Theoretical Analysis of Isotope Effect Exponent of Diboride and Iron-Based Superconductors: Three-Square-Well Model Approach

Analytical calculations of isotope effect exponent of both s-wave and π-phase-shifted s-wave two-band superconductors are presented within the framework of Bogoliubov–Valatin formalism using three-square-well model approach. The effective pairing interaction consists of contributions from the attractive acoustic electron–phonon, optical electron–phonon contributions in addition to repulsive electron–electron or antiferromagnetic fluctuation mediated pairing contributions for the diboride or pnictide superconductors, respectively. These are used to obtain analytical results that are applied in studying the isotope effect exponent in the diboride and pnictide superconductors, and the results are compared with experimental data.