Many body effects in the electronic and optical properties of the (1 1 1) surface of diamond

The (1 1 1) face is the cleavage surface of diamond. Understanding its properties is very important for the growing technological interest on the chemistry of diamond surfaces. Within DFT the most stable reconstruction is the Pandey chain model, the atoms on the chain being neither buckled nor dimerised. However this geometry gives rise to a semi metallic band structure in contrast with experimental findings that show the presence of a gap ranging from 0.5 to 2 eV. Here we show that the same equilibrium geometry and thus the same metallic band structure is found relaxing the surface using screened exchange (sX) or Hartree-Fock (HF) functionals. We will discuss in detail how breaking the equivalence of the atoms on the chain affects the band structure and we will show that a buckling would yield a semiconducting surface, but is energetically unfavorable. A semiconducting character can be restored, within the equilibrium geometry, if quasiparticle corrections are carefully included within an iterative GW scheme. The result of the theoretical reflectance anisotropy spectra (RAS) at a DFT-RPA level are also presented and discussed. As expected, a strong anisotropy signal is found at low energies due to transitions between surface states inside the fundamental gap.