Dc and ac transport in silicene

We investigate dc and ac transport in silicene in the presence of a perpendicular electric field Ez that tunes its band gap, finite temperatures, and level broadening. The interplay of silicene's strong spin-orbit interaction and the field Ez gives rise to topological phase transitions. We show that at a critical value of Ez the dc spin-Hall conductivity undergoes a transition from a topological insulator phase to a band insulator one. We also show that the spin- and valley-Hall conductivities exhibit a strong temperature dependence. In addition, the longitudinal conductivity is examined as a function of the carrier density ne, for screened Coulomb impurities of density ni, and found to scale linearly with ne/ni. It also exhibits an upward jump at a critical value of ne that is associated with the opening of a new spin subband. Furthermore, the contributions of the spin-up and spin-down carriers to the power absorption spectrum depend sensitively on the topological phase and valley index. Analytical results are presented for both dc and ac conductivities in the framework of linear response theory.