Correlation between superconductivity and normal-state properties in the ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}\left({\mathrm{Cu}}_{1-x}{\mathrm{Zn}}_x\right){\mathrm{O}}_4$ system

Superconducting and normal-state properties have been studied in the ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}\left({\mathrm{Cu}}_{1-x}{\mathrm{Zn}}_x\right){\mathrm{O}}_4$ system with $0\le x\le 0.06$. The value of $T_c$ decreases rapidly with the Zn content and vanishes as 2.1 at.% of Zn is doped into the Cu sublattice. Metallic resistivity is observed when superconductivity disappears at $x=0.02\mathrm{}$. The suppression of $T_c$ is not caused by the reduction of carrier concentration which should remain constant in the Zn-doped samples, but rather due to the filling of the local Cu $d_{x^2-y^2}$ state. The residual resistivity scales linearly with the Zn content as expected from the impurity scattering due to disorder. Quantitative analysis of the residual resistivity indicates that the mean free path due to disorder is about twice as large as the coherence length when $T_c$ is suppressed to zero. The implication of this finding on the disorder pair-breaking effect will be discussed. The value of $T_c$ is found to strongly correlate with the slope of the resistivity in relation to temperature. Qualitative analysis is carried out in both inelastic and elastic scattering process between carriers and other excitations.