High temperature thermal transport in insulators has been conjectured to be subject to a Planckian bound on the transport lifetime τ τ Pl ≡ /(k B T ), despite phonon dynamics being entirely classical at these temperatures. We argue that this Planckian bound is due to a quantum mechanical bound on the sound velocity: v s < v M . The 'melting velocity' v M is defined in terms of the melting temperature of the crystal, the interatomic spacing and Planck's constant. We show that for several classes of insulating crystals, both simple and complex, τ /τ Pl ≈ v M /v s at high temperatures. The velocity bound therefore implies the Planckian bound.

Strongly correlated metals often display anomalous transport, including T -linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for bad metals, by supplementing the well-known Hubbard model -with hopping t and on-site repulsion U -with a 'screened Coulomb' interaction between charge densities that decays exponentially with spatial separation. This interaction entirely lifts the extensive degeneracy in the spectrum of the t = 0 Hubbard model, allowing us to fully characterize the small t electric, thermal and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe T -linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Weidemann-Franz law and a large thermopower that can undergo sign change.

The bilayer perovskite Sr3Ru2O7 has been widely studied as a canonical strange metal. It exhibits T-linear resistivity and a T log(1/T) electronic specific heat in a field-tuned quantum critical fan. Criticality is known to occur in “hot” Fermi pockets with a high density of states close to the Fermi energy. We show that while these hot pockets occupy a small fraction of the Brillouin zone, they are responsible for the anomalous transport and thermodynamics of the material. Specifically, a scattering process in which two electrons from the large, “cold” Fermi surfaces scatter into one hot and one cold electron renders the ostensibly noncritical cold fermions a marginal Fermi liquid. From this fact the transport and thermodynamic phase diagram is reproduced in detail. Finally, we show that the same scattering mechanism into hot electrons that are instead localized near a 2D van Hove singularity explains the anomalous transport observed in strained Sr2RuO4.

The room-temperature thermal diffusivity of high Tc materials is dominated by phonons. This allows the scattering of phonons by electrons to be discerned. We argue that the measured strength of this scattering suggests a converse Planckian scattering of electrons by phonons across the room-temperature phase diagram of these materials. Consistent with this conclusion, the temperature derivative of the resistivity of strongly overdoped cuprates is noted to show a kink at a little below 200 K that we argue should be understood as the onset of a high-temperature Planckian T-linear scattering of electrons by classical phonons. This kink continuously disappears toward optimal doping, even while strong scattering of phonons by electrons remains visible in the thermal diffusivity, sharpening the long-standing puzzle of the lack of a feature in the T-linear resistivity at optimal doping associated with the onset of phonon scattering.

The room temperature thermal diffusivity of high T c materials is dominated by phonons. This allows the scattering of phonons by electrons to be discerned. We argue that the measured strength of this scattering suggests a converse Planckian scattering of electrons by phonons across the room temperature phase diagram of these materials.Consistent with this conclusion, the temperature derivative of the resistivity of strongly overdoped cuprates is noted to show a kink at a little below 200 K that we argue should be understood as the onset of a high temperature Planckian T -linear scattering of electrons by classical phonons. This kink continuously disappears towards optimal doping, even while strong scattering of phonons by electrons remains visible in the thermal diffusivity, sharpening the long-standing puzzle of the lack of a feature in the T -linear resistivity at optimal doping associated to onset of phonon scattering. BackgroundThe thermal conductivity of conventional metals at room temperature obeys the Wiedemann-Franz law [1]. This establishes that heat transport is dominated by electrons and that the electronic scattering is elastic. Indeed, at these temperatures electrons are scattered elastically off classical phonons, leading to a T -linear resistivity with an underlying scattering rate of 1/τ ≈ k B T / [2]. This rate has come to be known as 'Planckian ' [3].The thermal conductivity of unconventional metals such as high T c cuprates and pnictides at room temperature does not obey the Wiedemann-Franz law [4][5][6][7][8]. The Lorenz ratio