A bipolar spin-filtering effect in graphene zigzag nanoribbons with spin-orbit coupling.

We predict a large spin-filtering effect in graphene zigzag nanoribbons in the presence of Rashba spin-orbit coupling. The spin polarization of the transmitted current reaches a maximum when the incoming electrons occupy only one subband and the outgoing electrons occupy two subbands (spin is not taken into account). This situation can be reached by applying a potential barrier or a width constriction to the incoming lead of the ribbon. A simple physical picture is provided to explain the spin-filtering effect. Because of the electron-hole symmetry and the time-reversal symmetry, the spin-filtering is antisymmetric for the hole when compared with that for the electron. So the bipolar spin-polarized current can be generated by tuning the Fermi energy across the Dirac point. Besides, the wedge-shaped constriction can modify the conductance spin polarization.