Interface edge states and quantum Hall effect in graphene under a modulated magnetic field

Graphene properties can be manipulated by a periodic potential. Based on the tight-binding model, we study graphene under a one-dimensional modulated magnetic field which contains both a uniform and a staggered component. The chiral current-carrying edge states generated at the interfaces where the staggered component changes direction, lead to an unusual integer quantum Hall effect in graphene, which can be observed experimentally by a standard four-terminal Hall measurement. When Zeeman splitting is taken into account, an anomalous state is predicted where the electron edge currents with opposite spin polarization propagate in the opposite directions at one sample boundary, whereas propagate in the same directions at the other sample boundary. Furthermore, all the interface edge currents are fully spin polarized with the same spin direction, which is expected to have potential application in spintronic devices.