Effect of density of state on isotope effect exponent of two-band superconductors

TL;DR

This paper derives formulas for the critical temperature and isotope effect exponent in two-band superconductors considering different densities of states, revealing the dominant role of interband interactions and fitting experimental data.

Contribution

It introduces a model incorporating constant and van Hove singularity densities of states, highlighting the impact of interband electron-phonon interactions on isotope effects.

Findings

Interband electron-phonon interaction significantly influences isotope exponent.

Constant density of states model fits experimental data better than van Hove singularity.

Derived formulas applicable in weak-coupling limit for two-band superconductors.

Abstract

The exact formula of Tc's equation and the isotope effect exponent of two-band s-wave superconductors in weak-coupling limit are derived by considering the influence of two kinds of density of state : constant and van Hove singularity. The pairing interaction in each band consisted of 2 parts : the electron-phonon interaction and non-electron-phonon interaction are included in our model. We find that the interband interaction of electron-phonon show more effect on isotope exponent than the intraband interaction and the isotope effect exponent with constant density of state can fit to an experimental data,MgB2, and high-Tc superconductors, better than van Hove singularity density of state.