Theory of polarization: A modern approach

Raffaele Resta, David Vanderbilt

Research output: Chapter in Book/Report/Conference proceedingChapter

268 Scopus citations


In this Chapter we review the physical basis of the modern theory of polarization, emphasizing how the polarization can be defined in terms of the accumulated adiabatic flow of current occurring as a crystal is modified or deformed. We explain how the polarization is closely related to a Berry phase of the Bloch wavefunctions as the wavevector is carried across the Brillouin zone, or equivalently, to the centers of charge of Wannier functions constructed from the Bloch wavefunctions. A resulting feature of this formulation is that the polarization is formally defined only modulo a "quantum of polarization" - in other words, that the polarization may be regarded as a multi-valued quantity. We discuss the consequences of this theory for the physical understanding of ferroelectric materials, including polarization reversal, piezoelectric effects, and the appearance of polarization charges at surfaces and interfaces. In so doing, we give a few examples of realistic calculations of polarization-related quantities in perovskite ferroelectrics, illustrating how the present approach provides a robust and powerful foundation for modern computational studies of dielectric and ferroelectric materials.

Original languageEnglish (US)
Title of host publicationPhysics of Ferroelectrics
Subtitle of host publicationA Modern Perspective
EditorsKarin Rabe, Charles Ahn, Jean-Marc Triscone
Number of pages38
StatePublished - 2007

Publication series

NameTopics in Applied Physics
ISSN (Print)0303-4216
ISSN (Electronic)1437-0859

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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