Photoinduced quantum spin/valley Hall effect and its electrical manipulation in silicene

Based on the Kubo linear response theorem, we have investigated theoretically the quantum spin/valley Hall (QS/VH) conductivities and longitudinal conductivity of silicene in the presence of a perpendicular electric field and off-resonant circularly polarized light at the high frequency limit. It has been demonstrated that the electronic structure for silicene can be effectively modulated to be spin degenerate, (Floquet) topologically insulated, valley-spin polarized metallic, and band insulated states by the electric field and/or off-resonant light. Both the spin and valley Hall conductivities of the system for different effective energies induced by the off-resonant light behave a pronounced stepwise structure with the quantized values of (0, ±1, ±2)e2∕h and are symmetry with the back-gate voltage controllable staggered sublattice potential. The step-like quantum spin and valley Hall conductivities should be smoothed with the increase in the temperature. Wherever the system longitudinal conductivity exh...