Anomalous integer quantum Hall effect in AA -stacked bilayer graphene

Abstract

Recent experiments indicate that AA -stacked bilayer graphenes (BLGs) 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 therefore calculated the quantized Hall conductivity σxy and also longitudinal conductivity σxx 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 ν̄ =0 plateau) and chirality for | μ̄ | <t, where ν̄ is the filling factor, μ̄ is the chemical potential, and t is the interlayer hopping energy, in striking contrast to the monolayer graphene and AB -stacked BLG. We also find that for | μ̄ | ≠ [(√ n2 +√ n1) / (√ n2 -√ n1)] t, where n1 =1,2,3,..., n2 =2,3,4,..., and n2 > n1, the Hall conductivity is quantized as σxy =± 4 e2 h n, n=0,1,2,..., if | μ̄ | <t and σxy =± 4 e2 h n, n=1,2,3,..., if | μ̄ | >t. However, if | μ̄ | = [(√ n1 +√ n2) / (√ n 2 -√ n1)] t, the ν̄ =±4 (n 1 + n2) n plateaus are absent, where n=1,2,3,... Furthermore, we find that when the magnetic field B=π t2 /Neh υF2, N=1,2,3,..., the ν̄ =0 plateau across μ̄ =0 would disappear and the 8 e2 /h step at μ̄ =t would occur. Finally, we show that in the low-disorder and high-magnetic-field regime, σxx →0, as long as the Fermi level is not close to a Dirac point. © 2010 The American Physical Society.