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New Journal of Physics

Emergent mesoscopic quantum vortex and Planckian dissipation in the strange metal phase

Rong Li, Zhen-Su She

Published Mar 15, 2021• 6 citations
Publisher

Abstract

Abstract A major puzzle of condensed-matter physics is the physics behind the linear-in-temperature law of resistivity in many exotic metallic systems, including cuprates, pnictides, and heavy fermions. In this work, we propose, based on a symmetry-breaking analysis, that the strange metal phase is a novel emergent mesoscopic quantum state, beyond Landau’s quasiparticle excitation, which is composed of fluctuating vortices. The model predicts, in a straightforward way, the local magnetic field with a correlation time determined by the Coulomb potential, validated by observations of dynamic muon spin relaxation rates in both 3d cuprates and 5d iridate without fitting parameter. Furthermore, the model resolves the underlying quantum mechanism of the Planckian dissipation in terms of carrier scattering by fluctuating vortex, which predicts a scattering rate proportional to the vortex density, thus deriving both linear-in temperature and linear-in field laws, with a universal scattering coefficient validated by data of several dozens of samples for cuprates and iron pnictides. These findings offer a new phenomenology for non-Fermi liquid in strongly correlated materials.

DOI
10.1088/1367-2630/abeeba

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Abstract A major puzzle of condensed-matter physics is the physics behind the linear-in-temperature law of resistivity in many exotic metallic systems, including cuprates, pnictides, and heavy fermions. In this work, we propose, based on a symmetry-breaking analysis, that the strange metal phase is a novel emergent mesoscopic quantum state, beyond Landau’s quasiparticle excitation, which is composed of fluctuating vortices. The model predicts, in a straightforward way, the local magnetic field with a correlation time determined by the Coulomb potential, validated by observations of dynamic muon spin relaxation rates in both 3d cuprates and 5d iridate without fitting parameter. Furthermore, the model resolves the underlying quantum mechanism of the Planckian dissipation in terms of carrier scattering by fluctuating vortex, which predicts a scattering rate proportional to the vortex density, thus deriving both linear-in temperature and linear-in field laws, with a universal scattering coefficient validated by data of several dozens of samples for cuprates and iron pnictides. These findings offer a new phenomenology for non-Fermi liquid in strongly correlated materials.
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.
The mysterious metallic phase showing perfect TTT-linear resistivity and a universal scattering rate 1/τ=αPkBT/ℏ1/τ= α_P k_B T /\hbar1/τ=αP​kB​T/ℏ with a universal prefactor αP∼1α_P \sim 1αP​∼1 and logarithmic-in-temperature singular specific heat coefficient, so-called Planckian metal phase was observed in various overdoped high-TcT_cTc​ 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 ttt-JJJ 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\hbar ω/k_B Tℏω/kB​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.
The authors introduce exactly solvable models of the quantum phase transition, marking the breakdown of the heavy Fermi liquid in heavy-fermion materials. The solutions capture the puzzling non-Fermi liquid transport with linear-in-temperature resistivity, as seen in experiments. Furthermore, they reveal a broad regime in which a ``Planckian'' strange metal is established, namely the quasiparticle lifetime in this regime is set only by fundamental constants and the temperature. The new large-NNN approach introduced in the paper may be useful for describing a broader class of quantum critical points in systems with strong electronic correlations.
The breakdown of the celebrated Fermi liquid theory in the strange metal phase is the central enigma of correlated quantum matter. Motivated by recent experiments reporting short-lived carriers, along with the ubiquitous observations of modulated excitations in the phase diagram of cuprates, we propose a phenomenological boson-fermion model for this phase. Along with the fermions, we consider fluctuating bosons emerging from the remnants of a pair density wave as additional current carriers in the strange metal phase. These bosonic excitations are finite-momentum Cooper pairs and thus carry twice the electronic charge, and their net spin can either be zero or one arising from the two spin-1/21/21/2 electrons. We show in a perturbative calculation within Kubo formalism that such a model displays a TlogTTlogTTlogT dependence of the resistivity with temperature and manifests the Drude form of the ac conductivity. Furthermore, such bosons are incoherent and hence do not contribute to the Hall conductivity. Finally, the bosons emerging from finite-momentum pairs of spin-triplet symmetry also reproduce the recently observed linear-in-field magnetoresistance in the optimally doped and overdoped cuprates [P. Giraldo-Gallo et al., Science 361, 479 (2018); J. Ayres et al., Nature 595, 661 (2021)].
“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.
Fermi liquid theory forms the basis for our understanding of the majority of metals, which is manifested in the description of transport properties that the electrical resistivity goes as temperature squared in the limit of zero temperature. However, the observations of strange metal states in various quantum materials, notably high-temperature superconductors, bring this spectacularly successful theoretical framework into crisis. When electron scattering rate 1/τ hits its limit, kBT/{\hbar} where {\hbar} is the reduced Planck's constant, T represents absolute temperature and kB denotes Boltzmann's constant, Planckian dissipation occurs and lends strange metals a surprising link to black holes, gravity, and quantum information theory. Here, we show the characteristic signature of strange metallicity arising unprecedentedly in a bosonic system. Our nanopatterned YBa2Cu3O7-δ(YBCO) film arrays reveal T-linear resistance as well as B-linear magnetoresistance over an extended temperature and magnetic field range in a quantum critical region in the phase diagram. Moreover, the slope of the T-linear resistance α_cp appears bounded by α_cp {\approx} h/2e^2 [1/T]_c^onset where T_c^onset is the temperature at which Cooper pairs form, intimating a common scale-invariant transport mechanism corresponding to Planckian dissipation.In contrast to fermionic systems where the temperature and magnetic field dependent scattering rates combine in quadrature of {\hbar}/τ {\approx} {\sqrt} (((k_B T)^2+(μ_B B)^2)), both terms linearly combine in the present bosonic system, i.e. {\hbar}/τ {\approx} (k_B T+[γμ]_B B), where γ is a constant. By extending the reach of strange metal phenomenology to a bosonic system, our results suggest that there is a fundamental principle governing their transport which transcends particle statistics.