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   <subfield code="a">In this contribution we present a comprehensive explanation for the origin of the band shifts observed in dHvA and ARPES experiments. Using a four-band Eliashberg analysis, we show that they are a natural consequence of the multiband character of these systems and of the strong particle-hole asymmetry of the bands. We also show that the relative sign of such shifts provides a direct experimental evidence of a dominant interband scattering. A quantitative analysis in LaFePO yields a spin-mediated interband coupling of the order V≈0.46eV, which corresponds to a mass enhancement Z≈1.4. We also employ such four-band model to investigate the magnitude of the superconducting gap on different Fermi sheets of Ba0.6K0.4Fe2As2, and we show that the same four-band model provides a simple explanation of the different gap values on different Fermi sheets and of the thermodynamics properties (specific heat, superfluid density, ...).</subfield>
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