We show that the density of states and the thermodynamic properties of a 2D d-wave superconductor in the vortex state with applied magnetic field H in the plane depend on the angle between H and the order parameter nodes. Within a semiclassical treatment of the extended quasiparticle states, we obtain fourfold oscillations of the specific heat, measurement of which provides a simple probe of gap symmetry. The frequency dependence of the density of states and the temperature dependence of thermodynamic properties obey different power laws for field in the nodal and anti-nodal direction. The fourfold pattern is changed to twofold when orthorhombicity is considered.

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.

When a bilayer of graphene is placed in a suitably configured field effect device, an asymmetry gap can be generated and the carrier concentration made different in each layer. This provides a tunable semiconducting gap, and the valence and the conductance band no longer meet at the two Dirac points of the graphene Brillouin zone. We calculate the optical conductivity of such a semiconductor with particular emphasis on the optical spectral weight redistribution brought about by changes in gap and chemical potential due to charging. We derive an algebraic formula for arbitrary value of the chemical potential for the case of the bilayer conductivity without a gap.

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.