On the theory of isotope-effect in the d-wave superconductors

The isotope-effect in a two-dimensional model of the d-wave phonon-exchange superconductor is studied. It is shown that the mean-field critical temperature, the Berezinskii-Kosterlitz-Thouless critical temperature and the superconducting gap strongly depend on the phonon frequency only in some range of the model parameters. These dependencies have different from the BCS theory forms. A qualitative comparison of the results with experimental data on some high-temperature superconductors is made. In particular, it is shown that the isotope-effect is significant in the case of strong electron-phonon coupling, when the phonon frequency is small compared to the free electron bandwidth.