Direct Calculation of Modal Contributions to Thermal Conductivity via Green-Kubo Modal Analysis: Crystalline and Amorphous Silicon

TL;DR

This paper introduces GKMA, a novel method combining lattice dynamics and Green-Kubo formulas to directly compute modal contributions to thermal conductivity across various materials, including crystalline and amorphous silicon.

Contribution

The paper presents a new, generalizable method for calculating modal thermal conductivity contributions without defining phonon velocities, applicable to diverse materials.

Findings

Applicable to crystalline, amorphous, and molecular systems

Provides insight into phonon transport via mode-mode correlations

Unifies formalism for different material classes

Abstract

In this letter we derive a new method for direct calculation of the modal contributions to thermal conductivity, which is termed Green-Kubo modal analysis (GKMA). The GKMA method combines the lattice dynamics formalism with the Green-Kubo formula for thermal conductivity, such that the thermal conductivity becomes a direct summation of modal contributions, where one need not define the phonon velocity. As a result the GKMA method can be applied to any material/group of atoms where the atoms vibrate around stable equilibrium positions, which includes not only crystalline line compounds, but also random alloys, amorphous materials and even molecules. The GKMA method provides new insight into the nature of phonon transport, as it casts the problem in terms of mode-mode correlation instead of scattering, and provides a general unified formalism that can be used to understand phonon-phonon interactions in essentially any class of materials or structures where the atoms vibrate around stable equilibrium sites.