Effect of Zeeman splitting and interlayer bias potential on electron transport in bilayer graphene

Motivated by the recent experiments [Weitz , ScienceSCIEAS0036-807510.1126/science.1194988 330, 812 (2010) and Kim , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.016803 107, 016803 (2011)], we present here a theoretical analysis for the Hall resistance, the longitudinal resistance, and the Hall conductance of a six-terminal bilayer graphene Hall bar under a perpendicular magnetic field. The Landauer-Büttiker formalism combined with the nonequilibrium Green function method is applied. In the presence of both the Zeeman splitting and interlayer bias potential U, the spin and valley degeneracies of Landau levels are lifted, which leads to the result that the filling factor ν can be an arbitrary integer number and the Hall resistance exhibits a quantum plateau at 1/ν(h/e²). While ν=0, the system can be in both the spin-polarized and valley-polarized regions. For the valley-polarized ν=0 region, the longitudinal resistance is predicted to have a very large value which means that the system is a quantum Hall insulator even though there are four states in the Fermi surface. However, in the spin-polarized ν=0 region, the system is predicted to display a quantum spin Hall effect, in which the spin-up and spin-down edge states are counterpropagating. In both the spin-polarized and valley-polarized ν=0 regions, the Hall conductances show zero quantum plateaus, although the Hall resistances are very different. In addition, due to the counterpropagating edge states, the longitudinal resistance exhibits some fractional quantum plateaus with values 2/9(h/e²), 1/4(h/e²), 1/2(h/e²), etc.