Microscopic mechanism of low thermal conductivity in lead telluride

The microscopic physics behind low-lattice thermal conductivity of single-crystal rock salt lead telluride (PbTe) is investigated. Mode-dependent phonon (normal and umklapp) scattering rates and their impact on thermal conductivity were quantified by first-principles-based anharmonic lattice dynamics calculations that accurately reproduce thermal conductivity in a wide temperature range. The low thermal conductivity of PbTe is attributed to the scattering of longitudinal acoustic phonons by transverse optical phonons with large anharmonicity and small group velocity of the soft transverse acoustic phonons. This results in enhancing the relative contribution of optical phonons, which are usually minor heat carriers in bulk materials.

Figure 1

(a) Phonon dispersion relations of PbTe along Γ-X-K-Γ-L symmetry lines. Red open and blue filled circles indicate transverse and longitudinal modes, respectively, from inelastic neutron scattering (INS) experiments at 300 K.[24] (b) The mode-Grüneisen parameters.

Figure 2

(a) Frequency-dependent phonon relaxation times of PbTe at 300 K by anharmonic lattice dynamics (ALD) calculations with $N_{\mathbf{q}}$ $=$ 20. Frequency-dependent phonon relaxation times of (b) normal and (c) umklapp processes, respectively. The solid lines denote (a) $\tau =6\times {10}^{12}{\nu }^{-2}$, (b) $\tau =8.0\times {10}^{12}{\nu }^{-2}$, and (c) $\tau =8.0\times {10}^{24}{\nu }^{-3}$.

Figure 3

The scattering rate $w_{\mathbf{q}s}$ of (a) acoustic and (b) optical phonons along Γ-X line at 300 K calculated by ALD with $N_{\mathbf{q}}$ $=$ 20. The squares in (a) denote $w_{\mathbf{q}s}$ of LA phonons at 300 K from INS experiments.[13] The wave number $q$ is normalized by the wave number of X point.

Figure 4

(a) Comparison between the temperature-dependent bulk thermal conductivity ${\kappa }_{\mathrm{lat}}$ of PbTe obtained by the ALD calculations (square) and the experiments [circles (Ref. 28) and dashed line (Ref. 29)]. The inset figure shows the extrapolation of ${\kappa }_{\mathrm{lat}}^{N_{\mathbf{q}}}$ performed to obtain the bulk thermal conductivity ${\kappa }_{\mathrm{lat}}$ at different temperatures. (b) Cumulative thermal conductivity ${\kappa }_{\mathrm{c}}$ as a function of mean free path (MFP) at 300 K calculated by ALD with $N_{\mathbf{q}}$ $=$ 20. TA${}_{\mathrm{ave}}$ denotes the averaged values of the two TA branches.