Modern Theory of Polarization
Wannier functions have recently found application in describing the polarization in crystals, for example, ferroelectrics. See for example, Berghold, and Nakhmanson., and a power-point introduction by Vanderbilt The polarization per unit cell in a solid can be defined as the dipole moment of the Wannier charge density:
where the summation is over the occupied bands, and Wn is the Wannier function localized in the cell for band n. The change in polarization during a continuous physical process is the time derivative of the polarization and also can be formulated in terms of the Berry phase of the occupied Bloch states.
Read more about this topic: Wannier Function
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