Isotope effect in impure high-Tcsuperconductors

Abstract

The influence of various kinds of impurities on the isotope shift exponent $\ensuremath{\alpha}$ of high-temperature superconductors has been studied. In these materials the dopant impurities, like Sr in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4},$ play different roles and usually occupy different sites than impurities like Zn, Fe, Ni, etc., intentionally introduced into this system to study its superconducting properties. In this paper the in-plane and out-of-plane impurities present in layered superconductors have been considered. They differently affect the superconducting transition temperature ${T}_{c}.$ The relative change of isotope shift coefficient, however, is a universal function of ${T}_{c}{/T}_{c0}$ ${(T}_{c0}$ refers to an impurity-free system), i.e., for angle independent scattering rate and density of states function it does not depend on whether the change of ${T}_{c}$ is due to in- or out-of-plane impurities. The role of the anisotropic impurity scattering in changing oxygen isotope coefficient of superconductors with various symmetries of the order parameter is elucidated. The comparison of the calculated and experimental dependence of $\ensuremath{\alpha}/{\ensuremath{\alpha}}_{0},$ where ${\ensuremath{\alpha}}_{0}$ is the clean system isotope shift coefficient, on ${T}_{c}{/T}_{c0}$ is presented for a number of cases studied. The changes of $\ensuremath{\alpha}$ calculated within the stripe model of superconductivity in copper oxides reasonably well describe the data on ${\mathrm{La}}_{1.8}{\mathrm{Sr}}_{0.2}{\mathrm{Cu}}_{1\ensuremath{-}x}(\mathrm{F}\mathrm{e},\mathrm{N}\mathrm{i}{)}_{x}{\mathrm{O}}_{4},$ without any fitting parameters.