Development of the computational method for determining the electronic structure of semi-infinite crystal surfaces

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In this research program, we have developed a computer code that determines the ground-state electronic structure of semi-infinite crystal surfaces from first-principles. In doing so, the surface region is treated as a localized defect in the surface-normal direction, and the. one-electron Green function in the surface region is calculated with the use of the embedding technique of Inglesfield. The present computer code adopts norm-conserving pseudo-potentials to represent ion cores, and the Green function is expanded by a plane-wave-like basis set. Although the true embedding surface dividing the substrate and surface regions weaves in a complex way in order to avoid crossing the ion-cores where the potential is non-local, we have invented a new method that replaces this curvy embedding surface by an equivalent plane surface. In this method, there is no need to specify' the true curvy surface throughout all the computational procedure at all. Our method can evaluate not only the Green … More function but also one-electron wavefunctions appropriate for the semi-infinite surface geometry. At present, we aredeveloping and testing a computer code for calculating the electronic structure of three-dimensional periodic systems containing localized 2p and transition-metal atomic elements using the augmented plane wave (APW) basis set and also usingthe linearized APW basis set. With this code, it becomes possible to generate the embedding potential of semi-infinite transition metal substrates. As a concrete subject that cannot be treated with the standard repeating-slab-based computational methods, we investigatedsurface resistivity caused by the elastic scattering of conducting electrons at the surface. For this purpose, we derived a general expression of the surface resistivity that can be applicable to arbitrary semi-infinite metallic crystal surfaces. Our calculation for the low-index clean Al surfaces led to an apparently counter-intuitive result that the resistivity of the close-packed (111) surface is nearly 46 times larger than that of the more loosely packed (001) surface. The large difference between the two surfaces.can be attributed to the fact thatthe conduction electrons impinging on the (111) surface of foc crystals cannot be reflected in specular direction because of the lack of the reflection symmetrywith respect to the (111) crystalplane. Thus, all the conduction electrons change their velocity in the plane when they are incident on the (111) surface, thus contributing to the resistivity of the system. Less