Time-reversal breaking and spin transport induced by magnetic impurities in a 2D topological insulator

We employed the formalism of bond currents, expressed in terms of non-equilibrium Green's function to obtain the local currents and transport features of zigzag silicene ribbon in the presence of magnetic impurity. When only intrinsic and Rashba spin-orbit interactions are present, silicene behaves as a two-dimensional topological insulator with gapless edge states. But in the presence of finite intrinsic spin-orbit interaction, the edge states start to penetrate into the bulk of the sample by increasing Rashba interaction strength. The exchange interaction induced by local impurities breaks the time-reversal symmetry of the gapless edge states and influences the topological properties strongly. Subsequently, the singularity of partial Berry curvature disappears and the silicene nanoribbon becomes a trivial insulator. On the other hand, when the concentration of the magnetic impurities is low, the edge currents are not affected significantly. In this case, when the exchange field lies in the x-y plane, the spin mixing around magnetic impurity is more profound rather than the case in which the exchange field is directed along the z-axis. Nevertheless, when the exchange field of magnetic impurities is placed in the x-y plane, a spin-polarized conductance is observed. The resulting conductance polarization can be tuned by the concentration of the impurities and even completely polarized spin transport is achievable.