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Estimation of the influence of ionic dielectricity on the dynamic superconducting order parameter
Author(s) -
Peter M.,
Weger M.,
Pitaevskii L. P.
Publication year - 1998
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.2090070304
Subject(s) - physics , condensed matter physics , coupling constant , dielectric , renormalization , phonon , superconductivity , constant (computer programming) , pairing , wave vector , quantum electrodynamics , quantum mechanics , computer science , programming language
We consider the influence of an ω‐dependent ionic dielectric constant ϵ(ω) on the properties of a superconductor. Assuming that the pairing interaction is proportional to ϵ 2 we have solved the Eliashberg equations for this case, both for imaginary and real frequencies. The interaction potential depends on a coupling constant λ and on a longitudinal phonon frequency ω. The dielectric constant is assumed to be independent of wavevector q , and to depend on frequency through the expression: ϵ(ω) = (ω 2 ‐ ω 2 long )/(ω 2 ‐ ω 2 trans ), where ω long , ω trans are the frequencies of optical phonons of the dielectric. We find that along the imaginary frequency axis (but not for real frequencies) the weighted phonon propagator can be modeled by an appropriate choice of a cutoff frequency and an effective coupling constant. The influence of ϵ(ω) on T c , the gap Δ(ω), and the renormalization function Z (ω) are studied and it is found that these quantities increase significantly with the dielectric constant.