Energy spectrum and quantum Hall effect in twisted bilayer graphene

Abstract

We investigate the electronic structure and the quantum Hall effect in twisted bilayer graphenes with various rotation angles in the presence of magnetic field. Using a low-energy approximation, which incorporates the rigorous interlayer interaction, we computed the energy spectrum and the quantized Hall conductivity in a wide range of magnetic field from the semi-classical regime to the fractal spectrum regime. In weak magnetic fields, the low-energy conduction band is quantized into electronlike and holelike Landau levels at energies below and above the van Hove singularity, respectively, and the Hall conductivity sharply drops from positive to negative when the Fermi energy goes through the transition point. In increasing magnetic field, the spectrum gradually evolves into a fractal band structure called Hofstadter's butterfly, where the Hall conductivity exhibits a nonmonotonic behavior as a function of Fermi energy. The typical electron density and magnetic field amplitude characterizing the spectrum monotonically decrease as the rotation angle is reduced, indicating that the rich electronic structure may be observed in a moderate condition.

Model for the metal-insulator transition in graphene superlattices and beyond

“…This is, however, a nontrivial task that has not been accomplished so far. Thanks to extensive studies using various methods [6,[11][12][13][14][15][16][17][18][19][20][21][22][23], the band structure of TBG at small twist angle is known to be rather complex and depends sensitively on microscopic details such as lattice relaxation. Near the socalled magic twist angle, various methods find four nearly flat minibands at low energy, but differ significantly on important features such as their bandwidth and the gap to excited bands.…”

Many‐body effects in optical response of graphene‐based structures

“…The structural and physical properties originated in graphene samples from the stacking order are reviewed in a recent account. [77] As the twist angle decreases, the size of the unit cell enlarges [78] and the number of atoms comprising it may reach a few thousands. [79] The calculations of such configurations require invoking of the TB approaches, whereas band electronic structures of bilayers with reasonably small cells were obtained within DFT.…”

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

“…The electronic properties of moiré crystals depend sensitively on the ratio of the interlayer hybridization strength, which is independent of twist angle, to the band energy shifts produced by momentum space rotation (5)(6)(7)(8)(9)(10)(11)(12). In bilayer graphene, this ratio is small when twist angles exceed about 2° (10,13), allowing moiré crystal electronic structure to be easily understood using perturbation theory (5). At smaller twist angles, electronic properties become increasingly complex.…”