Doping phase diagram of ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{1-y}{\mathrm{Zn}}_y\right)}_3{\mathrm{O}}_{7-\delta }$ from transport measurements:  Tracking the pseudogap below $T_c$

The effects of planar hole concentration, $p$, and magnetic field on the resistivity, $\rho \left(T\right)$, of high-quality $c$-axis oriented crystalline thin films and sintered ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{1-y}{\mathrm{Zn}}_y\right)}_3{\mathrm{O}}_{7-\delta }$ samples were investigated over a wide range of Ca, Zn, and oxygen contents. Zn was used to suppress superconductivity and this enabled us to extract the characteristic pseudogap temperature, $T*\left(p\right)$ below $T_{c0}\left(p\right)[\equiv T_c(x=0,y=0)]$. We have also located the characteristic temperature, $T_{\mathrm{scf}}$, marking the onset of significant superconducting fluctuations above $T_c$, from the analysis of $\rho (T,H,p)$ and $\rho (T,p)$ data. From this we are able to identify $T*\left(p\right)$ near the optimum doping level where the values of $T*\left(p\right)$ and $T_{\mathrm{scf}}\left(p\right)$ are very close and hard to distinguish. We again found that $T*\left(p\right)$ depends only on the hole concentration $p$, and not on the level of disorder associated with Zn or Ca substitutions. We conclude that (i) $T*\left(p\right)$ (and therefore, the pseudogap) persists below $T_{c0}\left(p\right)$ on the overdoped side and does not merge with the $T_{c0}\left(p\right)$ line and (ii) $T*\left(p\right)$ and the pseudogap energy extrapolate to zero at the doping $p=0.19\pm 0.01$.

Figure 1

Resistivity data for (a) ${\mathrm{Y}}_{0.95}{\mathrm{Ca}}_{0.05}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ ($T_c=81.8\mathrm{K}$, $p=0.133$, $T_{\mathrm{scf}}=105\mathrm{K}$, and $T*=210\mathrm{K}$) thin film and (b) ${\mathrm{Y}}_{0.80}{\mathrm{Ca}}_{0.20}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ ($T_c=81\mathrm{K}$, $p=0.136$, $T_{\mathrm{scf}}=107\mathrm{K}$, and $T*=202\mathrm{K}$) sintered sample. Insets show the identification of $T*$ and $T_{\mathrm{scf}}$. Notice that $d^2\rho \left(T\right)∕d{T}^2$ is completely featureless at $T*$. ◻ denotes $[\rho \left(T\right)-{\rho }_{\mathrm{LF}}]$ data and $엯$ denotes $d\rho \left(T\right)∕dT$ data. The dashed-dotted straight lines in the insets are drawn as guides to the eye.

Figure 2

Determination of $T_{\mathrm{scf}}$ from $\rho (T,H)$ data. Main panel, $[\rho (H=6\text{Tesla})∕\rho (H=0\text{Tesla})]$ vs $T$ data. Insets, $\rho \left(T\right)$ and its linear fit (the dashed-dotted thick straight line) near $T_c$ and $d^2\rho \left(T\right)∕d{T}^2$ (a) ${\mathrm{Y}}_{0.80}{\mathrm{Ca}}_{0.20}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{0.97}{\mathrm{Zn}}_{0.03}\right)}_3{\mathrm{O}}_{7-\delta }$ (sintered, $p=0.185$, and $T_c=45.8\mathrm{K}$), (b) ${\mathrm{Y}}_{0.80}{\mathrm{Ca}}_{0.20}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{0.96}{\mathrm{Zn}}_{0.04}\right)}_3{\mathrm{O}}_{7-\delta }$ (sintered, $p=0.198$, and $T_c=36.7\mathrm{K}$), and (c) ${\mathrm{Y}}_{0.95}{\mathrm{Ca}}_{0.05}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ (thin film, $p=0.148$ and $T_c=85.2\mathrm{K}$). The straight line in the main panel of (c) is drawn as a guide to the eye.

Figure 3

(Color online) Main panel, $T_c\left(p\right)$ and $T_{\mathrm{scf}}\left(p\right)$ for sintered ${\mathrm{Y}}_{0.80}{\mathrm{Ca}}_{0.20}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{1-y}{\mathrm{Zn}}_y\right)}_3{\mathrm{O}}_{7-\delta }$. Inset, $\Delta T_{\mathrm{scf}}\left(p\right)$ for sintered and thin films of ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{1-y}{\mathrm{Zn}}_y\right)}_3{\mathrm{O}}_{7-\delta }$. Zn and Ca contents ($x$ and $y$) are shown in the figure.

Figure 4

(a) $d^2{\rho }_{ab}\left(T\right)∕d{T}^2$, $d^2{\rho }_{\mathrm{tot}}∕d{T}^2$, and $d^2{\rho }_{\mathrm{tot}\text{−}\mathrm{Ec}}∕d{T}^2$ vs $T$ for optimally doped $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ thin film ($T_c=92.4\mathrm{K}$, $p=0.163$) and (b) $d^2\rho \left(T\right)∕d{T}^2$ and $d^2{\rho }_{\mathrm{tot}}∕d{T}^2$ vs $T$ of an underdoped sintered ${\mathrm{Y}}_{0.90}{\mathrm{Ca}}_{0.10}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ sample ($T_c=83\mathrm{K}$, $p=0.149$). Arrows indicate $T_{\mathrm{scf}}$. Insets show $\rho \left(T\right)$ and its linear fit (dashed-dotted straight line) near the superconducting transition.

Figure 5

$[\left(\epsilon _{\mathrm{scf}}{}^{3}T_{\mathrm{scf}}{}^2\right)∕(2+{\epsilon }_{\mathrm{scf}})]$ vs ${\rho }^2\left(T_{\mathrm{scf}}\right)$ [see Eq. (3)] for the sintered ${\mathrm{Y}}_{0.80}{\mathrm{Ca}}_{0.20}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{1-y}{\mathrm{Zn}}_y\right)}_3{\mathrm{O}}_{7-\delta }$ samples. Zn contents ($y$ in %) are shown in the figure. The dashed straight line is drawn as a guide to the eye.

Figure 6

(Color) $T*$ for (a) sintered ${\mathrm{Y}}_{0.80}{\mathrm{Ca}}_{0.20}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{0.96}{\mathrm{Zn}}_{0.04}\right)}_3{\mathrm{O}}_{7-\delta }$($(p=0.174\pm 0.003)$, (b) sintered ${\mathrm{Y}}_{0.80}{\mathrm{Ca}}_{0.20}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{0.985}{\mathrm{Zn}}_{0.015}\right)}_3{\mathrm{O}}_{7-\delta }$ $(p=0.177\pm 0.003)$, and (c) thin film of ${\mathrm{Y}}_{0.95}{\mathrm{Ca}}_{0.05}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{0.98}{\mathrm{Zn}}_{0.02}\right)}_3{\mathrm{O}}_{7-\delta }$ $(p=0.167\pm 0.003)$. Top inset shows $d^2\rho \left(T\right)∕d{T}^2$ data. Notice that $d^2\rho \left(T\right)∕d{T}^2$ is featureless at $T*$ (yellow region in the bottom inset). $T_{\mathrm{scf}}$ is also marked in the bottom inset. The straight lines in the bottom inset are drawn as a guide to the eye. Strong superconducting fluctuations persist in the blue region.

Figure 7

(Color) Magnetic field dependence of $T*$ and $T_{\mathrm{scf}}$. (a) A second slightly overdoped ${\mathrm{Y}}_{0.95}{\mathrm{Ca}}_{0.05}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{0.98}{\mathrm{Zn}}_{0.02}\right)}_3{\mathrm{O}}_{7-\delta }$ thin film ($p=0.168\pm 0.003$ and $T_c=64\mathrm{K}$) and (b) an underdoped ${\mathrm{Y}}_{0.95}{\mathrm{Ca}}_{0.05}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ thin film ($p=0.148\pm 0.003$ and $T_c=85.2\mathrm{K}$).

Figure 8

(Color) Characteristic pseudogap energies ($T*$ and $E_g∕k_B$) for ${\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{1-y}{\mathrm{Zn}}_y\right)}_3{\mathrm{O}}_{7-\delta }$: The thick black dashed line shows $T_{c0}\left(p\right)$ for pure Y123, drawn using Eq. (1) with $T_{c0-\max }=93\mathrm{K}$. The thick black straight line is a guide to the eye. The dashed blue line represents the large asymmetric error bar associated with the data point for ${\mathrm{Y}}_{0.80}{\mathrm{Ca}}_{0.20}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{0.96}{\mathrm{Zn}}_{0.04}\right)}_3{\mathrm{O}}_{7-\delta }$ $(p=0.184\pm 0.003)$ compound (see text for details).

Figure 9

Two examples where $T_{\mathrm{scf}}⩾T*$ (see text for details): (a) ${\mathrm{Y}}_{0.90}{\mathrm{Ca}}_{0.10}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{0.985}{\mathrm{Zn}}_{0.015}\right)}_3{\mathrm{O}}_{7-\delta }$ ($p=0.180\pm 0.003$ and $T_c=64\mathrm{K}$) and (b) ${\mathrm{Y}}_{0.80}{\mathrm{Ca}}_{0.20}{\mathrm{Ba}}_2{\left({\mathrm{Cu}}_{0.96}{\mathrm{Zn}}_{0.04}\right)}_3{\mathrm{O}}_{7-\delta }$ ($p=0.184\pm 0.003$ and $T_c=42.25\mathrm{K}$).