A valley and spin filter based on gapped graphene

We study highly valley- and spin-polarized current in single-layer gapped graphene without spin-orbit coupling. The structure considered is a three-barrier structure with one spin-splitting barrier and two electrical potential barriers with vector potentials. The electrons in the two valleys transmit differently because of the valley-dependent reflection between two adjacent barriers, while the spin-up and spin-down electrons transmit differently because of the spin splitting. The structure is different from other structures in which spin-orbit coupling plays an important role in the observation of valley- and spin-polarized current. We can control the spin and valley polarization by changing the width of the barrier or the strength of the spin splitting. The structure proposed in this paper can be used to make valley and spin devices.