Electronic-structure theory of crystalline insulators under homogeneous electric field

Based on the conventional energy band theory, an approach is presented to describe the electronic structure of crystalline insulators in the presence of a finite homogeneous electric field. The expression of polarization is derived which extends the ``Berry-phase'' theory of polarization to nonzero fields. The characteristics of the solutions are studied in details and the associations with the existing perturbation theories and computational schemes are discussed.