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

TL;DR

This paper proposes a microscopic quantum-critical mechanism involving charge Kondo fluctuations that explains the universal Planckian metal phase observed in overdoped cuprate superconductors, aligning with various experimental findings.

Contribution

It introduces a novel quantum-critical model based on charge Kondo effects within the heavy-fermion framework to explain the Planckian metal phase in cuprates.

Findings

Identifies a quantum-critical metallic phase with universal scattering rate scaling.

Matches experimental optical conductivity, magnetoresistance, ARPES, and Hall coefficient data.

Provides a microscopic understanding of the Planckian metal phase in cuprates.

Abstract

The mysterious metallic phase showing perfect $T$-linear resistivity and a universal scattering rate $1/\tau = \alpha_P k_B T /\hbar$ with a universal prefactor $\alpha_P \sim 1$ and logarithmic-in-temperature singular specific heat coefficient, so-called Planckian metal phase was observed in various overdoped high-$T_c$ cuprate superconductors over a finite range in doping. Here, we propose a microscopic mechanism for this exotic state based on quantum-critical 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. Using a controlled perturbative renormalization group (RG) analysis, we examine the competition between the pseudogap phase, characterized by Anderson's Resonating-Valence-Bond spin-liquid, and the Fermi-liquid state, characterized by the electron hoping (effective charge Kondo effect). We find a quantum-critical metallic phase with a universal Planckian $\hbar \omega/k_B T$ scaling in scattering rate near a localized-delocalized (pseudogap-to-Fermi liquid) charge Kondo breakdown transition. Our results are in excellent agreement with the recent experimental observations on optical conductivity (without fine-tuning) in Nat. Commun. 14, 3033 (2023), universal doping-independent field-to-temperature scaling in magnetoresistance in Nature 595, 661 (2021), and the marginal Fermi-liquid spectral function observed in ARPES (Science 366, 1099 (2019)) as well as Hall coefficient in various overdoped cuprates in Nature 595, 661 (2021) and Annu. Rev. Condens. Matter Phys. 10, 409 (2019). Our mechanism offers a microscopic understanding of the quantum-critical Planckian metal phase observed in cuprates d-wave superconducting, and Fermi liquid phases.