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.

The thermoelectric power factor of hierarchically nanostructured materials is investigated using the non-equilibrium Green's function method for quantum transport, including interactions of electrons with acoustic and optical phonons. We describe hierarchical nanostructuring by superlatticelike potential barriers/wells, combined with quantum dot barriers/wells nanoinclusions as well as voids in the intermediate region. We show that these structures can be designed in a way that the power factor is not only largely immune to the presence of the nanostructure features, but under certain conditions benefits can be achieved as well. Interestingly, we show that these design approaches are linked to the energy relaxation of the current flow and whether charge carrier scattering is limited by elastic or inelastic processes. In particular, when nanostructures form potential barriers, the power factor can be substantially enhanced under elastic scattering conditions, irrespective of nanostructuring density and potential barrier heights. When inelastic scattering processes dominate, however, the power factor is inevitably degraded. In the case in which nanostructures form potential wells, despite a slight decrease, the power factor is quite resilient under either elastic or inelastic scattering processes. These nanostructuring design approaches could help open the path to the optimization of new generation nanostructured thermoelectric materials by not only targeting reductions in thermal conductivity, but simultaneous improvements in the power factor as well.

The low-energy physics of silicene is described by Dirac fermions with a strong spin-orbit interaction and its band structure can be controlled by an external perpendicular electric field E z . We investigate the commensurability oscillations in silicene modulated by a weak periodic potential V = V 0 cos(2πy/a 0 ) with a 0 as its period, in the presence of a perpendicular magnetic field B and of a weak sinusoidal electric field E z = E 0 cos(2πy/b 0 ), where b 0 is its period. We show that the spin and valley degeneracy of the Landau levels is lifted, due to the modulation, and that the interplay between the strong spin-orbit interaction and the potential and electric field modulations can result in spin-and valley-resolved magnetotransport. At very weak magnetic fields the commensurability oscillations induced by a weak potential modulation can exhibit a beating pattern depending on the strength of the homogenous electric field E z but this is not the case when only E z is modulated. The Hall conductivity plateaus acquire a step structure, due to spin and valley intra-Landau-level transitions, that is absent in unmodulated silicene. The results are critically contrasted with those for graphene and the two-dimensional electron gas.

We study ballistic electron transport through silicene barriers, of width d and height U, in the presence of an exchange field M and a normal electric field Ez. Away from the Dirac point (DP), the spin- and valley-resolved conductances, as functions of U, exhibit resonances while close to it there is a pronounced dip that can be transformed into a transport gap by varying Ez. The charge conductance gc changes from oscillatory to a monotonically decreasing function of d beyond a critical Ez and this can be used to realize electric-field-controlled switching. Further, the field M splits each resonance of gc into two spin-resolved peaks. The spin polarization near the DP increases with Ez or M and becomes nearly perfect above certain of their values. Similar results hold for double barriers.