Indicators for phonon hydrodynamics from first principles predictions of thermal conductivity

TL;DR

This study introduces a computationally efficient indicator based on the ratio of thermal conductivities from different phonon transport models to identify materials exhibiting phonon hydrodynamics, aiding the discovery of unconventional heat flow regimes.

Contribution

The paper demonstrates that the ratio of thermal conductivities from the LPBE and RTA models serves as a low-cost indicator for phonon hydrodynamics, surpassing traditional scattering-based approaches.

Findings

The ratio $\,ppa_{LPBE}/ppa_{RTA}$ correlates with collective phonon drift and hydrodynamic behavior.

Conventional scattering-based methods are inadequate to predict phonon hydrodynamics.

The indicator ratio decreases with increasing Brillouin zone sampling density, affecting predictions.

Abstract

Hydrodynamic heat flow, where out-of-equilibrium phonons collectively drift in response to an applied temperature differential, has attracted renewed interest following its experimental observation in graphite at temperatures as high as 300 K. To accelerate discovery of material alternatives to graphite and suitable experimental conditions for realizing this non-Fourier heat flow regime, computationally efficient indicators derived from predictive first principles approaches are necessary. Here we show that the ratio of thermal conductivity ($\kappa$) obtained from the complete solution of the linearized Peierls-Boltzmann equation (LPBE) for phonon transport ($\kappa_{{LPBE}}$), to that from the relaxation time approximation (RTA) for phonon decay ($\kappa_{{RTA}}$), is a low cost indicator for phonon hydrodynamics. We show that collectively drifting non-equilibrium phonons amplify the ratio of $\kappa_{{LPBE}}$ to $\kappa_{{RTA}}$, while a small $\kappa_{{LPBE}}/\kappa_{{RTA}}$ correlates with predominantly diffusive phonon transport. On the other hand, we find that conventional approaches that rely only on momentum-conserving Normal and momentum-dissipating Umklapp scattering rates, such as the RTA and the Callaway approximations to the LPBE, are inadequate to predict phonon hydrodynamics. Furthermore, our study reveals that the indicator ratio - $\kappa_{{LPBE}}/\kappa_{{RTA}}$, and therefore the strength of hydrodynamic signatures, decrease with increasing Brillouin zone (BZ) sampling density for several ultrahigh-$\kappa$ materials at low temperatures, thus underscoring the need for careful BZ sampling convergence studies to ensure robust predictions of phonon hydrodynamics. This computationally inexpensive indicator of phonon hydrodynamics will accelerate the search for new materials that exhibit such unconventional heat flow regimes.