Anomalous integer quantum Hall effect in AA-stacked bilayer graphene

Abstract

Recent experiments indicate that -stacked bilayer graphenes (BLGs) could exist. Since the energy bands of the -stacked BLG are different from both the monolayer and -stacked bilayer graphenes, different integer quantum Hall effect in the -stacked graphene is expected. We have therefore calculated the quantized Hall conductivity and also longitudinal conductivity of the -stacked BLG within the linear-response Kubo formalism. Interestingly, we find that the -stacked BLG could exhibit both conventional insulating behavior (the plateau) and chirality for , where is the filling factor, is the chemical potential, and is the interlayer hopping energy, in striking contrast to the monolayer graphene and -stacked BLG. We also find that for , where , , and , the Hall conductivity is quantized as , if and , if . However, if , the plateaus are absent, where Furthermore, we find that when the magnetic field , , the plateau across would disappear and the step at would occur. Finally, we show that in the low-disorder and high-magnetic-field regime, , as long as the Fermi level is not close to a Dirac point.