Localized dimers drive strong anharmonicity and low lattice thermal conductivity in $\mathrm{Zn}{\mathrm{Se}}_2$

We calculate the lattice thermal conductivities of the pyrite-type $\mathrm{Zn}{\mathrm{Se}}_2$ at pressures of 0 and 10 GPa by using the linearized phonon Boltzmann transport equation. We obtain a very low value (0.69 W/mK at room temperature at 0 GPa), comparable to the best thermoelectric materials. The vibrational spectrums are characterized by the isolated high-frequency optical phonon modes due to the stretching of Se-Se dimers and the low-frequency optical phonon modes with a strong anharmonicity due to the rattling modes of Zn atoms, especially the rotations of Zn atoms around these dimers. This means that the existence of localized Se-Se dimers leads to the strong anharmonicity of the low-frequency optical phonon modes. Interestingly, two transverse acoustic phonon modes with similar frequencies and wave vectors have very different degrees of anharmonicity. We show that the anharmonicities of the transverse acoustic phonon modes are connected to the corresponding changes in the pyrite parameters. Furthermore, to determine the thermoelectric performances of $\mathrm{Zn}{\mathrm{Se}}_2$, we also investigate its electrical transport properties. Our results show that both $p$-type and $n$-type $\mathrm{Zn}{\mathrm{Se}}_2$ can possess promising electrical transport properties contributed by the complex energy isosurfaces of both valence and conduction bands. The low thermal conductivities and promising electrical transport properties lead to a large thermoelectric figure of merit of $\mathrm{Zn}{\mathrm{Se}}_2$ for both $p$-type and $n$-type doping at different pressures. Our study reveals the effect of the localized nonmetallic dimers on the anharmonicity and lattice thermal conductivity in the pyrite-type compound, which can be used to guide researchers to seek promising thermoelectric materials containing nonmetallic dimers.

Figure 1

(a) The pyrite-type crystal structures of $\mathrm{Zn}{\mathrm{Se}}_2$ (space group $\mathrm{Pa}\overline{3}$). (b) DFT calculated pressure-composition phase diagrams of $\mathrm{Z}{\mathrm{n}}_x\mathrm{S}{\mathrm{e}}_{1-x}$ at 0 (black), 9.7 (red), and 15 (blue) GPa, respectively.

Figure 2

Phonon dispersions of $\mathrm{Zn}{\mathrm{Se}}_2$ at 0 (a) and 10 GPa (c). The first Brillouin zone of $\mathrm{Zn}{\mathrm{Se}}_2$ with the high-symmetry points is illustrated as an inset in (a). (b) The corresponding phonon density of states (PDOS) of per atom in $\mathrm{Zn}{\mathrm{Se}}_2$ at 0 GPa.

Figure 3

(a) 3D electron localization function (ELF) of $\mathrm{Zn}{\mathrm{Se}}_2$ at 0 GPa. The ELF value of the isosurface is 0.7. (b) Projected 2D ELF in (001) plane of $\mathrm{Zn}{\mathrm{Se}}_2$ at 0 GPa. (c) Calculated atomic displacement parameters (ADPs) of Zn and Se atoms along different directions.

Figure 4

Calculated ${\kappa }_l$ of $\mathrm{Zn}{\mathrm{Se}}_2$ as a function of temperature at 0 and 10 GPa, respectively.

Figure 5

(a) The phonon dispersions and the corresponding distributions of ${\gamma }_{iq}$ in $\mathrm{Zn}{\mathrm{Se}}_2$ at 0 GPa. The color in (a) denotes the values of ${\gamma }_{iq}$. (b) The ${\kappa }_l$ contribution with respect to phonon frequency at 300 K.

Figure 6

(a) The contribution of the motions of Zn rotations around Se-Se dimers to the phonon dispersions around $50\mathrm{c}{\mathrm{m}}^{-1}$. The motion of Zn rotations around Se-Se dimers vector is illustrated as an inset in (a). (b) The distribution of the changed pyrite parameters ($\mathrm{\Delta }u$) at the acoustic phonons.

Figure 7

Calculated band structures of $\mathrm{Zn}{\mathrm{Se}}_2$ at 0 GPa for (a) PBE and (b) HSE approximations. (c) is the calculated band structures of $\mathrm{Zn}{\mathrm{Se}}_2$ at 10 GPa for PBE approximation.

Figure 8

The energy isosurfaces at 0.2 eV low VBM (a) and 0.15 eV above CBM (b) of $\mathrm{Zn}{\mathrm{Se}}_2$ at 0 GPa.

Figure 9

(a) The orbital-resolved projected crystal orbital Hamilton population (COHP) of $\mathrm{Zn}{\mathrm{Se}}_2$ at 0 GPa. (b) The projected decomposed band structures of $\mathrm{Zn}{\mathrm{Se}}_2$ at 0 GPa. The thickness of the band feature represents the weights of the electronic state.

Figure 10

Calculated $\tau$ (a), $S$ (b), $\sigma$ (c), and $PF$ (d) of $p$-type and $n$-type $\mathrm{Zn}{\mathrm{Se}}_2$ as a function of the carrier concentration at 0 GPa, at 300, 600, and 900 K, respectively.

Figure 11

Calculated $\tau$ (a), $S$ (b), $\sigma$ (c), and $PF$ (d) of $p$-type and $n$-type $\mathrm{Zn}{\mathrm{Se}}_2$ as a function of the carrier concentration at 10 GPa, at 300, 600, and 900 K, respectively.

Figure 12

Calculated $ZT$ values of $p$-type and $n$-type $\mathrm{Zn}{\mathrm{Se}}_2$ as a function of temperature and carrier concentration at 0 (a) and 10 (b) GPa, respectively.