Valley polarization of electrons in a graphene under modulations of the electrostatic potential barrier and the magnetic field

The valley polarization is a fundamental concept in valleytronic applications. However, the combined effects of the electrostatic potential barrier and the magnetic field as well as strains on the valley polarization in a graphene have been rarely reported. Therefore, in this paper, we use the transfer-matrix method to illustrate effects of the height and width of the electrostatic barrier and the strength of the applied magnetic field on the valley polarization of electrons in a graphene, and we find that the valley polarization strongly depends on the strength and width of the electrostatic barrier. We also find that the 100% valley polarization can be achieved continuously and smoothly over a wide range of Fermi energy region by controlling the strength of the applied magnetic field. This point makes it easier to design novel valleytronic devices based on graphene with the presence of the magnetic field and the electrostatic potential barrier as well as strains.