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

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.

Perturbation theory and thermal transport in mass-disordered alloys: Insights from Green's function methods

“…Simoncelli's paper establishes a Wigner formalism for complex crystals that separates two terms in the thermal conductivity: diagonal propagative transport described by Boltzmann-Peierls theory and off-diagonal diffusive transport involving phonon modes mixing via mode-dependent broadening due to anharmonicity and disorder [35]. In addition, a very recent paper by Caldarelli extends this formalism to the overdamped regime by using the Green-Kubo formula on the basis of the phonon modes and, neglecting vertex corrections (dressed bubble approximation), writing it in terms of the phonon spectral function [36]. Isaeva's approach to thermal transport in disordered systems uses the Green-Kubo formula expressed on the basis of disordered normal modes of the supercell and introduces a constant anharmonic lifetime in the Green's function for each normal mode [37].…”

“…Our approach is essentially equivalent to Isaeva's, but the Green-Kubo formula is implemented in real-space (not using the normal modes) and the anharmonicity is included through a frequencydependent lifetime, allowing us to study very large systems (tens of millions of atoms) through the CPGF algorithm. In Caldarelli's language, disorder is treated at the 'FSF' level (actually beyond FSF, because vertex corrections are included) and anharmonicity at the 'LSFA' level [36]. Thus, our approach can describe systems simultaneously featuring arbitrarily strong disorder (phonons overdamped by disorder, including localization effects) and wave-like tunneling through anharmonic overlap of normal modes.…”