Influence of out of plane response on optical properties of two dimensional materials: First principles approach
The ab initio calculation of optical spectra of sheet crystals usually arranges them in a three dimensional superlattice with a sufficiently large interlayer distance. We show how the resulting frequency dependent dielectric tensor is related to the anisotropic optical conductivity of an individual sheet or to the dielectric tensor of a corresponding film with thickness $d$ Their out of plane component is taken into account, in contrast to usual treatments. We demonstrate that the generalized transfer matrix method to model the optical properties of a layer system containing a sheet crystal accounts for all tensor components. As long as $d\ensuremath{\ll}\ensuremath{\lambda} \ensuremath{\lambda} wavelength of light) this generalized formulation of the optical properties for anisotropic two dimensional (2D) systems of arbitrary thickness reproduces the limits found in literature that are based either on electromagnetic boundary conditions for a conducting surface or on an isotropic dielectric tensor. For $s$ polarized light, the results are independent of the sheet description. For oblique incidence of $p$ polarized light, the tensor nature of the optical conductivity (or the dielectric function) of the sheet crystal strongly impacts on reflectance, transmittance, and absorbance due to the out of plane optical conductivity. The limit $d\ensuremath{\rightarrow}0$ should be taken in the final expressions. Example spectra are given for the group IV honeycomb 2D crystals graphene and silicene.