A high-quality spin and valley beam splitter in WSe₂ tunnelling junction through the Goos-Hänchen shift

We have theoretically studied the Goos-Hänchen shift of spin and valley electron in single and double barrier WSe₂ tunnelling junctions. For single barrier structure, it has shown that a two-fold degenerate lateral shift induced by the spin-valley locking occurs at Fabry-Perot resonance width. By introducing the ferromagnetic exchange field, one spin and valley dependent lateral shift can be further obtained. Different from single barrier structure, the double barrier structure exhibits two series of Fabry-Perot interferences with lateral shifts exceeding thousands of Fermi wavelengths due to the effect of localized states, and more important, these interferences generated between two potential barriers are even higher than the shift formed inside of two potential barriers. In addition, for a specified Fermi energy, one can modulate the desired spatial separation of spin and valley beam by controlling the incident angle or potential barrier. Our results demonstrate that the proposed WSe₂ double barrier structure is a fascinating candidate for designing high-quality spin and valley beam splitter.