Fig. 1
a Schematic diagram of the precession process of the states (K,↑)(red sphere) and (K′,↓)(blue sphere) through a silicene sheet with two parallel line defects, where the blue (red) circle denotes the A(B) sublattice. The states (K,↑) and (K′,↓) circulate along the pseudo-edge, and the RSOC as well as electric field is assumed to exist on the french grey region. W(W=2) and WR(WR=1) represent the width of the scattering region in units of \(\sqrt {3}a\). b The simplifed lattice model of the infnite silicene with a line defect, where θ=kya and the dotted rectangle corresponds to a supercell. In the unit cell, the lattice points are specified by a set of indices (L,l). c The transmission for one spin state in the K(K′) valley across line defect with inversion domain boundaries. The insets show the orientation of the crystalline lattice in the two domains separated by the line defect (dashed line). The thick/thin lines indicate that the transmission is restrained across the line defect due to the helical edge states flowing inversely along the pseudoedge