Spin-Valley Beam Splitter in Graphene

The fourfold spin-valley degenerate degrees of freedom in bulk graphene can support rich physics and novel applications associated with multicomponent quantum Hall effects and linear conductance filtering. In this work, we study how to break the spin-valley degeneracy of electron beams spatially. We propose a spin-valley beam splitter in a gated ferromagnetic/pristine/strained graphene structure. We demonstrate that, in a full resonant tunneling regime for all spin-valley beam components, the formation of quasi-standing waves can lead four giant lateral Goos-H\"{a}nchen shifts as large as the transverse beam width, while the interplay of the two modulated regions can lead difference of resonant angles or energies for the four spin-valley flavors, manifesting an effective spin-valley beam splitting effect. The beam splitting effect is found to be controllable by the gating and strain.