Symmetry properties of the localized potentials in the electron-phonon interaction

The electron-phonon interaction in a metal or semiconductor was expressed in terms of the matrix elements of the 'localized potentials', the localized potential being equal to the displacement of the jth nucleus of the basis multiplied by some vector field W j . The symmetry properties of the W j fields and some sum rules for these fields were investigated. The results were applied, in particular, to the long range multipole interactions in semiconductors; it was shown that the W j field decreases-for increasing distance from the displaced nucleus-no faster than this distance to the power of minus four (which corresponds to the octupole interaction). The symmetry properties of the matrix elements of the W j fields were studied in both the Bloch and Wannier representations.