MACROSCOPIC POLARIZATION IN CRYSTALLINE DIELECTRICS : THE GEOMETRIC PHASE APPROACH

Macroscopic electric polarization is a fundamental concept in the physics of matter, upon which the phenomenological description of dielectrics is based (Landau and Lifshitz, 1984). Notwithstanding, this concept has long evaded even a precise microscopic definition. A typical incorrect statement — often found in textbooks — is that the macroscopic polarization of a solid is the dipole of a unit cell. It is easy to realize that such a quantity is neither measurable nor model-independent: the dipole of a periodic charge distribution is in fact ill defined (Martin, 1974), except in the extreme Clausius-Mossotti model, in which the total charge is unambiguously decomposed into an assembly of /ocalized and neutral charge distributions. One can adopt an alternative viewpoint by considering a macroscopic and finite piece of matter and defining its polarization P as the dipole per unit volume: 1