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Calculation of the Superconducting State Parameters with Retarded Electron-Phonon Interaction

Calculation of the Superconducting State Parameters with Retarded Electron-Phonon Interaction The energy gap and other parameters of the superconducting state are calculated from the Bardeen-Cooper-Schrieffer theory in Gor'kov-Eliashberg form, using a realistic retarded electron-electron interaction via phonons and including the Coulomb repulsion. The solution is facilitated by observing that only the local phonon interaction, mediated entirely by short-wavelength phonons, is important, and that a good approximation for the phonon spectrum is therefore an Einstein model rather than Debye model. The resulting equation is solved by an approximate iteration procedure. The results are similar to earlier gap equations but the derivation gives a precise meaning to the interaction and cutoff parameters of earlier theories. The numerical results are in good order-of-magnitude agreement with the observed transition temperatures but lead to an isotope effect at least 15% less than the accepted -½ exponent ( T c proportional to M - 1 2 ). Also, the present theory predicts that all metals should be superconductors, although those not observed to do so would have remarkably low transition temperatures. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review American Physical Society (APS)

Calculation of the Superconducting State Parameters with Retarded Electron-Phonon Interaction

Physical Review , Volume 125 (4) – Feb 15, 1962
9 pages

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References (4)

Publisher
American Physical Society (APS)
Copyright
Copyright © 1962 The American Physical Society
ISSN
1536-6065
DOI
10.1103/PhysRev.125.1263
Publisher site
See Article on Publisher Site

Abstract

The energy gap and other parameters of the superconducting state are calculated from the Bardeen-Cooper-Schrieffer theory in Gor'kov-Eliashberg form, using a realistic retarded electron-electron interaction via phonons and including the Coulomb repulsion. The solution is facilitated by observing that only the local phonon interaction, mediated entirely by short-wavelength phonons, is important, and that a good approximation for the phonon spectrum is therefore an Einstein model rather than Debye model. The resulting equation is solved by an approximate iteration procedure. The results are similar to earlier gap equations but the derivation gives a precise meaning to the interaction and cutoff parameters of earlier theories. The numerical results are in good order-of-magnitude agreement with the observed transition temperatures but lead to an isotope effect at least 15% less than the accepted -½ exponent ( T c proportional to M - 1 2 ). Also, the present theory predicts that all metals should be superconductors, although those not observed to do so would have remarkably low transition temperatures.

Journal

Physical ReviewAmerican Physical Society (APS)

Published: Feb 15, 1962

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