Tunable wavevector and spin filtering in graphene induced by resonant tunneling

The resonant tunneling in graphene superlattices with an exchange field is studied theoretically. The results show that a resonant tunneling occurs in the transmission gap by virtue of the transverse wave vector. The position, width, and number of resonant tunneling can be effectively manipulated by adjusting the barrier strength, barrier width, and well width, respectively, which indicates the remarkable wavevector filtering behavior. This resonant effect together with the exchange splitting can be utilized to design an efficient spin filter. It is also found that the energy spectrum in the bound region displays bandlike distribution due to the coupling of eigenstates.