Twisted bilayer graphene with interlayer potential asymmetry*

A twisted stack of two graphene layers (twisted bilayer graphene) exhibits an extremely long potential period arising from the moir\'{e} interference between the layers \footnote{C. Berger et al., Science 312, 1191 (2006).} \footnote{P. Moon and M. Koshino, Phys. Rev. B 85, 195458 (2012).} \footnote{P. Moon and M. Koshino, Phys. Rev. B 87, 205404 (2013).}. We investigate the band structure and optical absorption spectrum of twisted bilayer graphenes with changing interlayer bias and Fermi energy simultaneously \footnote{P. Moon, Y.-W. Son, and M. Koshino, Phys. Rev. B 90, 155427 (2014).}. We show that the interlayer bias lifts the degeneracy of the superlattice Dirac point, while the amount of the Dirac point shift is significantly suppressed in small rotation angles, and even becomes opposite to the applied bias, by the interlayer interaction. In addition, we show that the spectroscopic features are highly sensitive to the interlayer bias and the Fermi energy, and widely tunable by the external field effect.