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.
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Loktev, V.M., Turkowski, V.M. On The Theory of Isotope-effect in the d-wave Superconductors. J Low Temp Phys 143, 115–130 (2006). https://doi.org/10.1007/s10909-006-9212-x
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DOI: https://doi.org/10.1007/s10909-006-9212-x