Negative Isotope Effect in Superconductivity from Non-Retarded Repulsive Interaction

Abstract

We have examined the isotope effect in superconductivity due to the repulsive interaction. The equation for the temperature of transition to the superconducting state is derived in terms of the temperature Bethe–Salpeter equation for a bound state of two fermions in the spin-singlet state. The effective interaction in the equation for Tc is written in terms of the effective scattering amplitude, thus providing the validity of the equation for the non-retarded interaction. The superconducting phase transition occurs due to non-retarded repulsive inter-particle interaction. In contrast, additional retarded electron-phonon interaction contributes to the pair-breaking effect. We have shown that the isotope effect coefficient α is negative in this case.