Electronic inhomogeneity appears to be an inherent characteristic of the enigmatic cuprate superconductors. Here we report the observation of charge–density–wave correlations in the model cuprate superconductor HgBa₂CuO_4+δ (T_c=72 K) via bulk Cu L₃-edge-resonant X-ray scattering. At the measured hole-doping level, both the short-range charge modulations and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which these two phenomena are preceded at the higher pseudogap temperature by q=0 magnetic order and the build-up of significant dynamic antiferromagnetic correlations. The magnitude of the charge modulation wave vector is consistent with the size of the electron pocket implied by quantum oscillation and Hall effect measurements for HgBa₂CuO_4+δ and with corresponding results for YBa₂Cu₃O_6+δ, which indicates that charge–density–wave correlations are universally responsible for the low-temperature quantum oscillation phenomenon.

We report in-plane resistivity ($\rho$) and transverse magnetoresistance (MR) measurements for underdoped ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ (Hg1201). Contrary to the long-standing view that Kohler’s rule is strongly violated in underdoped cuprates, we find that it is in fact satisfied in the pseudogap phase of Hg1201. The transverse MR shows a quadratic field dependence, $\delta \rho /{\rho }_0=a{H}^2$, with $a(T)\propto T^{-4}$. In combination with the observed $\rho \propto T^2$ dependence, this is consistent with a single Fermi-liquid quasiparticle scattering rate. We show that this behavior is typically masked in cuprates with lower structural symmetry or strong disorder effects.