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High-temperature superconductivity (HTS) emerges in quite different electronic materials: cuprates, diborides, and iron-pnictide superconductors. Looking for unity in the diversity we find in all these materials a common lattice architecture: they are practical realizations of heterostructures at atomic limit made of superlattices of metallic active layers intercalated by spacers as predicted in 1993 by one of us. The multilayer architecture is the key feature for the presence of electronic topological transitions where the Fermi surface of one of the subbands changes dimensionality. The superlattice misfit strain  between the active and spacer layers is shown to be a key variable to drive the system to the highest critical temperature  that occurs at a particular point of the 3D phase diagram (,) where  is the charge transfer or doping. The plots of  as a function of misfit strain at constant charge transfer in cuprates show a first-order quantum critical phase transition where an itinerant striped magnetic phase competes with superconductivity in the proximity of a structural phase transition, that is, associated with an electronic topological transition. The shape resonances in these multigap superconductors is associated with the maximum .

Misfit Strain in Superlattices Controlling the Electron-Lattice Interaction via Microstrain in Active Layers