Empirical rule to reconcile BCS theory with electron-phonon interaction in normal state

Xue-Heng Zheng, D George Walmsley

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We introduce a simple empirical rule wherein the pairing interaction in superconductors is cancelled when normal and umklapp phonon scattering coexist. Superconductivity then arises solely from the residual umklapp contribution. As a result the deduced electron-phonon interactions in niobium, tantalum, lead and aluminum become virtually identical in both the normal and superconducting states. Transition temperatures calculated under the rule are accurate within a few percent when compared with experimental data. Features of the Matthias relations are also explained. The high Tc so far predicted for metallic hydrogen is probably overly optimistic.
Original languageEnglish
Pages (from-to)095803-095811
Number of pages9
JournalPhysica Scripta
Issue number9
Publication statusPublished - 25 Jul 2014



  • superconductivity, BCS theory, Tc prediction, Matthias relations

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