Some background regarding the evolution of calculations, predictions, and approaches to understand and increase T c 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 T c. It is then argued that in the search for high T cs 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 T c materials in this class of superconductors.
KeywordsSuperconductivity electron-phonon interactions superconducting transition temperature maximizing
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