Anomalous integer quantum Hall effect in AA-stacked bilayer graphene

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 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 (v) over bar = 0 plateau) and chirality for vertical bar(mu) over bar vertical bar is the filling factor, (mu) over bar 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 vertical bar(mu) over bar vertical bar not equal [(root n(2) + root n(1))/(root n(2) - root n(1))]t, where n(1)= 1,2,3,..., n(2)= 2,3,4,..., and n(2) > n(1), the Hall conductivity is quantized as sigma(xy) = +/- 4e(2)/h n, n= 0,1,2,..., if vertical bar(mu) over bar vertical bar < t and sigma(xy) = +/- 4e(2)/h n, n=1,2,3,..., if vertical bar<(mu)over bar>vertical bar > t. However, if vertical bar(mu) over bar vertical bar= [(root n(2) + root n(1))/(root n(2) - root n(1))]t, the (v) over bar = +/- 4 (n(1)+n(2))n plateaus are absent, where n= 1,2,3,... Furthermore, we find that when the magnetic field B=pi t(2)/Nehv(F)(2) N = 1,2,3,..., the (v) over bar = 0 plateau across (mu) over bar = 0 would disappear and the 8e(2)/h step at (mu) over bar = t would occur. Finally, we show that in the low-disorder and high-magnetic-field regime, sigma(xx)-> 0, as long as the Fermi level is not close to a Dirac point.