Pure spin current and perfect valley filter by designed separation of the chiral states in two-dimensional honeycomb lattices

We propose a realization of pure spin currents and perfect valley filters based on a quantum anomalous Hall insulator, around which edge states with up spin and down spin circulate. By applying staggered sublattice potential on the strips along the edges of sample, the edge states with down spin can be pushed into the inner boundaries of the strips while the other edge states with up spin remain on the outer boundaries, resulting in spatially separated chiral states with perfect spin polarization. Moreover, a valley filter, which is immune to both long-range and short-range scatterers, can be engineered by additionally applying boundary potentials on the outmost lattices of the sample. We also find that the boundary potential can be used to control the size effect induced oscillation of the inner chiral states. The connection of the boundary potential to size effect is revealed.