Dielectric band structure of crystals: General properties and calculations for silicon

We develop the dielectric band-structure method, originally proposed by Baldereschi and Tosatti, for the description of microscopic electronic screening in crystals. Some general properties are examined first, including the requirements of causality and stability. The specific test case of silicon is then considered. Dielectric bands are calculated, according to several different prescriptions for the construction of the dielectric matrix. It is shown that the results allow a very direct appraisal of the screening properties of the system, as well as of the quality of the dielectric model adopted. The electronic charge displacement induced by ${\Gamma }_{25}^{\prime }$ and $X_3$ phononlike displacements of the atoms is also calculated and compared with the results of existent fully self-consistent calculations. Conclusions are drawn on the relative accuracies of the dielectric band structures.