32. The Response of Extended Systems to Electrostatic Fields

We present an overview of our understanding of how extended materials exposed to an electrostatic field can be treated theoretically. We concentrate on materials that are regular so that they can be approximated as being infinite and periodic. We show how expressions for the dipole moment per unit that were suggested previously within the so-called modern theory of polarization can be obtained. Subsequently, we present the single-particle equations that describe how the electrons respond to an external, electrostatic field and present a numerically efficient method of solution. We also discuss how structural responses in the presence of an electrostatic field can be calculated automatically. We demonstrate that bulk properties of macroscopic systems will depend upon the surfaces and demonstrate how these properties may be evaluated from calculations on the infinite and periodic system even though the latter does not contain surfaces. As one example, we show how the surfaces will contribute to the so-called converse piezoelectric effect. In addition, the polarizabilities induced by the structural response may be larger than the corresponding electronic polarizabilities. Finally, problems related to the description of the responses within density-functional theory are briefly discussed.