Anomalous integer quantum Hall effect in AA-stacked bilayer graphene

Recent experiments indicate that AA-stacked bilayer graphenes (BLG) could exist. Since the energy bands of the AA-stacked BLG are different from both the monolayer and AB-stacked bilayer graphenes, different integer quantum Hall effect in the AA-stacked graphene is expected. We have thus calculated the quantized Hall conductivity $\sigma_{xy}$ and also longitudinal conductivity $\sigma_{xx}$ of the AA-stacked BLG within the linear response Kubo formalism. Interestingly, we find that the AA-stacked BLG could exhibit both conventional insulating behavior (the $\bar{\nu}=0$ plateau) and chirality for $|\bar{\mu}|<t$, where $\bar{\nu}$ is the filling factor ($\bar{\nu}=\sigma_{xy}h/e^{2}$), $\bar{\mu}$ is the chemical potential, and $t$ is the interlayer hopping energy, in striking contrast to the monlayer graphene (MLG) and AB-stacked BLG. We show that in the low-disorder and high-magnetic-field regime, $\sigma_{xx}\rightarrow0$ as long as the Fermi level is not close to a Dirac point, where $\Gamma$ denotes the Landau level broadening induced by disorder. Furthermore, when $\sigma_{xy}$ is plotted as a function of $\bar{\mu}$, a $\bar{\nu}=0$ plateau appears across $\bar{\mu}=0$ and it would disappear if the magnetic field $B=\pi t^2/Neh\upsilon^2_F$, $N = 1, 2, 3,\cdot\cdot\cdot$. Finally, the disappearance of the zero-Hall conductivity plateau is always accompanied by the occurence of a $8e^2/h$-step at $\bar{\mu}=t$.