Energy spectrum and quantum Hall effect in twisted bilayer graphene

Abstract

We investigate the electronic spectra and quantum Hall effect in twisted\nbilayer graphenes with various rotation angles under magnetic fields, using a\nmodel rigorously including the interlayer interaction. We describe the spectral\nevolution from discrete Landau levels in the weak field regime to the fractal\nband structure in the strong field regime, and estimate the quantized Hall\nconductivity for each single gap. In weak magnetic fields, the low-energy\nconduction band of the twisted bilayer is quantized into electron-like Landau\nlevels and hole-like Landau levels above and below the van Hove singularity,\nrespectively, reflecting a topological change of the Fermi surface between\nelectron pocket and hole pocket. Accordingly the Hall conductivity exhibits a\nsharp drop from positive to negative at the transition point. In increasing\nmagnetic field, the spectrum gradually evolves into fractal band structure\nso-called Hofstadter's butterfly, where the Hall conductivity exhibits a\nnonmonotonic behavior varying from a minigap to a minigap. The magnetic field\nstrength required to invoke the fractal band structure is more feasible in\nsmaller rotating angle.\n

Keywords

Affiliated Institutions

• Tohoku University JP

Related Publications