Giant Goos-H\"{a}nchen Shift in Graphene Double-barrier Structures

We report giant Goos-H"{a}nchen shifts [Goos and H"{a}nchen, Ann. Phys. 436, 333 (1947)] for electron beams tunneling through graphene double barrier structures. We find that inside the transmission gap for the single barrier, the shift displays sharp peaks with magnitudes up to the order of electron beam width and rather small full-widths-at-half-maximum, which may be utilized to design valley and spin beam splitters with wide tunability and high energy resolution. We attribute the giant shifts to quasibound states in the structures. Moreover, an induced energy gap in the dispersion can increase the tunability and resolution of the splitters.