Macroscopic dielectric tensor at crystal surfaces

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Abstract
We formulate the theory of the macroscopic dielectric tensor for crystals of lower-than-cubic symmetry, using the local-orbital approach to the dielectric response. In the case of noncubic infinite crystals we give a definition of the macroscopic dielectric tensor that is simpler than any previous formulation and allows us to perform realistic calculations with roughly the same computational effort needed in cubic crystals. In the case of semi-infinite crystals, we give for the first time a definition of the macroscopic dielectric tensor and outline a way of computing it from the two-particle Green's function, which can be computed according to the method of Hanke and Sham, including local-field and excitonic effects. A remarkable result is that in both cases the long-range part of the Coulomb interaction does not affect the macroscopic dielectric tensor. Previous formulations of the optical properties of surfaces, which neglected local-field effects, are shown to be yet valid, provided that the macroscopic dielectric tensor replaces the microscopic one.
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