transition in Twisted Bilayer Graphene
• Magnetic Breakdown in Twisted Bilayer Graphene
• Effects of a tilted magnetic field in a Dirac double layer
• Antiferromagnetism and chiral d-wave superconductivity from an effective $t-J-D$ model for twisted bilayer graphene
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Nodal Surfaces in Photoemission from Twisted Bilayer Graphene
• Probing Layer Localization in Twisted Graphene Bilayers via Cyclotron Resonance
• Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials