Dc and ac transport in silicene

We investigate dc and ac transport in silicene in the presence of a perpendicular electric field E-z that tunes its band gap, finite temperatures, and level broadening. The interplay of silicene's strong spin-orbit interaction and the field E-z gives rise to topological phase transitions. We show that at a critical value of E-z 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 n(e), for screened Coulomb impurities of density n(i), and found to scale linearly with n(e)/n(i). It also exhibits an upward jump at a critical value of n(e) 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.