| Similar to graphene, silicene has a honeycomb geometry, where the charge carries behave like massless Dirac fermions. The energy spectrum of silicene is the linear dispersion relation. The most stable configuration in the silicene prefers to occur as a low buckled structure, which means that the sublattice A and B with an equilibrium buckling of 0.066 nm, which provides a possibility to tune the energy band gap and the topological properties of silicene by an external electric field. The buckling also provides a convenient method to tune stagger potential by normally applying an electric field. Distinct from graphene, silicene possesses a stronger intrinsic spin-orbit(SO) coupling. Therefore, silicene becomes a good candidate to realize the quantum spin Hall(QSH) state at room temperature, which will provide potential applications in spintronics. In device fabrications and applications, silicene’s allotropic affinity with bulk silicon suggest a more direct integration with ubiquitous semiconductor technology. Recently, the growth of silicene on different substrates was reported by several experiments. With the development of technology, better silicene has been synthesized.Firstly, we investigate the topological insulator state of gated bilayer silicene in the presence of extrinsic Rashba SO coupling. The system exhibits a band insulator(BI)phase for small Rashba SO coupling, and then translate to a strong topological insulator(TI) phase with both spin and valley filtered at large Rashba SO coupling. The strong TI phase is robust in the presence of intrinsic SO and intrinsic Rashba SO couplings. When a titled electric field is introduced, the in-plane component of the electric field gives rise to an interlayer Rashba SO coupling, and the system turns to a BI phase no matter how large the Rashba SO coupling and bias voltage are. Moreover, the system shows a topological phase transition from BI phase to strong TI phase by removing the titled external electric filed.Secondly, we find the topological properties of bilayer silicene is different from that of bilayer graphene. Hence, we systematically investigate the topological insulator states of the two-dimensional hexagon lattice bilayers. The system exhibits a quantum valley Hall(QVH) state when the interlayer interaction t⊥ is smaller than the nearest neighbor hooping energy t, and then translates to a trivial BI state when t⊥/t > 1. Interestingly,the system is found to be a single-edge QVH state with t⊥/t = 1. The QVH states have different edge modes carrying valley current but no net charge current. The bias voltage and external electric field can be tuned easily in experiments. So the present results will provide potential applications in valleytronics.Finally, we show the spin-charge separation in the quantum spin Hall(QSH) state,which is a partially gated silicene ribbon with a unitary magnetic field and exchange field. By manipulating the bias voltage, the electron current with given spin direction can emerged on different interfaces and edges of the nonuniform gated silicene ribbon. And in this progress, the direction and the spin direction of the electron current are unchanged, so that the QSH state persists. The spin Hall conductance is quantized and robust to disorder or impurity scattering. Moreover, the spin-filtered electron current is also presented. |
