Onset of anharmonicity and thermal conductivity in SnSe

The anharmonicity in SnSe is investigated through the analysis of moments of ${}^{119}\mathrm{Sn}$ nuclear resonant inelastic x-ray scattering and ab initio molecular dynamics calculations. Experimental evidences show that the anharmonic behavior started around 300 K, substantially lower than the usually suggested structural transition at 800 K. Both theory and experiments reveal substantial lifetime broadening and frequency renormalization of the optical phonons. Thermal conductivities calculated from the temporal energy moment using the Einstein diffusion equation are in good agreement with previous experiments. The abrupt increase of the thermal power near 800 K is driven by an electronic factor and not by the enhanced anharmonicity due to structural change.

Figure 1

Sn partial phonon DOS derived from NRIXS measurements. DOS are normalized to 1.

Figure 2

Temperature dependence of $f$ factor and the third moment $R_3$ (a), and $R_3$ vs $\langle {\delta }_{\widehat{\mathit{k}}}^2\rangle$ (b) as derived from NRIXS measurements. In (a), $f$ factors are represented by small dots with scale on the left axis, while $R_3$ are squares and scale on the right.

Figure 3

Sn partial phonon DOS derived from AIMD simulations.

Figure 4

Comparison of phonon DOS measured using NRIXS and calculated with AIMD to phonon dispersions from athermal LD calculation.

Figure 5

The $x$, $y$, and $z$ components of energy momenta ${\mathit{R}}_k$ are found to propagate with increasing time (left). The slopes of the MSD of ${\mathit{R}}_k$ [Eq. (13)] give the thermal conductivity along the three directions. The corresponding thermal conductivities as a function of time are shown on the right. In each case, the function reaching a steady state appears as a plateau which gives the limiting thermal conductivity. The statistical errors were estimated from the averages over multiple time origins by subdividing equal segments of the long MD trajectory.