Lattice thermal conductivity decomposition: Peierls vs. non-Peierls contributions

TL;DR

This study compares different computational methods for lattice thermal conductivity in crystalline solids, revealing small differences between quadratic and Peierls contributions and highlighting the significance of optical phonons in quartz.

Contribution

It provides a detailed comparison of Green-Kubo, quadratic, and Peierls heat current methods across multiple crystalline materials, including the relaxation time approximation.

Findings

Quadratic and Peierls heat currents yield similar thermal conductivities.

Optical phonons dominate thermal conductivity in $ ext{α}$-quartz.

Relaxation time approximation underestimates conductivity systematically.

Abstract

The Green-Kubo lattice thermal conductivity computed using the full classical heat current of a crystalline solid is compared with results obtained from the quadratic component of the heat current and from the commonly used Peierls heat current. In addition, thermal conductivity within the relaxation time approximation is evaluated. Three crystalline systems are investigated: solid argon, a model of solid argon with alternating masses, and $\alpha$-quartz. For all materials considered, the thermal conductivities calculated using the quadratic and Peierls heat currents differ only slightly. In the case of $\alpha$-quartz, the optical phonon contribution to the thermal conductivity is found to exceed that of the acoustic modes. The relaxation time approximation systematically underestimates the thermal conductivity in all three systems.