Ab initio calculations of the electronic and phonon states on the HfC(001)-(1x1) surface

We have investigated the structural and electronic properties of the HfC(001)-(1x1) surface using the density functional theory and the pseudopotential method. The most important feature of the HfC(001) surface relaxation is that both in the surface and subsurface layers C atoms move out of the surface and Hf atoms move inward. In general, our structural results are in good agreement with previous experimental and theoretical works. We have identi fi ed surface electronic states on the HfC(001) surface in the bulk gap pocket around the Fermi energy. Using our calculated atomic and electronic structures, zone-centre and X point surface phonon modes are calculated by employing a linear response approach based on the density functional perturbation theory. Good agreement has been observed between our calculated surface phonons and available experimental results. A hitherto unidenti fi ed surface localized mode has been predicted and its polarization characterists has been examined.