Valley current and spin-valley filter in topological domain wall

The gapless edge states with a certain spin and valley index can be realized in topological domain walls. In this work, we study various domain walls thoroughly and demonstrate that multiple kinds of edge states with a perfect spin and valley polarization can be realized, leading to the possibility of establishing spin filters and spin-valley filters. Moreover, the spin and valley index of the edge states can be tuned by an external electric field. We also investigate the finite size effect on the edge states when two domain walls approach each other. Generally, the finite size effect can cause the hybridization of edge states and open a gap. We find that the evolutions of the bandgap as a function of the finite size effect for different topological edge states are distinguished from each other.