Intrinsic localized mode and low thermal conductivity of PbSe

Lead chalcogenides such as PbS, PbSe, and PbTe are of interest for their exceptional thermoelectric properties and strongly anharmonic lattice dynamics. Although PbTe has received the most attention, PbSe has a lower thermal conductivity and a nonlinear temperature dependence of thermal resistivity despite being stiffer, trends that prior first-principles calculations have not fully reproduced. Here, we use ab initio calculations that explicitly account for strong anharmonicity and a computationally efficient stochastic phase-space sampling scheme to identify the origin of this low thermal conductivity as an anomalously large anharmonic interaction, exceeding in strength that in PbTe, between the transverse optic and longitudinal acoustic branches. The strong anharmonicity is reflected in the striking observation of an intrinsic localized mode that forms in the acoustic frequencies. Our work shows the deep insights into thermal phonons that can be obtained from ab initio calculations that do not rely on perturbations from the ground-state phonon dispersion.

Figure 1

(a) Thermal resistivity of PbS, PbSe, and PbTe as a function of temperature with $\pm 1\%$ variation of the lattice parameter. (b) Thermal resistivity of PbS, PbSe, and PbTe (lines) for +1% lattice constant. Experimental data (symbols) for PbS, PbSe, and PbTe are taken from Ref. [55] between 300 and 700 K. Experimental data at low temperatures for PbS are taken from Refs. [56, 57, 58], those for PbSe are taken from Refs. [56, 59], and those for PbTe are taken from Refs. [56, 60].

Figure 2

(a) Cumulative thermal conductivity as a function of mean free path at $T=300$ K for PbS, PbSe, and PbTe. The vertical dashed lines indicates where $50\%$ of thermal conductivity is accumulated. Cumulative thermal conductivity for (b) PbS, (c) PbSe, and (d) PbTe decomposed per branch. The gray region gives the contribution from the acoustic branches, while the yellow region gives the contribution from the optical modes. In PbSe and PbTe, 50% of the contribution to the thermal conductivity comes from the phonons with mean free paths smaller than 5 nm.

Figure 3

Left panels: spectral function (logarithmic intensity scale) along the high-symmetry directions for PbS (left), PbSe (middle), and PbTe (right) at (a) 300 K, (b) 600 K, and (c) 1000 K. Right panels: total spectral thermal conductivity and spectral thermal conductivity for the longitudinal acoustic mode vs frequency.

Figure 4

Phonon line shapes for (a) PbS, (b) PbSe, and (c) PbTe at 600 K at $\mathrm{\Gamma }$. The arrows indicate the main and secondary peaks with the original force constants. By setting the strongest three-body interaction to zero, in all cases the line shapes revert to the narrow Lorentzian peaks. Comparing the line shapes between PbSe and PbTe, we observe the split peak, but the secondary peaks differ. In PbTe, the peak is broader and weaker than the main peak, but in PbSe it is much sharper and with equal intensity to the main peak, corresponding to an intrinsic localized mode. In (d) we show the impact of the secondary peak on the scaled spectral thermal conductivity for the longitudinal mode. The dip in the spectral thermal conductivity in PbSe is three times larger in magnitude than that in PbTe, which is $\approx 15\%$ and 5% of the maximum spectral thermal conductivity for the LA mode, respectively.

Figure 5

Pair vector distribution of PbS (left), PbSe (middle), and PbTe (right) projected on the [001] and [010] planes at (a) 300 K, (b) 600 K, and (c) 1000 K. The radial distribution function is shown in (d). There is a strong asymmetry of the peak around the equilibrium position, indicative of strong anharmonicity, however the center of mass is positioned exactly at the zero and no off-centering observed. In a harmonic material, these distributions would be Gaussian.