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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 $σ_{xy}$ and also longitudinal conductivity $σ_{xx}$ 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 $\barν=0$ plateau) and chirality for $|\barμ|<t$, where $\barν$ is the filling factor ($\barν=σ_{xy}h/e^{2}$), $\barμ$ 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, $σ_{xx}\rightarrow0$ as long as the Fermi level is not close to a Dirac point, where $Γ$ denotes the Landau level broadening induced by disorder. Furthermore, when $σ_{xy}$ is plotted as a function of $\barμ$, a $\barν=0$ plateau appears across $\barμ=0$ and it would disappear if the magnetic field $B=πt^2/Neh\upsilon^2_F$, $N = 1, 2, 3,\cdot\cdot\cdot$. Finally, the disappearance of the zero-Hall conductivity plateau is always accompanied by the occurence of a $8e^2/h$-step at $\barμ=t$.