The resistivity phase diagram of cuprates revisited

The past three decades have seen extraordinary efforts to understand the cuprate high-transition temperature (high-$T_c$) superconductors. The phase diagram of these complex lamellar oxides is characterized by Mott-insulating and Fermi-liquid states at zero and high hole doping, respectively, and by an unusual regime at intermediate doping out of which the superconducting state emerges upon cooling. Here we report a detailed analysis of the temperature and doping dependence of the planar resistivity of simple tetragonal HgBa$_2$CuO$_{4+delta}$ (Hg1201), the single-CuO$_2$-layer cuprate with the highest optimal $T_c$. The data allow us to test a recently proposed phenomenological model that combines a universal scattering rate with spatially inhomogeneous (de)localization gap of the Mott-localized hole. We find that the model provides an excellent description of the data. We then extend this analysis to prior results for several other cuprates, and find little compound-to-compound variation in (de)localization gap scale. This points to a universal structural origin of the inherent gap inhomogeneity that is unrelated to doping-induced disorder.