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.
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