Anomalous integer quantum Hall effect in AA-stacked bilayer graphene

Abstract

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, ${\sigma }_{xx}\to 0$ 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 $B=\pi t^2/Neh{\upsilon }_F^2$, $N=1,2,3,\cdot \cdot \cdot$. Finally, the disappearance of the zero-Hall conductivity plateau is always accompanied by the occurence of a $8e^2/h$-step at $\bar{\mu }=t$.

submitted to Physical Review B

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• Holographic fermions in external magnetic fields
• Electronic Instabilities of the AA-Honeycomb Bilayer
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• Holographic description of strongly correlated electrons in external magnetic fields