Many-body Green's function approach to lattice thermal transport

TL;DR

This paper develops a comprehensive quantum Green's function approach to lattice thermal transport, clarifying theoretical differences and extending analysis to regimes where phonon quasiparticles are ill-defined, with practical implications for complex crystals.

Contribution

It introduces a full quantum Green's function method for thermal transport, comparing it with existing formalisms and extending applicability to overdamped vibrational regimes.

Findings

Differences between approaches are negligible in the quasiparticle regime.

The method is validated on complex crystals with ultralow thermal conductivity.

Extended description covers regimes where phonon quasiparticles break down.

Abstract

Recent progress in understanding thermal transport in complex crystals has highlighted the prominent role of heat conduction mediated by interband tunneling processes, which emerge between overlapping phonon bands (i.e. with energy differences smaller than their broadenings). These processes have recently been described in different ways, relying on the Wigner or Green-Kubo formalism, leading to apparently different results which question the definition of the heat-current operator. Here, we implement a full quantum approach based on the Kubo formula, elucidating analogies and differences with the recently introduced Wigner or Green-Kubo formulations, and extending the description of thermal transport to the overdamped regime of atomic vibrations, where the phonon quasiparticle picture breaks down. We rely on first-principles calculations on complex crystals with ultralow conductivity to compare numerically the thermal conductivity obtained within the aforementioned approaches, showing that at least in the quasiparticle regime the differences are negligible for practical applications.