Influence of Pair Breaking and Phase Fluctuations on Disordered High $T_c$ Cuprate Superconductors

Electron irradiation has been used to introduce point defects in a controlled way in underdoped and optimally doped ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ crystals. This technique allows us to perform very accurate measurements of $T_c$ and of the $ab$ plane resistivity in a wide range of defect contents $x_d$ down to $T_c=0$. The variation of $T_c$ and of the transition width with $x_d$ do not follow current predictions of pair-breaking theories. The data are rather compatible, at least for the highly damaged regime, with the expected influence of phase fluctuations. These results open new questions about the evolution of the defect induced $T_c$ depression over the phase diagram of the cuprates.

Figure 1

The resistivity is plotted versus temperature for the single crystal ${\mathrm{Y}\mathrm{B}\mathrm{C}\mathrm{O}}_7$ No. 2 irradiated at low temperature by 2.5 MeV electrons. Data taken either after annealing at 150 K (curve 6) or 300 K (curve 7) are shown to coincide. The initial increase of ${\rho }_{ab}$ (without annealing at room $T$) is equal to $18\mu \Omega \mathrm{c}\mathrm{m}$ per ${10}^{19}e/{\mathrm{c}\mathrm{m}}^2$.

Figure 2

Decrease of $T_c$ versus defect content $x_d$. The latter is proportional to $\Delta {\rho }_{ab}$ measured at 150 K for ${\mathrm{Y}\mathrm{B}\mathrm{C}\mathrm{O}}_7$. For ${\mathrm{Y}\mathrm{B}\mathrm{C}\mathrm{O}}_{6.6}$ the data are plotted versus $\Delta {\rho }_{ab}$ (empty circles) and $\Delta {\rho }_{ab}^{*}$ (full circles) which is a best estimate of $x_d$ as explained in the text. The Abrikosov-Gorkov (AG) curve (dotted line) is represented in the top part. Linear fits (full lines) are also displayed together with those for Emery and Kivelson (EK) theory (dashed lines) as explained in the text.

Figure 3

Width $\delta T_c$ of the superconducting transition defined as shown in the inset as a function of $\Delta {\rho }_{ab}$ for ${\mathrm{Y}\mathrm{B}\mathrm{C}\mathrm{O}}_7$. The variations expected from the AG, EK theories and for a linear $T_c$ are plotted for $\delta x_d/x_d\sim 7\%$ (see text).

Figure 4

The decrease of $T_c$ as a function of $\rho (T_c)$ as defined in the inset of Fig. 3 is compared to EK theory [Eq. (2)]. The best fits are obtained for ${\rho }_Q$ equal to 600 and $1380\mu \Omega \mathrm{c}\mathrm{m}$, respectively, for ${\mathrm{Y}\mathrm{B}\mathrm{C}\mathrm{O}}_7$ and ${\mathrm{Y}\mathrm{B}\mathrm{C}\mathrm{O}}_{6.6}$. The data for $\rho (T_c)$ versus $\Delta {\rho }_{ab}$ are displayed in the inset together with analytical fits (merely exponential here).