Survival of the $d$-Wave Superconducting State near the Edge of Antiferromagnetism in the Cuprate Phase Diagram

In the cuprate superconductor ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{6+x}$, hole doping in the ${\mathrm{C}\mathrm{u}\mathrm{O}}_2$ layers is controlled by both oxygen content and the degree of oxygen ordering. At the composition ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{6.35}$, the ordering can occur at room temperature, thereby tuning the hole doping so that the superconducting critical temperature gradually rises from 0 to 20 K. Here we exploit this to study the $\widehat{c}$-axis penetration depth as a function of temperature and doping. The temperature dependence shows the $d$-wave superconductor surviving to very low doping, with no sign of another ordered phase interfering with the nodal quasiparticles. The only apparent doping dependence is a smooth decline of superfluid density as $T_c$ decreases.

Figure 1

Growth of critical temperature and $\widehat{c}$-axis screening with increasing hole doping in ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{6+x}$ ($x\sim 0.35$). $1/{\lambda }_c^2$ depends on the density of superconducting charge carriers that participate in the screening of applied fields and has been determined by a cavity perturbation measurement at microwave frequencies. The three sets of curves indicated by squares, triangles, and circles correspond to three slightly different oxygen contents and at each oxygen content the hole doping was allowed to drift up by way of gradual oxygen ordering at room temperature.

Figure 2

A plot of $1/{\lambda }_c^2(T)-1/{\lambda }_c^2(0)$ focuses attention on the depletion of the superfluid screening from its low temperature value, reflecting the loss of superfluid density as quasiparticles are thermally excited out of the condensate. The data for all of the doping levels shown in Fig. 1 nearly collapse onto a single curve at low $T$ with a power law close to $T^{2.5}$. The inset shows the same data over a temperature range that spans the highest $T_c$. The solid curve is a fit to the low temperature data of the higher $T_c$ samples, with a model that involves nodal quasiparticles in a $d$-wave superconductor, scattered as they tunnel from one ${\mathrm{C}\mathrm{u}\mathrm{O}}_2$ plane to the next.

Figure 3

Relationship between $T_c$ and the zero-temperature value of the $\widehat{c}$-axis screening length. The experimental correlation between these quantities (circles) can be modeled by nodal quasiparticles cut off by shrinking Fermi arcs. The inset shows the linear relationship between the cutoff energy $E_c$ needed to model $1/{\lambda }_c^2$ and the measured critical temperature $T_c$. This model produces a nearly quadratic dependence between $1/{\lambda }_c^2$ and $T_c$, as indicated by the solid curve in the main figure. The few degree discrepancy between the $T_c$ predicted by the model and the measured $T_c$ is likely a consequence of phase fluctuations that govern the behavior near $T_c$ [28].