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

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