Magnetic barrier on strained graphene: A possible valley filter

We put forward a two-terminal valley filter based on a bulk graphene sheet under the modulations of both a local perpendicular magnetic field and a substrate strain. When only one of the two modulations is present, no valley polarization can be generated. A combination of the two modulations leads to a different (but not opposite) shifts of the K and K' valleys, which could be utilized to generate a valley-polarized current. The degree of the valley polarization can be tuned by the strain strength and the inclusion of a scalar potential. The valley polarization changes its polarity as the local magnetic field switches its direction.