Surface electronic structure with the linear methods of band theory

Abstract

We present an ab initio method for calculating electron states in a semi-infinite crystal. The complex band structure is obtained by the extended linear augmented-plane-wave method within the exact $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ formulation of the band-structure problem. We also present a variational scheme of matching the wave functions at the interface. The practical applicability of the method is demonstrated by solving the Schr\odinger equation for the (100) surface of Al. We have calculated the normal incidence low-energy electron-diffraction spectra, the occupied surface state at the \ensuremath{\Gamma} point, and the normal-emission photoelectron spectra within the one-step model. The results are in a good agreement with available measurements. We have developed a simplified procedure to assess the conducting properties of a crystal surface in terms of the ${\mathit{k}}_{\ensuremath{\parallel}}$-projected real band structure. We introduce a new quantity, the conductance index, whose energy dependence is shown to yield gross features of the exact energy dependence of transmitted current.