Estimation of the influence of ionic dielectricity on the dynamic superconducting order parameter

M. Peter*, M. Weger, L. P. Pitaevskii

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

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 ε2 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) = (ω2 - ωlong2)/(ω2),where ωlong, ωtrans 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 cut-off frequency and an effective coupling constant. The influence of ε(ω) on Tc, 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.

Original languageEnglish
Pages (from-to)174-200
Number of pages27
JournalAnnalen der Physik
Volume7
Issue number3
DOIs
StatePublished - 1998

Keywords

  • Dielectricity
  • Eliashberg equations
  • High temperature superconductivity

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