A mechanism for quantum-critical Planckian metal phase in high-temperature cuprate superconductors

The mysterious metallic phase showingT-linear resistivity and a universal scattering rate1/τ=αPkBT/ℏwith a universal prefactorαP∼1and logarithmic-in-temperature singular specific heat coefficient, the so-called 'Planckian metal phase' was observed in various overdoped high-Tccuprate superconductors over a finite range in doping. Revealing the mystery of the Planckian metal state is believed to be the key to understanding the mechanism for high-Tcsuperconductivity. Here, we propose a generic microscopic mechanism for this state based on quantum-critical local bosonic charge Kondo fluctuations coupled to both spinon and a heavy conduction-electron Fermi surface within the heavy-fermion formulation of the slave-bosont-Jmodel. By a controlled perturbative renormalization group analysis, we examine the competition between the pseudogap phase, characterized by Anderson's Resonating-Valence-Bond spin-liquid, and the Fermi-liquid state, modeled by the electron hopping (effective charge Kondo effect). We find a quantum-critical metallic phase with a universal Planckianℏω/kBTscaling in scattering rate near an extended localized-delocalized (pseudogap-to-Fermi liquid) charge-Kondo breakdown transition. Thed-wave superconducting ground state emerges near the transition. Unprecedented qualitative and quantitative agreements are reached between our theoretical predictions and various experiments, including optical conductivity, universal doping-independent field-to-temperature scaling in magnetoresistance, specific heat coefficient, marginal Fermi-liquid spectral function observed in ARPES, and Fermi surface reconstruction observed in Hall coefficients in various overdoped cuprates. Our mechanism offers a microscopic understanding of the quantum-critical Planckian metal phase observed in cuprates and its link to the pseudogap,d-wave superconducting, and Fermi liquid phases. It offers a promising route for understanding howd-wave superconductivity emerges from such a strange metal phase in cuprates-one of the long-standing open problems in condensed matter physics since 1990s-as well as shows a broader implication for the Planckian strange metal states observed in other correlated unconventional superconductors.