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Theory of Polarization: A Modern Approach

  • Raffaele RestaEmail author
  • David Vanderbilt
Chapter
Part of the Topics in Applied Physics book series (TAP, volume 105)

Abstract

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.

Keywords

Brillouin Zone Lattice Vector Spontaneous Polarization Modern Theory Modern Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.INFM–DEMOCRITOS National Simulation CenterTriesteItaly
  2. 2.Dipartimento di Fisica TeoricaUniversità di TriesteTriesteItaly
  3. 3.Department of Physics and AstronomyRutgers UniversityPiscatawayUSA

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