Lattice thermal conductivity in the anharmonic overdamped regime

TL;DR

This paper introduces a novel computational approach combining Green-Kubo theory with the stochastic self-consistent harmonic approximation to accurately calculate lattice thermal conductivity in strongly anharmonic, overdamped regimes, including phase transitions.

Contribution

The authors develop a new method that accounts for anharmonicity and phase transitions, improving the accuracy of thermal conductivity predictions in complex materials.

Findings

Successfully applied to CsPbBr₃, matching experimental thermal conductivity data.

Eliminates the need for phonon lifetime assumptions in overdamped regimes.

Models complex dynamical thermal transport, including phase transitions.

Abstract

In crystalline materials, low lattice thermal conductivity is often associated with strong anharmonicity, which can cause significant deviations from the expected Lorentzian lineshape of phonon spectral functions. These deviations, occurring in an overdamped regime, raise questions about the applicability of the Boltzmann transport equation. Furthermore, strong anharmonicity can trigger structural phase transitions with temperature, which cannot be adequately described by the standard harmonic approximation. To address these challenges, we propose a novel approach for computing the lattice thermal conductivity. Our method combines the Green-Kubo linear response theory with the stochastic self-consistent harmonic approximation. The latter allows us to describe the temperature-dependent evolution of the crystal structure, including first- and second-order phase transitions, as well as the vibrational properties in highly anharmonic materials. The Green-Kubo method considers the entire lineshapes of phonon spectral functions in the calculation of the lattice thermal conductivity, thus eliminating the questionable use of phonon lifetimes in the overdamped regime, as well as naturally including coherent transport effects. Additionally, we extend our theory to model complex dynamical lattice thermal conductivity, enhancing our understanding of time-dependent thermoreflectance experiments. As a practical application, we employ this approach to calculate the lattice thermal conductivity of CsPbBr$_3$, a complex crystal known for its anomalous thermal transport behavior with a complex phase diagram. Our method is able to determine the thermal conductivity across different phases in good agreement with experiments.