Possible quantized charge pump in bilayer and trilayer graphene

We report a theoretic study of the two-parameter adiabatic charge pump based on the bilayer and trilayer graphene systems. The two perpendicular time-dependent electric fields with a phase lag between them are taken as the pumping potentials, which induce an instant energy gap in each pumping region. Based on both a continuum model and a lattice model, we show that the pumping results from the bilayer and trilayer graphene systems are very different when the Fermi energy happens to reside in the opened energy gap: there is no pumping current for the bilayer system whereas a quantized charge pumping effect emerges in the trilayer-graphene based pump device. This difference can be accounted for by the different Berry phases of Dirac electrons in the two systems. Our findings may shed a light on developing a quantized charge pumping device.