The phase diagram of the cuprate superconductors has posed a formidable scientific challenge for more than three decades. This challenge is perhaps best exemplified by the need to understand the normal-state charge transport as the system evolves from Mott insulator to Fermi-liquid metal with doping. Here we report a detailed analysis of the temperature (T) and doping (p) dependence of the planar resistivity of simple-tetragonal HgBa2CuO4+δ (Hg1201), the single-CuO2-layer cuprate with the highest optimal superconducting transition temperature, Tc. The data allow us to test a recently proposed phenomenological model for the cuprate phase diagram that combines a universal transport scattering rate with spatially inhomogeneous (de)localization of the Mott-localized hole. We find that the model provides a good description of the data. We then extend this analysis to prior transport results for several other cuprates, including the Hall number in the overdoped part of the phase diagram, and find little compound-to-compound variation in the (de)localization gap scale. The results point to a robust, universal structural origin of the inherent gap inhomogeneity that is unrelated to doping-related disorder. They are inconsistent with the notion that much of the phase diagram is controlled by a quantum-critical point, and instead indicate that the unusual electronic properties exhibited by the cuprates are fundamentally related to strong nonlinearities associated with subtle nanoscale inhomogeneity.
Bibliographical noteFunding Information:
We thank M. K. Chan for contributions to the crystal growth and transport measurements. The work at the University of Minnesota was funded by the Department of Energy through the University of Minnesota Center for Quantum Materials under Award No. DE-SC0016371. The work at the TU Wien was supported by the European Research Council (ERC Consolidator Grant No 725521); the work at the University of Zagreb was supported by the CeNIKS project cofinanced by the Croatian Government and the European Union through the European Regional Development Fund—Competitiveness and Cohesion Operational Programme (Grant No. KK.01.1.1.02.0013) and the Croatian-Swiss Research Program of the Croatian Science Foundation and the Swiss National Science Foundation with funds obtained from the Swiss-Croatian Cooperation Programme.
© 2020 American Physical Society.