Valley beam splitter based on strained graphene

We investigate theoretically the lateral displacements of valley-unpolarized electron beams in graphene after traversing a strained region. Valley double refraction occurs at the interface between the incident (unstrained) region and the strained region, in analogy with optical double refraction. It is shown that the exiting positions of K and K 0 transmitted beams, together with their distance D, can be tuned by the strain strength and the inclusion of an electrostatic potential. In addition, D can be enhanced by the wave effect near the valley-dependent transmission resonances. The enhancement is remarkable for graphene n-p-n (or p-n-p) junctions. Thus the Goos-Hanchen effect of transmitted beams for a normal/strained/normal graphene junction can be utilized to design a valley beam splitter.