Microscopic theory of surface resistivity

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Abstract
A microscopic expression of surface resistivity for semi-infinite metallic systems is derived based on linear response theory. The surface resistivity in the present model is determined by asymptotic behaviors of one-electron wave functions at the Fermi energy alone. Moreover, it coincides with the semiclassical result based on the Boltzmann equation if the probability of diffuse scattering at the surface was independent of the direction of scattered waves. As an application, we evaluate the surface resistivity of clean and stepped Al surfaces. The surface resistivity increases greatly when the direction of the current is perpendicular to steps.