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 σ_{xy} and also longitudinal conductivity σ_{xx} of the AA stacked BLG within the linearresponse 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≠[(n_{2}+n_{1})/(n_{2}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 σ_{xy}=±(4e^{2})/(h)n,n=0,1,2,… , if μ̄<t and σ_{xy}=±(4e^{2})/(h)n,n=1,2,3,… , if μ̄>t . However, if μ̄=[(n_{1}+n_{2})/(n_{2}n_{1})]t , the ν̄=±4(n_{1}+n_{2})n plateaus are absent, where n=1,2,3,… Furthermore, we find that when the magnetic field B=πt^{2}/Nehυ_{F}^{2} , N=1,2,3,… , the ν̄=0 plateau across μ̄=0 would disappear and the 8e^{2}/h step at μ̄=t would occur. Finally, we show that in the lowdisorder and highmagneticfield regime, σ_{xx}→0 , as long as the Fermi level is not close to a Dirac point.
 Publication:

Physical Review B
 Pub Date:
 October 2010
 DOI:
 10.1103/PhysRevB.82.165404
 arXiv:
 arXiv:1008.0748
 Bibcode:
 2010PhRvB..82p5404H
 Keywords:

 73.43.Cd;
 71.70.Di;
 72.80.Vp;
 73.22.Pr;
 Theory and modeling;
 Landau levels;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 submitted to Physical Review B