Electron self-energy and generalized Drude formula for infrared conductivity of metals

Gotze and Wolfle (GW) [Phys. Rev. B 6, 1226 (1972) (http://dx.doi.org/10.1103/PhysRevB.6.1226)] wrote the conductivity in terms of a memory function M( omega ) as [sigma]( omega + i[eta]) = (ine super(2)/m) [ omega + M( omega + i[eta])] super(-1), where M( omega + i[eta]) = i/[tau] in the Drude limi...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2015-08, Vol.92 (5), Article 054305
Main Author: Allen, Philip B.
Format: Article
Language:English
Subjects:
Approximation
Condensed matter
Derivation
Green's functions
Infrared
Mathematical analysis
Perturbation methods
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Summary:Gotze and Wolfle (GW) [Phys. Rev. B 6, 1226 (1972) (http://dx.doi.org/10.1103/PhysRevB.6.1226)] wrote the conductivity in terms of a memory function M( omega ) as [sigma]( omega + i[eta]) = (ine super(2)/m) [ omega + M( omega + i[eta])] super(-1), where M( omega + i[eta]) = i/[tau] in the Drude limit. The analytic properties of -M( omega + i[eta]) are the same as those of the self-energy capital sigma of a retarded Green's function. In the approximate treatment of GW, -M closely resembles a self-energy with differences, e.g., the imaginary part is twice too large. The correct relation between -M and capital sigma and is known for the electron-phonon case and is conjectured to be similar for other perturbations. When vertex corrections are ignored there is a known relation. A derivation using Matsubara temperature Green's functions is given.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.92.054305