Linearized augmented plane-wave method for the electronic band structure of thin films

Abstract

We present a new method for treating the electronic structure of thin films which is based on a generalization of the bulk linearized augmented-plane-wave (LAPW) method. This method avoids using the slab-superlattice geometry and combines the advantages of energy-independent muffin-tin Hamiltonian methods [fast root evaluation and rapid convergence for $d$-band metals as well as for nearly-free-electron (NFE) crystals] with the simple matrix element determination of the original augmented plane-wave (APW) method. As in the bulk LAPW method, the asymptote problem of the APW method is avoided, and the basis functions are everywhere continuous and differentiable. In addition, the film LAPW method retains such desirable features of the APW method as the ability to treat general potentials with no shape approximations, the ease with which relativistic effects can be included, and the fact that the basis size does not increase substantially for heavier elements. As a first application and test of the method, non-self-consistent calculations are performed in the local-density approximation for exchange and correlation and with the one-electron potential constructed from a superposition of atomic charge densities. A semirelativistic formulation is employed in which the Dirac equation is solved in the limit of zero spin-orbit coupling inside the muffin-tin spheres. Results are reported for up to five atomic layer thin films (slabs) of the transition metals Fe, Co, Ni, and Cu and a nine-layer film of the NFE metal Al. The results are in generally good agreement with other theoretical calculations. Some trends in the transition-metal band structures are discussed. A surface-state surface-resonance band for Al(001) is found to completely account for and clarify behavior observed in very recent photoemission measurements.