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Physical review. B./Physical review. B

Non-Fermi-liquid behavior of the scattering rate in the three-orbital Emery model

Tianzong Mao, Mi Jiang

Published Jun 3, 2024• 2 citations
Publisher

Abstract

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 $\mathrm{O-2}p$ 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.

DOI
10.1103/physrevb.109.245102

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Motivated by the recent findings on the TTT-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 \ensuremathϵp{\ensuremath{\epsilon}}_{p}\ensuremathϵp​ of O−2p\mathrm{O-2}pO−2p orbital relevant to cuprates and nickelates separately, our exploration discovered that, for \ensuremathϵp=3.24{\ensuremath{\epsilon}}_{p}=3.24\ensuremathϵp​=3.24 relevant to cuprates, the scattering rate can exhibit a linear-TTT dependence at low temperature for a range of intermediate densities. In contrast, for larger \ensuremathϵp=6.0{\ensuremath{\epsilon}}_{p}=6.0\ensuremathϵp​=6.0 presumably relevant to nickelates, a wide range of densities support a downturn of the scattering rate below the temperature scale T\ensuremath∼0.1T\ensuremath{\sim}0.1T\ensuremath∼0.1 with possibly two consecutive nearly linear-TTT regimes connected via a smooth crossover around T\ensuremath∼0.1T\ensuremath{\sim}0.1T\ensuremath∼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 TTT-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 εpε_pεp​ of O-2ppp orbital relevant to cuprates and nickelates separately, our exploration discovered that, for εp=3.24ε_p=3.24εp​=3.24 relevant to cuprates, the scattering rate can exhibit a linear-TTT dependence at low temperature for a range of intermediate densities. In contrast, for larger εp=6.0ε_p=6.0εp​=6.0 presumably relevant to nickelates, a wide range of densities support a downturn of the scattering rate below the temperature scale T∼0.1T\sim0.1T∼0.1 with possibly two consecutive nearly linear-TTT regimes connected via a smooth crossover around T∼0.1T\sim0.1T∼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 experimental demonstration of the doping dependence of the linear-in-temperature resistivity coefficient in cuprates, we numerically investigated the three-orbital Emery model focusing on the slope of the TTT-linear electronic and quasiparticle scattering rates by adopting dynamical cluster quantum Monte Carlo simulations. Our exploration discovered that the slope of electronic scattering rate evolves linearly with the electron-doping; while it is inversely proportional to the hole-doping level at intermediate doping regime and then crossovers to the linear-like dependence on further hole doping. These features remarkably match with the experimental findings qualitatively. We further discuss the doping-dependent slope of the quasiparticle scattering rate and also estimate the resistivity coefficient. Our presented work provides promising insight on the three-orbital Emery model, particularly its doping evolution and connection to the underlying mechanism of the TTT-linear resistivity in cuprates.
Motivated by the recent experimental demonstration of the doping dependence of the linear-in-temperature resistivity coefficient in cuprates, we numerically investigated the three-orbital Emery model focusing on the slope of the TTT-linear electronic and quasiparticle scattering rates by adopting dynamical cluster quantum Monte Carlo simulations. Our exploration discovered that the slope of electronic scattering rate evolves linearly with the electron doping; while it is inversely proportional to the hole-doping level at the intermediate doping regime and then crossovers to the linearlike dependence on further hole doping. These features remarkably match with the experimental findings qualitatively. We further discuss the doping-dependent slope of the quasiparticle scattering rate and also estimate the resistivity coefficient. Our presented work provides promising insight on the three-orbital Emery model, particularly its doping evolution and connection to the underlying mechanism of the TTT-linear resistivity in cuprates.
We use the numerically unbiased determinant quantum Monte Carlo method to systematically investigate the three-orbital Emery model in the normal state in a wide range of local interactions, charge transfer energy, and doping levels. We focus on the influence of the on-site Hubbard Udd{U}_{dd}Udd​ and the charge transfer energy scale ${\ensuremath{\epsilon}}_{p}$ on the electronic properties via the orbital occupancies, local moments, spin correlations, and spectral properties. Rich features of the orbital-resolved local and momentum-dependent spectra are revealed to be associated with the possible Zhang-Rice singlet breakdown reflected by the peak splitting near the Fermi level in the heavily overdoped regime. Moreover, the pseudogap features at a small charge transfer energy scale (relevant to cuprates) are shown to diminish at larger ${\ensuremath{\epsilon}}_{p}$, which implies the weakening or absence of the pseudogap in the infinite-layer nickelates. Besides, an optimal value of ${\ensuremath{\epsilon}}_{p}$ is identified for maximizing the antiferromagnetic spin correlations. Our large-scale simulations provide additional insights into the well-established Emery model, particularly in the regime of heavily overdoped and/or large charge transfer energy scale.
The microscopic origin of high-temperature superconductivity in cuprates remains one of the central open questions in condensed matter physics. Growing experimental and theoretical evidence suggests that the bare single-band Fermi-Hubbard model may not fully capture properties of cuprates such as superconductivity, motivating us to revisit the canonical three-band model of the copper-oxide planes - the Emery model - from which the single-band counterpart was originally derived. Here, we propose and analyze a quantum simulation scheme for realizing the Emery model in regimes relevant to cuprates and infinite-layer nickelates with today's ultracold atom quantum simulation platforms, enabling the exploration of the three-band physics on system sizes that are challenging for current numerical methods. Specifically, we show that a two-dimensional optical lattice with a superimposed pattern of repulsive potentials can be designed to study low-temperature properties for variable parameter regimes of the Emery model relevant to cuprates as well as infinite-layer nickelates. Our results pave the way for real material simulations with ultracold atom quantum simulators and a better understanding of the physics of unconventional superconductors.
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.