We present first-principles studies of the optical absorbance of the group IV honeycomb crystals graphene, silicene, germanene, and tinene. We account for many-body effects on the optical properties by using the non-local hybrid functional HSE06. The optical absorption peaks are blueshifted due to quasiparticle corrections, while the influence on the low-frequency absorbance remains unchanged and reduces to a universal value related to the Sommerfeld fine structure constant. At the Dirac points spin-orbit interaction opens fundamental band gaps; parabolic bands with a very small effective mass emerge. Consequently, the low-frequency absorbance is modified with a spin-orbit-induced transparency region and an increase of the absorbance at the fundamental absorption edge.

We show that the low-frequency absorbance of undoped graphene, silicene, and germanene has a universal\ud value, only determined by the Sommerfeld fine-structure constant. This result is derived by means of ab initio\ud calculations of the complex dielectric function for optical interband transitions applied to two-dimensional (2D)\ud crystals with honeycomb geometry. The assumption of chiral massless Dirac fermions is not necessary. The\ud low-frequency absorbance does not depend on the group-IV atom, neither on the sheet buckling nor on the orbital\ud hybridization. We explain these findings via an analytical derivation of the relationship between absorbance and\ud fine-structure constant for 2D Bloch electrons. The effect of deviations of the electronic bands from linearity is\ud also discussed

We compute the optical conductivity of 2D honeycomb crystals beyond the usual Dirac-cone approximation. The calculations are mainly based on the independent-quasiparticle approximation of the complex dielectric function for optical interband transitions. The full band structures are taken into account. In the case of silicene, the influence of excitonic effects is also studied. Special care is taken to derive converged spectra with respect to the number of k points in the Brillouin zone and the number of bands. In this way both the real and imaginary parts of the optical conductivity are correctly described for small and large frequencies. The results are applied to predict the optical properties reflection, transmission and absorption in a wide range of photon energies. They are discussed in the light of the available experimental data.

Calculating the complex dielectric function for optical interband transitions we show that the\ud two-dimensional crystals silicene and germanene possess the same low-frequency absorbance as\ud graphene. It is determined by the Sommerfeld finestructure constant. Deviations occur for higher\ud frequencies when the first interband transitions outsideKorK\ud 0\ud contribute. The low-frequency results are a consequence of the honeycomb geometry but do not depend on the group-IV atom, the sheet buckling,\ud and the orbital hybridization. The two-dimensional crystals may be useful as absorption normals in\ud silicon technolog

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By means of first-principles calculations we predict the stability of silicene layers as buckled honeycomb lattices on Cl-passivated Si(1 1 1) and clean CaF2(1 1 1) surfaces. The van der Waals interaction between silicene and the inert substrate stabilizes the adsorbate system while not destroying the Si pz-derived linear bands forming Dirac cones at the Brillouin zone corners. Only small gaps of about 3 and 52 meV are opened.

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