Abstract: Using the tight-binding formalism, we study spin and charge transport through a zigzag silicene ribbon subject to an external electric field E-z. The effect of an exchange field M-z is also taken into account and its consequences on the band structure as well as spin transport are evaluated. We show that the band structure lacks spin inversion symmetry in the presence of intrinsic spin-orbit interaction in combination of E-z and M-z fields. Our quantum transport calculations indicate that for certain energy ranges of the incoming electrons the silicene ribbon can act as a controllable high-efficiency spin polarizer. The polarization maxima occur simultaneously with the van Hove singularities of the local density of states. In this case, the combination of electric and exchange fields is the key to achieving nearly perfect spin polarization, which also leads to the appearance of additional narrow plateaus in the quantum conductance. Moreover, we demonstrate that the output current still remains completely spin-polarized for low-energy carriers even when a few edge vacancies are present.

Abstract: 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(2 pi y/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(2 pi y/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 Ez but this is not the case when only Ez 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.

Abstract: We derive an exact solution to the problem of spin snake states induced in a nonhomogeneous magnetic field by a combined action of the Rashba spin-orbit and Zeeman fields. The electron spin behavior as a function of the cyclotron orbit center position and an external homogeneous magnetic field was obtained. It is shown that in an antisymmetric magnetic field the electron spin in the snake states has only an in-plane projection, perpendicular to the magnetic interface, which vanishes at large positive momenta. Applying an external homogeneous magnetic field adds a finite out-of-plane spin component and simultaneously gaps out the spectral branches, which results in regular beating patterns of the spin current components.

Abstract: We investigate the effect of Rashba and intrinsic spin-orbit couplings on the electronic properties and spin configurations of Dirac fermions confined in: (i) a flat graphene sheet, (ii) a graphene wire with p-n-p structure, and (iii) a superlattice of graphene wires. The interplay between the spin-orbit interaction mechanisms breaks the electron-hole symmetry and the spin configuration induced by Rashba spin-orbit coupling lacks inversion symmetry in k space. We show that the Rashba spin-orbit interaction doubles the Fabry-Perot resonant modes in the transmission spectrum of a graphene wire and opens new channels for the electron transmission. Moreover, it leads to the appearance of spin split extra Dirac cones in the energy spectrum of a graphene superlattice. It is shown that the spin of the electrons and holes confined in a flat graphene sheet is always perpendicular to their motion while this is not the case for the other nanostructures.