Electronic Phase Diagram of High-$T_c$ Cuprate Superconductors from a Mapping of the In-Plane Resistivity Curvature

We propose that resistivity curvature mapping (RCM) based on the in-plane resistivity data is a useful way to objectively draw electronic phase diagrams of high-$T_c$ cuprates, where various crossovers are important. In particular, the pseudogap crossover line can be conveniently determined by RCM. We show experimental phase diagrams obtained by RCM for ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_{2-z}{\mathrm{L}\mathrm{a}}_z{\mathrm{C}\mathrm{u}\mathrm{O}}_{6+\delta }$, ${\mathrm{L}\mathrm{a}}_{2-x}{\mathrm{S}\mathrm{r}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_4$, and ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_y$, and demonstrate the universal nature of the pseudogap crossover. Intriguingly, the electronic crossover near optimum doping depicted by RCM appears to occur rather abruptly, suggesting that the quantum-critical regime, if it exists, must be very narrow.

Figure 1

(a) ${\rho }_{ab}(T)$ data of BSLCO for $p=0.11–0.18$ at 0.01 intervals; the data for underdoped (overdoped) samples are shown in blue (red), while that for optimum doping is shown in green. (b) Resistivity curvature mapping, namely, a false color mapping of $d^2{\rho }_{ab}^{\mathrm{n}}/d{T}^2$ in the $T$ vs $p$ plane, for BSLCO. The solid green circles show $T_c$'s for the measured compositions.

Figure 2

(a),(b) ${\rho }_{ab}(T)$ data of LSCO for $x=0.01–0.22$ at 0.01 intervals. (c) Electronic phase diagram depicted by RCM for LSCO; here ${\rho }_{ab}^{\mathrm{n}}={\rho }_{ab}/{\rho }_{ab}(400\mathrm{K})$. The dashed line is a guide to the eyes to emphasize $T_{pg}$, and the solid green circles show $T_c$'s for the measured compositions.

Figure 3

(a),(b) ${\rho }_a(T)$ data of YBCO for $y=6.30–7.00$ at 0.05 intervals. (c) Electronic phase diagram depicted by RCM for YBCO, where the solid green circles show $T_c$'s for the measured compositions.