Valleytronic topological filters in silicene-like inner-edge systems

Inner edge state with spin and valley degrees of freedom is a promising candidate for designing a dissipationless device due to the topological protection. The central challenge for the application of the inner edge state is to generate and modulate the polarized currents. In this work, we discover a new mechanism to generate fully valley- and spin-valley-polarized current caused by the Bloch wavevector mismatch (BWM). Based on this mechanism, we design some serial-typed inner-edge filters. By using once of the BWM, the coincident states could be divided into transmitted and reflected modes, which can serve as a valley or spin-valley filter. In particular, while with twice of the BWM, the incident current is absolutely reflected to support an off state with a specified valley and spin, which is different from the gap effect. These findings give rise to a new platform for designing valleytronics and spin-valleytronics.