Isotope Effect in Multi-Band and Multi-Channel Attractive Systems and Inverse Isotope Effect in Iron-Based Superconductors

Recently reported inverse isotope effect is investigated on the basis of the two-band and two-channel attractive model by using the weak coupling Bardeen-Cooper-Schrieffer (BCS) scheme. If we assume the several attractive or repulsive interactions for Cooper pairs, which works in different energy ranges, the isotope exponent alpha takes values even in the range of alpha < 0 (negative) and alpha > 0.5, depending on the strength and the range of interactions. We apply the theory to recently observed remarkable inverse isotope effect a approximate to -0.18 for the Fe-pnictide (Ba,K)Fe2As2 superconductor. The large inverse isotope effect naturally originates from the competition between the magnetically induced pair interaction and the inter-band electron-phonon coupling. It evidently indicates that the superconductivity in Fe pnictides arises from the magnetically induced attractive interaction.