Adiabatic variation of the charge-density-wave phase diagram in the 123 cuprate (Ca$_x$La$_{1-x}$)(Ba$_{1.75-x}$La$_{0.25+x}$)Cu$_3$O$_y$

In order to explain the emergence of the anomalous pseudogap state and high-temperature superconductivity in the cuprates, intense research activity over three decades has focused on unravelling the connection between the various instabilities of the underdoped regime. In the high-temperature superconductor (Ca$_x$La$_{1-x}$)(Ba$_{1.75-x}$La$_{0.25+x}$)Cu$_3$O$_y$ (CLBLCO) isovalent chemical substitution produces smooth changes to the CuO$_2$ plane buckling and the Cu(II)-to-apical-oxygen distance, allowing us to study the interdependence of charge-density-wave (CDW) order, superconductivity and the pseudogap at constant hole doping in two adiabatically connected representations of the 123 cuprate structure. In this study, resonant soft x-ray scattering measurements reveal the first observation of incommensurate CDW correlations in CLBLCO and demonstrate a lack of correlation between $T_{\text{CDW}}$ and the pseudogap crossover temperature ($T^{\ast}$). This result disfavours a scenario in which the opening of the pseudogap at $T^{\ast}$ results from fluctuating CDW correlations.