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Possible very high transition temperatures in the infinite-layer ACuO$ _{2} $ cuprate superconductor for A={Mg, Ca, Sr, Ba}: A DFT study

We show from a bond valence sum correlation that very high superconducting $ T_{c} $ values should be found in optimally hole-doped infinite-layer ACuO$ _{2} $ cuprates - up to 160~K for A = Ba. The projected increase in $ T_{c} $ across the series arises from "internal pressure" effects as A runs from Mg to Ba. We then use density functional theory to investigate these pressure effects on the band structure in an attempt to understand this progressive increase in $ T_{c} $. Where these materials have been synthesised we find good agreement between our calculated structural parameters and the experimental ones. We find that internal pressure associated with increasing ion size does indeed enhance the superconducting energy gap, as observed, via modifications to the electronic dispersion. Furthermore, in our calculations, pressure alters the dispersion independently of how it is applied (internal or external) so that the superconducting energy gap correlates with the unit-cell volume and a Fermi-surface shape-parameter describing ratio of next-nearest-neighbor to nearest-neighbor hopping integrals. We infer an energy scale for the pairing interaction of the order of 1~eV, well above the magnetic energy scale.