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

Yung-Yeh Chang², Khoe Van Nguyen¹, Kim Remund¹, Chung-Hou Chung^1*

¹Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan
²Institute of Physics, Academia Sinica, Taipei, Taiwan

* Presenter:Chung-Hou Chung, email:chung0523@nycu.edu.tw

The mysterious metallic phase showing perfect T-linear resistivity and a universal scattering rate 1/τ= α_P k_B T/ℏ with an almost universal constant prefactor α_P ∼ 1 and logarithmic-in-temperature singular specific heat coefficient, so-called “Planckian metal phase” was observed in various 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 [1]. 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 hoping (effective charge Kondo effect). We find a quantum-critical metallic phase with a coupling-constant independent universal Planckian ℏω/k_B T scaling in scattering rate near an extended localized-delocalized (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. 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 paves the way and 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.

References:
[1] Yung-Yeh Chang, Khoe Van Nguyen, Kim Remund, and Chung-Hou Chung∗, arXiv:2406.14858.

Keywords: Strange metal, Quantum criticality, High-Tc superconductors, Non-Fermi liquid, Planckian metal