Isotope and interband effects in a multi-band model of superconductivity

Isotope effects (IEs) are essential in determining the pairing mechanism in superconductors. Whereas for Bardeen–Cooper–Schrieffer (BCS)-type superconductors, a clear consensus about IE exists, this is unknown in multiband superconductors (MBSs). We demonstrate here that for MBSs the IEs on the superconducting transition temperature can vary between the BCS value and zero as long as the intraband couplings are affected. It can, however, exceed the BCS value when interband effects are dominant. In both cases, a sign reversal is excluded. In addition, we show that interband coupling contributes substantially to enhancement of T c . The results are independent of the pairing symmetry and the system-specific band structure. Specifically, we do not address the IEs originating from the MBSs with respect to a specific superconductor, but rather study its emergence within this model and explore all possible sources within the weak coupling theory.