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Approximation of Local‐Field Effects in the Dielectric Formalism of Lattice Dynamics
Author(s) -
Falter C.,
Klenner M.,
Ludwig W.
Publication year - 1991
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221670110
Subject(s) - phonon , dielectric , condensed matter physics , physics , dispersion relation , diagonal , polarization (electrochemistry) , long wavelength limit , lattice (music) , quantum mechanics , statistical physics , mathematics , chemistry , acoustics , geometry
The phonon dispersion is investigated of a crystal where local field effects are taken into account using a first‐order perturbation expansion with respect to the off‐diagonal of the dielectric matrix. Such an expansion is used in other applications in the literature. It is shown that a straightforward application of this approach is not sufficient for a proper description of acoustic phonons in semiconductors and insulators in the limit of long wavelength because the acoustic sum rule is violated. A general expression for the correction term being of second order is given. Furthermore, the relations are illustrated with the phonon dispersion and certain phonon induced polarization charge densities in Si using a suitable model for the dielectric function.