Linear-combination-of-atomic-orbitals description of the electron states at the (0001) surface of hexagonal-close-packed metals

The tight-binding method for calculating the electronic structure of a slab of regulary stacked atomic planes has been extended to treat the case of a (0001) surface of a hexagonal-close-packed (hcp) transition metal. The symmetry of the Hamiltonian is discussed and the basis functions of the representations along high-symmetry lines of the two-dimensional Brillouin zone are given. The theory is applied to the study of a 13-layer slab of hcp scandium. We find that several surface states and resonances arise in the $d$-band region and we discuss the effects of the self-consistency on these surface features. Possible experiments to test the theoretical results are suggested.