Electronic properties in moiré superlattice in rotationally stacked atomic layers
Mikito Koshino1, Pilkyung Moon2
1Department of Physics, Tohoku University,
2Korean Institute for Advanced Study
We report recent theoretical studies on the electronic properties of rotationally stacked atomic layer systems, including graphene-graphene bilayer, and graphene-hBN (hexagonal boron nitride) composite bilayer. The misoriented atomic structure gives rise to a moiré superlattice structure with a long spatial period, and it strongly modifies the band structure in the low-energy region. We develop an effective continuum model based the tight-binding Hamiltonian, which correctly describes the electronic structure of moiré superlattice . In a magnetic field, the coexistence of the moiré pattern and the Landau quantization causes the fractal energy spectrum so-called Hofstadter’s butterfly. We calculate the spectral evolution as a function of magnetic field, and demonstrate that the quantized Hall conductivity changes in a complicated manner in changing Fermi energy and the magnetic field amplitude . We also calculate the optical absorption in the fractal band regime, and find that the absorption spectrum and the optical selection rule exhibit recursive self-similar structure as well, reflecting the fractal nature of the energy spectrum.
 P. Moon and M. Koshino, Phys. Rev. B 87, 205404 (2013)
 P. Moon and M. Koshino, Phys. Rev. B 85, 195458 (2012).
 P. Moon and M. Koshino, Phys. Rev. B 88, 241412(R) (2013).