Manipulating topological intravalley and intervalley scatterings of inner edge states in hybrid nanoribbons

We investigate the formation of inner edge states and their transport properties in hybrid nanoribbons. Some new inner edge states, such as spin-polarized, spin-valley-polarized and valley-polarized antichiral inner edge states, are obtained, different from the current existence of valley- and spin-valley-momentum locked inner edge states. We also obtain general formula of local bond current with the wave-function matching technique and use it to discover three interesting transport phenomena of the intravalley and intervalley scatterings that depend on the propagating direction, propagating path, spin mode and wave-vector mismatches between inner edge states. In particular, these transport phenomena are further used to design topological spin, spin–valley and valley filters and be representative for graphene, silicene, germanene and stanene, supporting a potential application of inner edge states, which are robust against random vacancies.