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A characteristic feature of a superconductor made of multiple condensates isthe possibility of the shape resonances in superconducting gaps. Shaperesonances belong to class of Fano resonances in configuration interactionbetween open and closed scattering channels. The Shape resonances arise becauseof the exchange interaction, a Josephson-like term, for transfer of pairsbetween different condensates in different Fermi surface spots in the specialcases where at least one Fermi surface is near a 2.5 Lifshitz topologicaltransition. We show that tuning the shape resonances show first, the gapsuppression (like a Fano anti-resonance) driven by configuration interactionbetween a BCS condensate and a BEC-like condensate, and second, the gapamplification (like a Fano resonance) driven by configuration interactionbetween BCS condensates in large and small Fermi surfaces. Shape resonancesusually occur in granular nanoscale complex matter (called superstripes)because of the lattice instability near a 2.5 Lifshitz transition in presenceof interactions. Using a new imaging method, scanning nano-X-ray diffraction,we have shown the generic formation in high temperature superconductors of agranular superconducting networks made of striped puddles formed by orderedoxygen interstitials or ordered local lattice distortions (like static shortrange charge density waves). In the superconducting puddles the chemicalpotential is tuned to a shape resonance in superconducting gaps and the maximumTc occurs where the puddles form scale free superconducting networks.

Shape resonances in multi-condensate granular superconductors formed by networks of nanoscale-striped puddles