Energy spectrum and quantum Hall effect in twisted bilayer graphene

By P. Moon, M. Koshino. 2012

265 citations recorded by the source corpus.

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 semiclassical 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.

Subfields: Atomic and Molecular Physics, and Optics, Biomedical Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/4197fec329204366a7fa3b4f7b483b42c94fda82

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Biomedical Engineering

In Materials Chemistry

Citations in the corpus

Electronic properties of graphene-based bilayer systems (2015, methodology): “Koshino [429] applied the somewhat more complicated parametrization given by Eqs.”
Interlayer interaction in general incommensurate atomic layers (2015, background): “When the rotation angle is small, in particular, the system exhibits a moiré interference pattern of which period can be much greater than the atomic scale, and such a long-period modulation is known to strongly influence the low-energy electronic motion [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14].”
Correlated insulator behaviour at half-filling in magic-angle graphene superlattices (2018, methodology): “At approximately 1◦ < θ < 3◦, the superlattice densities ±ns are associated with a pair of single-particle bandgaps at their corresponding Fermi energy [1, 19].”
Symmetry, Maximally Localized Wannier States, and a Low-Energy Model for Twisted Bilayer Graphene Narrow Bands (2018, methodology): “[20] and the tight-binding model with different hopping range Lc based on the localized WSs obtained from the projection method.”
Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals Heterostructure (2013, methodology): “5nm, where the error is dominated by uncertainty in the value of the hBN dielectric constant[9].”