Significance Most metals display an electron-scattering rate 1 / τ that follows 1 / τ ∼ T 2 at low temperatures, as prescribed by Fermi liquid theory. But there are important exceptions. One of the most prominent examples is the “strange” metal regime in overdoped cuprate supercondcutors, which exhibits a linear T dependence of the scattering rate 1 / τ ∼ T that reaches a putative Planckian limit. Here, using cutting-edge computational approaches, we show that T -linear scattering rate can emerge from the overdoped Hubbard model at low temperatures. Our results agree with cuprate experiments in various aspects but challenge the Planckian limit. Finally, by identifying antiferromagnetic fluctuations as the physical origin of the T -linear scattering rate, we discover the microscopic mechanism of strange metallicity in cuprates.
Significance Most metals display an electron-scattering rate 1 / τ that follows 1 / τ ∼ T 2 at low temperatures, as prescribed by Fermi liquid theory. But there are important exceptions. One of the most prominent examples is the “strange” metal regime in overdoped cuprate supercondcutors, which exhibits a linear T dependence of the scattering rate 1 / τ ∼ T that reaches a putative Planckian limit. Here, using cutting-edge computational approaches, we show that T -linear scattering rate can emerge from the overdoped Hubbard model at low temperatures. Our results agree with cuprate experiments in various aspects but challenge the Planckian limit. Finally, by identifying antiferromagnetic fluctuations as the physical origin of the T -linear scattering rate, we discover the microscopic mechanism of strange metallicity in cuprates.
Abstract The mysterious metallic phase showing T-linear resistivity and a universal scattering rate 1 / τ = α P k B T / ℏ with a universal prefactor α P ∼ 1 and logarithmic-in-temperature singular specific heat coefficient, the so-called ‘Planckian metal phase’ was observed in various overdoped high- T c 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- T c 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 surface 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 ℏ ω / 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 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.
Two T-linear scattering-rate regimes in the triangular lattice Hubbard model
In recent years, the T T -linear scattering rate found at low temperatures, defining the strange metal phase of cuprates, has been a subject of interest. Since a wide range of materials have a scattering rate that obeys the equation $ / ≈ k_B T$, the idea of a universal Planckian limit on the scattering rate has been proposed. However, there is no consensus on proposed theories yet. In this work, we present our results for the T T -linear scattering rate in the triangular lattice Hubbard model obtained using the dynamical cluster approximation. We find two regions with T T -linear scattering rate in the T T - p p phase diagram: one emerges from the pseudogap to correlated Fermi liquid phase transition at low doping, whereas the other is solely caused by large interaction strength at large doping.
The mysterious metallic phase showing perfect T-linear resistivity and a universal scattering rate 1/τ=αPkBT/ℏ with a universal prefactor αP∼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. 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 ℏω/kBT 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.
“Strange” metals that do not follow the predictions of Fermi liquid theory are prevalent in materials that feature superconductivity arising from electron interactions. In recent years, it has been hypothesized that spatial randomness in electron interactions must play a crucial role in strange metals for their hallmark linear-in-temperature ( T ) resistivity to survive down to low temperatures where phonon and umklapp processes are ineffective, as is observed in experiments. However, a clear picture of how this happens has not yet been provided in a realistic model free from artificial constructions, such as large- N limits and replica tricks. We study a realistic model of two-dimensional metals with spatially random antiferromagnetic interactions in a nonperturbative regime, using numerically exact high-performance, large-scale hybrid Monte Carlo simulation and exact averages over the quenched spatial randomness. Our simulations reproduce strange metals’ key experimental signature of linear-in- T resistivity with a universal “Planckian” transport scattering rate Γ tr ∼ k B T / ℏ that is independent of coupling constants. We further find that strange metallicity in these systems is not associated with a quantum critical point and, instead, arises from a phase of matter with gapless antiferromagnetic fluctuations that lacks long-range correlations and spans an extended region of parameter space: A feature that is also observed in several experiments. These gapless antiferromagnetic fluctuations take the form of spatially localized overdamped modes, whose presence could possibly be detected using recently developed nanoscale magnetometry methods. Our work paves the way for an eventual microscopic understanding of the role of spatial disorder in determining important properties of correlated-electron materials.
Motivated by the recent findings on the T-linear electronic scattering rate in the two-dimensional Hubbard model, we have investigated the three-orbital Emery model and its temperature-dependent electronic and quasiparticle scattering rates by adopting dynamical cluster quantum Monte Carlo simulations. By focusing on two characteristic site energies ${\ensuremath{\epsilon}}_{p}$ of O−2p orbital relevant to cuprates and nickelates separately, our exploration discovered that, for ${\ensuremath{\epsilon}}_{p}=3.24$ relevant to cuprates, the scattering rate can exhibit a linear-T dependence at low temperature for a range of intermediate densities. In contrast, for larger ${\ensuremath{\epsilon}}_{p}=6.0$ presumably relevant to nickelates, a wide range of densities support a downturn of the scattering rate below the temperature scale $T\ensuremath{\sim}0.1$ with possibly two consecutive nearly linear-T regimes connected via a smooth crossover around $T\ensuremath{\sim}0.1$. Furthermore, the temperature-dependent quasiparticle scattering rate generically departs from the unity slope as predicted by the Planckian dissipation theory. Our presented work provides valuable insights on the extensively studied three-orbital Emery model, particularly on the quantitative examination of non-Fermi-liquid features of scattering rates.
Motivated by the recent findings on the T-linear electronic scattering rate in the two-dimensional Hubbard model, we have investigated the three-orbital Emery model and its temperature-dependent electronic and quasiparticle scattering rates by adopting dynamical cluster quantum Monte Carlo simulations. By focusing on two characteristic site energies εp of O-2p orbital relevant to cuprates and nickelates separately, our exploration discovered that, for εp=3.24 relevant to cuprates, the scattering rate can exhibit a linear-T dependence at low temperature for a range of intermediate densities. In contrast, for larger εp=6.0 presumably relevant to nickelates, a wide range of densities support a downturn of the scattering rate below the temperature scale T∼0.1 with possibly two consecutive nearly linear-T regimes connected via a smooth crossover around T∼0.1. Furthermore, the temperature dependent quasiparticle scattering rate generically departs from the unity slope as predicted by the Planckian dissipation theory. Our presented work provides valuable insights on the extensively studied three-orbital Emery model, particularly on the quantitative examination of non-Fermi liquid features of scattering rates.