First-order-type effects in ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6+x}$ at the onset of superconductivity

We present results of Raman-scattering experiments on tetragonal $\left({\text{Y}}_{1-y}{\text{Ca}}_y\right){\text{Ba}}_2{\text{Cu}}_3{\text{O}}_{6+x}$ for doping levels $p\left(x,y\right)$ between 0 and 0.07 holes/${\text{CuO}}_2$. Below the onset of superconductivity at $p_{\text{sc}1}\approx 0.06$, we find evidence of a diagonal superstructure. At $p_{\text{sc}1}$, lattice and electron dynamics change discontinuously with the charge and spin properties being renormalized at all energy scales. The results indicate that charge ordering is intimately related to the transition at $p_{\text{sc}1}$ and that the maximal transition temperature to superconductivity at optimal doping $T_c^{\text{max}}$ depends on the type of ordering at $p>p_{\text{sc}1}$.

Figure 1

(Color online) Response of charge-ordering fluctuations in $\left({\text{Y}}_{0.97}{\text{Ca}}_{0.03}\right){\text{Ba}}_2{\text{Cu}}_3{\text{O}}_{6.05}$ (Ref. 17). The points represent the experimental results and the full lines are the theoretical fits. (Reproduced with permission.) Two fluctuations with finite but opposite momenta are exchanged (Azlamazov-Larkin diagrams). The inset shows the peak positions of the response as a function of temperature in $\left({\text{Y}}_{0.97}{\text{Ca}}_{0.03}\right){\text{Ba}}_2{\text{Cu}}_3{\text{O}}_{6.05}$, ${\text{La}}_{1.98}{\text{Sr}}_{0.02}{\text{CuO}}_4$, and ${\text{La}}_{1.90}{\text{Sr}}_{0.10}{\text{CuO}}_4$. At similar doping $\left(p\simeq 0.02\right)$ the points essentially coincide.

Figure 2

(Color online) Raman response $R{\chi }^{″}\left(p,\Omega \right)$ of $\left({\text{Y}}_{1-y}{\text{Ca}}_y\right){\text{Ba}}_2{\text{Cu}}_3{\text{O}}_{6+x}$ at low doping and temperature outside the superconducting state (raw data). The response $R{\chi }^{″}\left(\Omega ,p\right)$ is obtained by dividing the experimental spectra by the Bose factor. All spectra are measured with the Ar laser line at 458 nm. The upper (a,c) and lower (b,d) panels correspond to the $B_{1g}$ and $B_{2g}$ symmetries, respectively, with the related polarizations and sensitivities in the Brillouin zone as indicated. Doping level and measuring temperatures of the samples are shown as full circles in the schematic phase diagram in the inset in (a), where AF and SC label antiferromagnetism and superconductivity, respectively, and are indicated explicitly in (b). Panels (a) and (b) show an energy range of $8000{\text{cm}}^{-1}$ equivalent to 1 eV. In (c) and (d) the low-energy and -intensity ranges are expanded as indicated by dashed boxes in (a) and (b). The inset in (c) shows the peak intensity of the $B_{1g}$ “buckling” phonon at $340{\text{cm}}^{-1}$ (43 meV). Triangles and squares represent Ca-free and Ca-doped Y-123, respectively.

Figure 3

(Color online) Raman responses $R{\chi }_{B_{2g}}^{″}\left(T,\Omega \right)$ of $\left({\text{Y}}_{1-y}{\text{Ca}}_y\right){\text{Ba}}_2{\text{Cu}}_3{\text{O}}_{6+x}$ at $p=0.07$ (a) and 0.04 (b). In the insets we plot the low-energy “Raman resistivities” ${\Gamma }_0\left(T\right)\propto {\left(\partial {\chi }^{″}/\partial \Omega \right)}_{\Omega =0}^{-1}$ (squares) corresponding to the initial slope of the spectra (Ref. 16) and compare them with the conventional resistivities (lines) from Ref. 22.

Figure 4

(Color online) Phase diagrams for “low”- (a) and “high”-$T_c$ (b) cuprates as derived from the earlier (Ref. 8) and present Raman data and from the neutron scattering (Refs. 6, 10, 11, 24) and scanning tunneling microscopy (Refs. 5, 9) measurements. The position of the onset point of superconductivity $p_{\text{sc}1}$ depends on the degree of disorder with the minimum at approximately 0.05 for clean materials (Ref. 1). The lines of different length qualitatively indicate doping and temperature ranges, density, orientation, and correlation lengths of stripes. The square pattern symbolizes checkerboard order which, however, is only established for $p>0.10$. For $p_{\text{sc}1}<p<0.10$, there are indications from the Raman results presented here for an interaction with structure in momentum space as sketched.