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

Abstract

The mysterious metallic phase showing T-linear resistivity and a universal scattering rate 1/τ = α_Pk_BT/ℏ with a universal prefactor α_P∼ 1 and logarithmic-in-temperature singular specific heat coefficient, so-called "Planckian metal phase" was observed in various overdoped high-Tc cuprate 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-Tc superconductivity. 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 surfaces within the heavy-fermion formulation of the slave-boson t-J model. 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 Planckian ℏω/kBT scaling in scattering rate near an extended localizeddelocalized (pseudogap-to-Fermi liquid) charge-Kondo breakdown transition. The d-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 how d-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.