Lattice Thermal Transport Beyond the Quasiparticle Approximation: Nontrivial Spectral Competition between Three- and Four-Phonon Interactions

Abstract

The breakdown of the quasiparticle approximation (QPA) for phonons in strongly anharmonic materials necessitates advanced first-principles frameworks for accurate lattice dynamics and thermal transport predictions. We develop a comprehensive beyond-quasiparticle approximation (BQPA) approach incorporating both three- (3ph) and four-phonon (4ph) interactions and apply it to investigate lattice thermal conductivity ($κ_{\rm L}$) in MgO, PbTe, and AgCl -- materials that span a broad spectrum of anharmonicity, from weak to severe anharmonic regimes with overdamped phonons. We reveal that while BQPA consistently increases $κ_{\rm L}$ relative to QPA due to phonon softening when considering only 3ph interactions, the inclusion of additional 4ph interactions hardens the phonon spectrum and suppresses this enhancement, bringing BQPA and QPA predictions into close agreement via subtle spectral competition effects across all three compounds. These findings highlight that accurate modeling of $κ_{\rm L}$ in strongly anharmonic materials requires treating both full phonon spectral function and higher-order anharmonicity on equal footing. Our work establishes a systematic framework for modeling thermal transport in systems with overdamped phonons and provides critical insights for materials design beyond the limits of conventional phonon transport theory.

Figures (6)

• Figure 1: (a) Diagrammatic representation of the self-consistent phonon (SCPH) propagator where the loop diagram is considered (also termed as Hartree-Fock approximation for phonons xiao2023anharmonic). The double line represents the SCPH propagator, while the sold line is that of a free phonon. (b) Bubble (3ph interactions) and (c) sunset (4ph interactions) diagrams defined on the basis of the SCPH propagator.
• Figure 2: Lattice thermal conductivity comparison across four theoretical approaches: 3ph-QPA (three-phonon interactions within the quasiparticle approximation), 3ph-BQPA (three-phonon interactions beyond the quasiparticle approximation), 3,4ph-QPA (three- and four-phonon interactions within the quasiparticle approximation), and 3,4ph-BQPA (three- and four-phonon interactions beyond the quasiparticle approximation) for (a) MgO, (b) PbTe, and (c) AgCl at 300 K. Self-consistent phonon is implicitly implied in all adopted theoretical approaches. Experimental values cahill1998thermalel1983thermophysicalmaqsood2004thermophysical at 300 K are shown as horizontal gray dashed lines for comparison. Dark and light portions of the bars represent the particle-like and wave-like/coherent contributions to the lattice thermal conductivity, respectively.
• Figure 3: (a) Comparison of calculated phonon lifetimes for three-phonon (3ph) scatterings within the quasiparticle approximation (QPA) and beyond the quasiparticle approximation (BQPA) from Eq.(\ref{['eq:renorm_lifetime']}) for MgO at 300 K. (b) Mode-resolved phonon spectral density (solid lines) considering only 3ph interactions compared with corresponding self-consistent phonon frequencies (vertical dashed lines) for MgO at 300 K. The selected phonon mode is at (0.2, 0, 0) along the $\Gamma$ to $X$ path. (c,d) Similar analysis to (a,b) but including additional four-phonon (4ph) interactions. (e-h) Corresponding analysis for PbTe at 300 K following the same theoretical approaches as panels (a-d). (i-l) Similar analysis for AgCl at 300 K. The black dashed lines in (a), (c), (e), (g), (i), and (k) indicate lifetimes equal to the inverse frequency. Full phonon spectral density for MgO, PbTe, and AgCl at 300 K along the $\Gamma-X$ direction in the first Brillouin zone is shown in Fig. \ref{['fig:em_fpsf']} in Appendix \ref{['sec:details']}.
• Figure 4: Calculated temperature-dependent lattice thermal conductivities using four theoretical approaches (3ph-QPA, 3ph-BQPA, 3,4ph-QPA, and 3,4ph-BQPA) in comparison with experimental measurements, which are shown as empty symbols (squares from Ref. [maqsood2004thermophysical]; diamonds from Ref. [el1983thermophysical]; triangles from Ref. [cahill1998thermal]; pentagons from Ref. [hofmeister2014thermal]).
• Figure 5: Calculated phonon spectral density for MgO, PbTe, and AgCl at 300 K along the $\Gamma$–$X$ direction in the first Brillouin zone (fractional coordinates shown in parentheses). Panels (a)–(c) include only three-phonon (3ph) interactions (bubble diagram in Fig. \ref{['fig:diagram']}(b)), while panels (d)–(f) additionally include four-phonon (4ph) interactions (sunset diagram in Fig. \ref{['fig:diagram']}(c)).