1202.4365 (Pilkyung Moon et al.)

Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene    [PDF]

Pilkyung Moon, Mikito Koshino

We investigate the electronic spectra and quantum Hall effect in twisted
bilayer graphenes with various rotation angles under magnetic fields, using a
model rigorously including the interlayer interaction. We describe the spectral
evolution from discrete Landau levels in the weak field regime to the fractal
band structure in the strong field regime, and estimate the quantized Hall
conductivity for each single gap. In weak magnetic fields, the low-energy
conduction band of the twisted bilayer is quantized into electron-like Landau
levels and hole-like Landau levels above and below the van Hove singularity,
respectively, reflecting a topological change of the Fermi surface between
electron pocket and hole pocket. Accordingly the Hall conductivity exhibits a
sharp drop from positive to negative at the transition point. In increasing
magnetic field, the spectrum gradually evolves into fractal band structure
so-called Hofstadter's butterfly, where the Hall conductivity exhibits a
nonmonotonic behavior varying from a minigap to a minigap. The magnetic field
strength required to invoke the fractal band structure is more feasible in
smaller rotating angle.

View original: http://arxiv.org/abs/1202.4365