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Some background regarding the evolution of calculations, predictions, and approaches to understand and increase Tc for phonon-mediated superconductivity is presented. This is followed by a description of a successful “after the fact” theoretical study of MgB2 and a description of current thinking about the relationship between phonon renormalization and Tc. It is then argued that in the search for high Tcs the evolution has gone from searching for high density of states materials to high electron–phonon couplings described by λ. Finally, it is suggested that the focus on finding large λ can be supplemented by a search for large electronic spring constants η. This is expected to be particularly relevant for the highest Tc materials in this class of superconductors.
KeywordsSuperconductivity electron-phonon interactions superconducting transition temperature maximizing
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