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Cited by 773

The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.

Microscopic Theory of Force Constants in the Adiabatic Approximation

Pick, Robert M., Cohen, Morrel H., Martin, Richard M.·1970·Physical Review B
DOI 10.1103/physrevb.1.910
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Abstract

The microscopic quantum-mechanical expressions for the Born-von Karman force constants in an arbitrary solid, crystalline or amorphous, are derived in terms of the complete inverse dielectric function ${\ensuremath{\epsilon}}^{\ensuremath{-}1}(\mathrm{r}, {\mathrm{r}}^{\ensuremath{'}})$ of the electrons The many-body nature of the electrons is treated exactly; only the Born-Oppenheimer approximation is made. Born's translation and rotation invariance conditions are shown to be satisfied by the microscopic force constants. In the case of a perfect crystal, it is shown for the first time that the microscopic formulas recapture completely the phenomenological form of the dynamical matrix; in particular, the microscopic expression for the effective charge in an insulator is found. We prove that the charge neutrality of the system implies the "effective charge neutrality" condition and that, consequently, all acoustic-mode frequencies vanish at long wavelength. This condition may be stated as a useful property of ${\ensuremath{\epsilon}}^{\ensuremath{-}1}$ which we term the acoustic sum rule. Many results of the phenomenological theory, e.g., the generalized Lyddane-Sachs-Teller relation, carry over exactly to the microscopic theory.

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Metadata

Authors
Pick, R. M., Cohen, M. H., & Martin, R. M.
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
1970-01-15
Volume
1
Issue
2
Pages
910-920
ISSN
0556-2805 (ISSN-L)
DOI
10.1103/physrevb.1.910
OpenAlex
W2012111359
Cited by
773
References
14
FWCI
9.19
Type
journal article
Language
en
Open access
closed

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