First-Principles Study of Anharmonic Lattice Dynamics in Low Thermal Conductivity ${\mathrm{AgCrSe}}_2$: Evidence for a Large Resonant Four-Phonon Scattering

We report a study of the anharmonic lattice dynamics in low lattice thermal conductivity (${\mathit{\kappa }}_{\mathit{l}}$) material ${\mathrm{AgCrSe}}_2$ by many-body perturbation theory. We demonstrate surprisingly giant four-phonon scattering exclusive for the heat-carrying transverse acoustic phonons due to large quartic anharmonicity and nondispersive phonon band structure, which lead to four-phonon Fermi resonance and breaks the classical ${\mathit{\tau }}^{-1}\sim {\mathit{\omega }}^{\mathit{m}}{\mathit{T}}^{\mathit{n}}$ relation for phonon-phonon interactions. This strong resonant scattering extends over the Brillouin zone and substantially suppresses the thermal transport, even down to a low temperature of 100 K. The present results provide fundamental insights into the four-phonon resonant dynamics in the low-${\mathit{\kappa }}_{\mathit{l}}$ system with flat phonon dispersions, i.e., cuprous halides and skutterudites.

Figure 1

(a) Atomic structure of low-temperature ordered phase ${\mathrm{AgCrSe}}_2$ (space group $R3m$). (b) Calculated phonon dispersion of ${\mathrm{AgCrSe}}_2$ at 100 K.

Figure 2

Theoretical spectral function $S_{\overrightarrow{k}}(\omega )$ (in logarithm scale) of ${\mathrm{AgCrSe}}_2$, as calculated at 100 K (a) with and (b) without second-order quartic anharmonic perturbations ${\mathrm{\Sigma }}^{(2)}$. Note the dramatic change of the low-lying transverse acoustic phonons.

Figure 3

Temperature dependent spectral function $S_{\overrightarrow{k},s}(\omega )$ (solid line calculated with ${\mathrm{\Sigma }}_{\overrightarrow{k},s}={\mathrm{\Sigma }}_{\overrightarrow{k},s}^{(1)}+{\mathrm{\Sigma }}_{\overrightarrow{k},s}^{(2)}$; dashed line calculated with ${\mathrm{\Sigma }}_{\overrightarrow{k},s}={\mathrm{\Sigma }}_{\overrightarrow{k},s}^{(1)}$) of the acoustic phonons at $F$ point, as calculated at (a) 100, (b) 200, and (c) 300 K, respectively. The colored vertical bars indicate the phonon eigenfrequency ${\omega }_{\overrightarrow{k},s}$ of each phonon mode (red, TA1; blue, TA2; green, LA). The phonon linewidth broadening and frequency shift due to the four-phonon interactions ${\mathrm{\Sigma }}_{\overrightarrow{k},s}^{(2)}$ can be clearly observed.

Figure 4

Schematic diagram showing the four-phonon recombination process or four-phonon Fermi resonance facilitated by flat transverse acoustic phonon dispersions. In comparison, the three-phonon scattering process is restricted by conservation of momentum and energy.