t exponent in the ${\mathrm{PrBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$-Ag percolation system

We have studied the electrical transport in the ${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$-Ag percolation system. The resistivity ratio of the former to the latter, ${\mathrm{\rho }}_{\mathrm{Pr}}$ 1:2:3/${\mathrm{\rho }}_{\mathrm{Ag}}$, had been systematically ‘‘tuned’’ by performing the resistance measurements at various selected temperatures between 30 and 300 K. The critical volume fraction ${\mathrm{\phi }}_{\mathit{c}}$ and a best value of the t exponent in the sample resistivity ρ∝(φ-${\mathrm{\phi }}_{\mathit{c}}$ ${)}^{\mathrm{-}\mathit{t}}$ above the percolation threshold were determined, where φ is the Ag volume fraction. We find that ${\mathrm{\phi }}_{\mathit{c}}$=0.135±0.005 and t=1.91±0.02. In addition, based on the results obtained at various measuring temperatures or ${\mathrm{\rho }}_{\mathrm{Pr}1:2:3\mathrm{}}$/${\mathrm{\rho }}_{\mathrm{Ag}}$, we show that the value of t extracted by presuming the above simple power-law behavior can be substantially smaller than the predicted value (≊2.0) if ${\mathrm{\rho }}_{\mathrm{Pr}1:2:3\mathrm{}}$/${\mathrm{\rho }}_{\mathrm{Ag}}$ is not sufficiently large. The scaling behavior of (${\mathrm{\rho }}_{\mathrm{Ag}}$/ρ)‖φ-${\mathrm{\phi }}_{\mathit{c}}$ ${\mathrm{\Vert }}^{\mathrm{-}\mathit{t}}$ as a function of (${\mathrm{\rho }}_{\mathrm{Ag}}$/${\mathrm{\rho }}_{\mathrm{Pr}}$ 1:2:3)‖φ-${\mathrm{\phi }}_{\mathit{c}}$ ${\mathrm{\Vert }}^{\mathrm{-}(\mathit{t}+\mathit{s})}$ has then been investigated, where s is the critical exponent governing the divergence of conductivity in a superconductor–normal-metal composite.