Evidence for a universal Fermi-liquid scattering rate throughout the phase diagram of the copper-oxide superconductors

The phase diagram of the cuprate superconductors continues to pose formidable scientific challenges. While these materials are typically viewed as doped Mott insulators, it is well known that they are Fermi liquids at high hole-dopant concentrations. It was recently demonstrated that at moderate doping, in the pseudogap (PG) region of the phase diagram, the charge carriers are also best described as a Fermi liquid. Nevertheless, the relationship between the two Fermi-liquid (FL) regions and the nature of the strange-metal (SM) state at intermediate doping have remained unsolved. Here we show for the case of the model cuprate superconductor HgBa₂CuO_4+δ that the normal-state transport scattering rate determined from the cotangent of the Hall angle remains quadratic in temperature across the PG temperature, upon entering the SM state, and that it is doping-independent below optimal doping. Analysis of prior transport results for other cuprates reveals that this behavior is universal throughout the entire phase diagram and points to a pervasive FL transport scattering rate. These observations can be reconciled with a variety of other experimental results for the cuprates upon considering the possibility that the PG phenomenon is associated with the gradual, non-uniform localization of one hole per planar CuO₂ unit.