Isotope effect in impure high T_c superconductors

TL;DR

This paper investigates how different impurities affect the isotope shift exponent in high-temperature superconductors, revealing a universal relationship with T_c/T_{c0} and explaining the role of anisotropic impurity scattering.

Contribution

It provides a theoretical analysis of impurity effects on isotope shifts in layered superconductors, including a comparison with experimental data using the stripe model.

Findings

The isotope shift coefficient change is a universal function of T_c/T_{c0}.

In-plane and out-of-plane impurities affect T_c differently but similarly influence isotope shifts.

The stripe model accurately describes experimental data without fitting parameters.

Abstract

The influence of various kinds of impurities on the isotope shift exponent \alpha of high temperature superconductors has been studied. In these materials the dopant impurities, like Sr in La_{2-x}Sr_xCuO_4, play different role and usually occupy different sites than impurities like Zn, Fe, Ni {\it etc} intentionally introduced into the system to study its superconducting properties. In the 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 an universal function of T_c/T_{c0} (T_{c0} reffers to impurity free system) {\it i.e.} for angle independent scattering rate and density of states function it does not depend 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 \alpha/\alpha_0, where \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 \alpha calculated within stripe model of superconductivity in copper oxides resonably well describe the data on La_{1.8}Sr_{0.2}Cu_{1-x}(Fe,Ni)_xO_4, without any fitting parameters.