We calculate the magneto-optical conductivity and electronic density of states for silicene, the silicon equivalent of graphene, and similar crystals such as germanene. In the presence of a perpendicular magnetic field and electric field gating, we note that four spin- and valley-polarized levels can be seen in the density of states, and transitions between these levels lead to similarly polarized absorption lines in the longitudinal, transverse Hall, and circularly polarized dynamic conductivity. While previous spin and valley polarization predicted for the conductivity is only present in the response to circularly polarized light, we show that distinct spin and valley polarization can also be seen in the longitudinal magneto-optical conductivity at experimentally attainable energies. The frequency of the absorption lines may be tuned by the electric and magnetic field to onset in a range varying from THz to the infrared. This potential to isolate charge carriers of definite spin and valley label may make silicene a promising candidate for spin- and valleytronic devices.

We explore the dielectric properties of graphene-like two-dimensional Kane-Mele topological insulators manifest in buckled honeycomb lattices (ex. silicene, germanene, etc.). The effect of an onsite potential difference (∆z) between sublattices is given particular attention. We present the results for the real and imaginary parts of the dynamical polarization function. We show that these results display features of three regimes (topological insulator, valley-spin polarized metal, and trivial band insulator) and may be used to extract information on the strength of the intrinsic spin-orbit coupling. We study the inverse dielectric function and provide numerical results for the plasmon branch. We discuss the behaviour of the plasmon as a function of sublattice potential difference and show that the behaviour of the plasmon branch as ∆z is varied is dependent on the location of the chemical potential with respect to the gaps. The static polarization is discussed and numerical results for the screening of a charged impurity are provided. We observe a beating phenomenon in the effective potential which is dependent on ∆z.PACS numbers: 71.45. Gm, 77.22.Ch, 81.05.eu II. LOW-ENERGY MODELIt has been shown 3,10,11,25 that the low-energy Hamiltonian of a buckled honeycomb lattice, with an intrinsic

We investigate the optical response of the silicene and similar materials, such as germanene, in the presence of an electrically tunable band gap for variable doping. The interplay of spin orbit coupling, due to the buckled structure of these materials, and a perpendicular electric field gives rise to a rich variety of phases: a topological or quantum spin Hall insulator, a valley-spin-polarized metal and a band insulator. We show that the dynamical conductivity should reveal signatures of these different phases which would allow for their identification along with the determination of parameters such as the spin orbit energy gap. We find an interesting feature where the electric field tuning of the band gap might be used to switch on and off the Drude intraband response. Furthermore, in the presence of spin-valley coupling, the response to circularly polarized light as a function of frequency and electric field tuning of the band gap is examined. Using right-and left-handed circular polarization it is possible to select a particular combination of spin and valley index. The frequency for this effect can be varied by tuning the band gap.

We calculate the dynamical conductivity of AA-stacked bilayer graphene as a function of frequency and in the presence of a finite chemical potential due to charging. Unlike the monolayer, we find a Drude absorption at charge neutrality in addition to an interband absorption with onset of twice the interlayer hopping energy. At finite doping, the interband absorption exhibits two edges which depend on both chemical potential and interlayer hopping energy. We study the behaviour as a function of varying chemical potential relative to the interlayer hopping energy scale and compute the partial optical sum. The results are contrasted with the previously published case of ABstacking. While we focus on in-plane conductivity, we also provide the perpendicular conductivity for both AB and AA stacking. We also examine conductivity for other variations with AA-stacking, such as AAA-stacked trilayer. Based on proposed models for topological insulators discussed in the literature, we also consider the effect of spin orbit coupling on the optical properties of an AA-stacked bilayer which illustrates the effect of an energy gap opening at points in the band structure.

Within a Kubo formalism, we study dc transport and ac optical properties of 3D Dirac and Weyl semimetals. Emphasis is placed on the approach to charge neutrality and on the differences between Dirac and Weyl materials. At charge neutrality, the zero-temperature limit of the dc conductivity is not universal and also depends on the residual scattering model employed. However, the Lorenz number L retains its usual value L0. With increasing temperature, the Wiedemann-Franz law is violated. At high temperatures, L exhibits a new plateau at a value dependent on the details of the scattering rate. Such details can also appear in the optical conductivity, both in the Drude response and interband background. In the clean limit, the interband background is linear in photon energy and always extrapolates to the origin. This background can be shifted to the right through the introduction of a massless gap. In this case, the extrapolation can cut the axis at a finite photon energy as is observed in some experiments. It is also of interest to differentiate between the two types of Weyl semimetals: those with broken time-reversal symmetry and those with broken spatialinversion symmetry. We show that, while the former will follow the same behaviour as the 3D Dirac semimetals, for the zero magnetic field properties discussed here, the latter type will show a double step in the optical conductivity at finite doping and a single absorption edge at charge neutrality. The Drude conductivity is always finite in this case, even at charge neutrality.