Isotope Effect at the Fano Resonance in Superconducting Gaps for Multiband Superconductors at a 2.5 Lifshitz Transition

Abstract The doping dependent isotope effect in cuprates is explained in the framework of shape resonances in the superconducting gaps (belonging to the class of Fano res-onances) in multicondensate superconductors. This new paradigm for high temperature superconductivity is based on the recent Fermiology scenario emerging from dHvA and quantum oscillation data showing a 2.5 Lifshitz topological transition due to the appearance of new small Fermi surface in the underdoped regime. The isotope effect is calculated for an electronic system near a band edge for a superlattice of stripes. The model reproduces the doping dependence of the isotope exponent behavior in cuprates and allows to identify the relative role of the intraband Cooper pairing and the configuration interaction between pairing channels from experimental data