Phonons, electrons and thermal transport in Planckian high Tc materials

Mousatov, Connie H.; Hartnoll, Sean A.

doi:10.1038/s41535-021-00383-w

Cited by 17 publications

(17 citation statements)

References 57 publications

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“…A key motivation behind our work was to clarify the role of electron-phonon interactions in strange metals. In particular, it is crucial to understand, quantitatively, the contribution of electron-phonon scattering to unconventional transport [36,37]. The transfer of energy to the lattice gives an unambiguous measure of the presence and strength of electron-phonon interactions, but making use of this fact requires a formula for energy relaxation that does not assume a conventional Lindhard continuum.…”

Section: Discussionmentioning

confidence: 99%

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Joule heating in bad and slow metals

Glorioso¹,

Hartnoll²

2022

Preprint

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Heat supplied to a metal is absorbed by the electrons and then transferred to the lattice. In conventional metals energy is released to the lattice by phonons emitted from the Lindhard continuum. However in a 'bad' metal, with short mean free path, the low energy Lindhard continuum is destroyed. Furthermore in a 'slow' metal, with Fermi velocity less than the sound velocity, particle-hole pairs are kinematically unable to emit phonons. To describe energy transfer to the lattice in these cases we obtain a general Kubo formula for the energy relaxation rate in terms of the electronic density spectral weight Im G R nn (ω k , k) evaluated on the phonon dispersion ω k . We apply our Kubo formula to the high temperature Hubbard model, using recent data from quantum Monte Carlo and experiments in ultracold atoms to characterize Im G R nn (ω k , k). We furthermore use recent data from electron energy-loss spectroscopy to estimate the energy relaxation rate of the cuprate strange metal to a high energy optical phonon.Finally, we obtain an expression for the energy relaxation rate of a slow metal in terms of the optical conductivity.

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Section: Discussionmentioning

confidence: 99%

“…where we have one longitudinal mode with ω 2 k = 2µ+λ ρ k 2 and d − 1 transverse modes with ω 2 k⊥ = µ ρ k 2 , and s i s i = δ ss . The first factor in the integrand of (36) has been determined by imposing that…”

Section: A Acoustic Phononsmentioning

confidence: 99%

Joule heating in bad and slow metals

Glorioso¹,

Hartnoll²

2022

Preprint

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“…It is worth pointing out that the observation of a Planckian timescale in these experiments can be just the effect of electronsphonons interactions as in any common metal[243].…”

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confidence: 87%

Holographic Axion Model: a simple gravitational tool for quantum matter

Baggioli,

Kim,

et al. 2021

Preprint

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This is a complete and exhaustive review on the so-called holographic axion model -a bottom-up holographic system characterized by the presence of a set of shift symmetric scalar bulk fields whose profiles are taken to be linear in the spatial coordinates. This simple model implements the breaking of translational invariance of the dual field theory by retaining the homogeneity of the background geometry and therefore allowing for controllable and fast computations. The usages of this model are very vast and they are a proof of the spectacular versatility of the framework. In this review, we touch upon all the up-to-date aspects of this model from its connection with massive gravity and effective field theories, to its role in modeling momentum dissipation and elastic properties ending with all the phenomenological features and its hydrodynamic description. In summary, this is a complete guide to one of the most used model in Applied Holography and a must-read for any researcher entering this field. CONTENTSScope of this review 2 Notations and conventions 2 I. Introduction 3 A. The Drude model 5 B. Effective field theories for solids and fluids 7 C. Gauge-Gravity duality briefing 9 D. From inhomogeneous lattices to massive gravity and homogeneous models 11 II. A simple model for momentum relaxation 12 A. The origins 12

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“…Let us also note the presence of mv 2 s . This is the kinetic energy of an electron drifting with the velocity of sound, a less common energy scale when electrons and phonons couple to each other [42].…”

Section: B From Phonon Drag To Thermal Hall Effectmentioning

confidence: 99%

Phonon drag thermal Hall effect in metallic strontium titanate

Jiang,

Li,

Fauqué

et al. 2022

Preprint

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SrTiO3, a quantum paralectric, displays a detectable phonon thermal Hall effect (THE). Here we show that the amplitude of THE is extremely sensitive to stoichiometry. It drastically decreases upon substitution of a tiny fraction of Sr atoms with Ca, which stabilizes the ferroelectric order. When even a lower density of oxygen vacancies turn the system to a dilute metal, one the other hand, THE is drastically amplified. The enhancement exceeds by far the sum of the electronic and the phononic contributions. We explain this observation as an outcome of three features: i) heat is mostly transported by phonons; ii) the electronic Hall angle is extremely large; and iii) there is substantial momentum exchange between electrons and phonons. Starting from Herring's picture of phonon drag, we demonstrate that a quantitative account of the enhanced THE can be achieved. Thus, phonon drag, hitherto detected as an amplifier of thermoelectric coefficients, can generate a purely thermal transverse response in a dilute metal with a large Hall angle. Our results reveal a hitherto unknown consequence of momentum-conserving collisions between electrons and phonons.

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Phonons, electrons and thermal transport in Planckian high Tc materials

Cited by 17 publications

References 57 publications

Joule heating in bad and slow metals

Joule heating in bad and slow metals

Holographic Axion Model: a simple gravitational tool for quantum matter

Phonon drag thermal Hall effect in metallic strontium titanate

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