Abstract
Highefficiency thermoelectric materials require simultaneously high power factors and low thermal conductivities. Aligning band extrema to achieve high band degeneracy, as realized in PbTe, is one of the most efficient approaches to enhance power factor. However, this approach usually relies on band structure engineering, e.g., via chemical doping or strain. By employing firstprinciples methods with explicit computation of phonon and carrier lifetimes, here we show two fullHeusler compounds Li_{2}TlBi and Li_{2}InBi have exceptionally high power factors and low lattice thermal conductivities at room temperature. The expanded rocksalt sublattice of these compounds shifts the valence band maximum to the middle of the Σ line, increasing the band degeneracy by a factor of three. Meanwhile, resonant bonding in the PbTelike sublattice and soft Tl–Bi (In–Bi) bonding interaction is responsible for intrinsic low lattice thermal conductivities. Our results present an alternative strategy of designing high performance thermoelectric materials.
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Introduction
Thermoelectric (TE) materials have important applications in energy harvesting, thermoelectric coolers, and thermal detectors as they can directly convert heat into electricity and vise versa. Highly efficient TE materials are required for practical applications and are characterized by the figure of merit zT = (S^{2}σT)/(κ_{L} + κ_{e}), where S, σ, κ_{e}, κ_{L}, and T are the Seebeck coefficient, electrical conductivity, electronic thermal conductivity, lattice thermal conductivity, and temperature, respectively. In order to maximize zT, both electronic transport properties and lattice thermal conductivity have to be optimized carefully. Many strategies have been successfully used to suppress κ_{L}^{1}. However, there are fewer approaches that can effectively improve the electronic properties, i.e., the power factor (PF = S^{2}σ)^{2,3,4}. One effective route is to increase the band degeneracy (N_{v}) and decrease the inertial effective mass \(\left( {m_{\mathrm{I}}^ \ast } \right)\) simultaneously since the figure of merit zT of a material is proportional to \(\frac{{N_{\mathrm{v}}}}{{m_{\mathrm{I}}^ \ast }}\)^{2,5}. Although a high density of states (DOS) effective mass (\(m_{\mathrm{d}}^ \ast\) = \(N_{\mathrm{v}}^{2/3}m_{\mathrm{b}}^ \ast\)) is preferred for generating a high S^{6,7}, the band effective mass \(m_{\mathrm{b}}^ \ast\) is also concomitantly high in a material with low N_{v}, leading to a low electrical conductivity as \(\sigma \propto \frac{\tau }{{m_{\mathrm{b}}^ \ast }}\) (τ is the carrier lifetime)^{5}.
A high value of N_{v} can be achieved either from a high valley multiplicity (the number of the carrier pockets of a band in the Brillouin zone) or a high orbital degeneracy (the number of bands with the same energy). Take the well studied TE material PbTe (rocksalt lattice, space group \(Fm\bar 3m\)) as an example, once the second maximum of the valence band (the middle of the Σ line, multiplicity is 12) is converged with the valence band maximum (VBM) (at the L point, multiplicity is 4) by alloying an appropriate amount PbSe, a significant enhancement of zT from 0.8 to 1.8 can be reached^{8}. In practice, many materials have very limited dopability or the energy band can not be properly converged. Therefore, TE materials with intrinsically high band degeneracy are highly desired. Unfortunately, most intrinsic semiconductors have very low valley multiplicity. A high valley multiplicity usually only appears in cubic crystal systems where the VBM or conduction band minimum (CBM) is located at a low symmetry point of the first Brillouin zone, such as the Σ line of the rocksalt structure^{2}. In addition to alloying, the band convergence could, in principle, be achieved through strain engineering. The lattice constant plays an important role on the alignment of Σ and L in PbTe^{8,9}. However, a completely alignment requires an extremely large strain, which is not reachable in practice. Therefore, an alternative material design strategy is desired.
Semiconducting halfHeusler (HH) (chemical formula XYZ; space group \(F\bar 43m\)) compounds have been widely studied as TE materials due to their high power factors^{10,11,12} and excellent dopability^{13,14}. Since semiconducting fullHeusler (FH) (chemical formula X_{2}YZ; space group \(Fm\bar 3m\)) compounds are very rare, the study of FH TE is highly limited^{15}. Owing to the structural similarity between HHs and FHs^{16}, semiconducting FH compounds are expected to have good TE performance as well. The FH structure is a face centered cubic crystal structure with the interpenetration of X_{2} cubic and YZ rocksalt sublattices. The embedded cubic sublattice extends the bond length between Y and Z atoms of the rocksalt sublattice. Therefore, FH structure is an ideal candidate for realizing expanded PbTe.
In this work, one stable (Li_{2}TlBi) and one metastable (Li_{2}InBi) FH compounds with PbTelike electronic structure, are discovered by combining a TE material design strategy and high throughput ab initio thermodynamic screening^{15,17}, see Supplementary Note 1 for details. The crystal structure of FH Li_{2}TlBi (Li_{2}InBi) is the interpenetration of Li_{2} cubic and TlBi (In–Bi) rocksalt sublattices. The electronic structure of [Li^{+}]_{2}[Tl^{+}Bi^{3−}] ([Li^{+}]_{2}[In^{+}Bi^{3−}]) is isoelectronic with PbTe (Pb^{2+}Te^{2−}) since the electrons donated by two Li atoms are delocalized in the whole system. However, the bond length of Tl–Bi (In–Bi) is considerably extended in the FH lattice. Consequently, both the VBM and CBM of these two compounds are located in the middle of the Σ line, with band degeneracy of N_{v} = 12 in the intrinsic compounds due to their large lattice constants (~7.15 Å). Our transport calculations, explicitly including phonon–phonon and electron–phonon interactions, show that these two compounds have low κ_{L} and high PF at room temperature. Benefiting from their low κ_{L} and high PF, Li_{2}InBi and Li_{2}TlBi are therefore identified as promising roomtemperature TE materials with ideal zT values of 1.5 and 2.0 at 300 K, respectively.
Results
Stability
Our density functional theory (DFT) calculations show that FH Li_{2}TlBi is on the T = 0 K convex hull, which means it is thermodynamically stable at zero Kelvin, and Li_{2}InBi is just 4 meV/atom above the convex hull, which indicates it is thermodynamically weakly unstable (metastable). The convex hull distance (stability) is the formation energy difference between the target compound and its competing phases included in the Open Quantum Material Database (OQMD)^{18}, which contains over 650,000 DFT calculations consisting of experimentally observed compounds from the international crystal structure database (ICSD)^{19,20} and hypothetical compounds with prototype structures. We also performed a ground state crystal structure search by using 21 distinct X_{2}YZ prototype structures (see Supplementary Table 1) and the particle swarm optimization method as implemented in the CALYPSO code^{21,22}, and we find the FH structure (see Fig. 1) is the lowest energy structure for both Li_{2}InBi and Li_{2}TlBi. Phonon calculations show that both Li_{2}TlBi and Li_{2}InBi are dynamically stable at T = 0 K. Free energy differences (ΔG = ΔH − TΔS, where ΔH and ΔS are formation energy and formation entropy, respectively, see Supplementary Table 2 for details.) between FH phases and their competing phases in the corresponding ternary phase space show that Li_{2}TlBi is thermodynamically stable and Li_{2}InBi is slight unstable (~4 meV/atom above the convex hull) up to 500 K, see Supplementary Fig. 1. We count Li_{2}InBi as synthesizable compound since such small convex hull distance is well within the threshold of Heusler compounds^{23,24}.
Electronic structure
The main features of the Li_{2}YBi (Y = In and Tl) band structure are determined by [Y^{+}Bi^{3−}]^{2−}, which is isoelectronic with Pb^{2+}Te^{2−} even though In/Tl (Bi) is cubiccoordinated with eight Li atoms as the nearest neighbors and octahedrally coordinated with six Bi (In/Tl) as the next nearest neighbor. This is because Li is the most electropositive element in these compounds and it donates its 2s electron to the crystal system. As shown in Fig. 2, Li 2s electron is completely delocalized in these compounds and therefore it has very limited influence on the electronic structures of Li_{2}YBi (Y = In and Tl) except for raising the Fermi level and opening the band gap, which is similar to the Li stabilized quaternary Heusler semiconductors^{16}. We further verified this conclusion by performing band structure calculations for [TlBi]^{2−} with the −2 charge balanced by a +2 Jellium background, see Supplementary Fig. 2. Since Tl is the nearest neighbor of Pb and Bi is close to Te in the periodic table, Li_{2}InBi and Li_{2}TlBi have very similar band structures with PbTe, as shown in Fig. 2a. Interestingly, Li_{2}InBi and Li_{2}TlBi have much larger lattice constants than PbTe because of the inserted Li_{2} cubic sublattice, which plays an important role in raising the energy level of the VBM at the middle of Σ line. As a consequence, the N_{v} of Li_{2}YBi reaches to 12, as observed in the PbTe under significant hydrostatic expansion. As depicted in Fig. 3, a remarkable decrease in the energy difference between Σ and L is observed when the lattice constant of PbTe is expanded to that of Li_{2}TlBi (Li_{2}InBi). At the same time, the large bonding distance (softer bonding interaction) between Bi and Y (Y = In and Tl) contributes to reducing κ_{L} as we will see later^{5}.
Since Li_{2}InBi has a very similar electronic structure to Li_{2}TlBi, we only take Li_{2}TlBi as an example here. The electronic structure of Li_{2}TlBi is shown in Fig. 2 (the band structure of Li_{2}InBi is shown in Supplementary Fig. 3). Li_{2}TlBi is a small band gap semiconductor (PBE: 0.06 eV; HSE06: 0.18 eV, including the spin–orbit coupling (SOC), which is consistent with a previous calculation^{25}. These calculated gaps are well comparable with many high zT TE materials, such as PbTe: 0.19 eV^{26} and CoSb_{3}: 0.05 ~ 0.22 eV^{27,28}). In Li_{2}TlBi, the band gap opens between the fully occupied Bi 6p and fully unoccupied Tl 6p states due to charge transfer from Tl to Bi. Tl atom loses its one 6p electron to the more electronegative Bi atom and becomes Tl^{+}, and its 6s^{2} electrons are deeply (~−5 eV below the Fermi level) buried below the Bi 6p orbitals (valence bands, from −4 to 0 eV), forming stereochemically inactive lonepair electrons. Two electropositive Li atoms lose their 2s electrons to Bi as well. Therefore, the 6p orbitals of Bi^{3−} (from −4 to 0 eV below the Fermi level) are fully filled with six electrons. The splitting of three occupied Bi 6p orbitals into two groups, ~−2 eV (single degeneracy) and ~−0.5 eV (double degeneracy) at the Γ point is due to SOC. The conduction bands are mainly from the Tl^{+} 6p orbitals. The electron localization function (ELF) is shown in Fig. 1 and Supplementary Fig. 4. We can clearly see that Bi and Li atoms have, respectively, the highest and lowest ELF values, consistent with our electronic structure analysis that Li donates its electrons to the system while Bi gains electrons. The inactive lonepair electrons of Tl^{+} 6s^{2} are clearly observed in Fig. 1 as well, which is analogous to Pb^{2+} in PbTe. Finally, the ELF of Li_{2}TlBi is very similar to that of PbTe, which is identified as a typical resonant bonding system^{29,30}.
As expected from the previous analysis, a remarkable feature of the Li_{2}TlBi band structure is that its VBM lies in the middle of Σ line of the first Brillouin zone of the FCC FH structure \(\left( {Fm\bar 3m} \right)\), which leads to an unexpected high valley degeneracy (N_{v} = 12), see the Fermi surface in Fig. 2. Hence the N_{v} = 12 of the VBM reaches a record high value, which only has been previously matched in the heavily doped PbTe and CoSb_{3} systems^{8,31}. The second hole pocket, which is ~40 meV lower than VBM, is located at the middle of the Δ line (between Γ and X) and possesses a valley degeneracy of 6. Therefore, an extremely high N_{v} = 18 is reachable in Li_{2}TlBi by means of hole doping. Although the CBM is located at L with the valley degeneracy of 4, the energy difference between CBM and the second highest electron pocket (in the middle of the Σ line) is only 7 meV. Therefore the N_{v} of the conduction band can potentially reach as high as 16 through light electron doping. The Fermi surfaces of the valence and conduction bands are displayed in Fig. 2. As mentioned above, although the band effective masses \(\left( {m_{\mathrm{b}}^ \ast } \right)\) for the VBM and CBM are small, which imply high carrier mobilities as \(\mu \propto \frac{\tau }{{m_{\mathrm{b}}^ \ast }}\), the Seebeck coefficient \(S \propto m_{\mathrm{d}}^ \ast\) still can be very high, provided N_{v} is sufficiently large, since \(m_{\mathrm{d}}^ \ast\) is related to the band effective mass by \(m_{\mathrm{d}}^ \ast = N_{\mathrm{v}}^{2/3}m_{\mathrm{b}}^ \ast\).
Electron transport
To quantitatively characterize the electron transport properties of Li_{2}YBi (Y = In and Tl), we calculate S and σ based on the semiclassical Boltzmann transport equation under relaxation time approximation. We assume that the predominant carrier scattering mechanisms at 200 K and above are all based on phonons: (1) deformation potentials of acoustic and optical phonons and (2) Fröhlich coupling due to polar optical phonons^{32,33}. Since the best thermoelectric efficiency is always achieved in the heavily doped region where the scattering on polar optical phonons is sufficiently screened and the dielectric constant is usually large in narrow band gap semiconductors^{32,33,34}, we mainly take into account deformation potential scattering using firstprinciples calculated electron–phonon interaction (EPI) matrix elements. As shown in Fig. 4 for the representative compound Li_{2}TlBi, the imaginary part of the electron selfenergy Im(Σ) shows a strong energy dependence and is roughly proportional to the density of electronic states. States with a long lifetime appear near the VBM and CBM. This indicates that the lifetime is linked to the phase space availability for electronic transitions, i.e., electrons and holes near the band edges are less scattered due to limited phase space^{35}.
To validate our calculations, we also computed the thermoelectric properties for a well studied ptype HH compound FeNbSb, for which a PF as large as 10.6 mW m^{−1} K^{−2} was recently measured at room temperature^{36}. Figure 5c shows that our calculation considering electron–phonon coupling predicts a maximum PF of 11.7 mW m^{−1} K^{−2} for FeNbSb at 300 K, representing the upper limit without considering other scattering sources such as defects and grain boundaries. Our calculated S, σ, and PF of FeNbSb at optimized carrier concentration and temperatures from 200 to 500 K also compare well with a recent theoretical study that employs the same methodology^{37}. The good agreement between our calculations and experimental data confirms our assumption that electron–phonon coupling dominates carrier scattering in this system. It is noteworthy that the optimal PF of FeNbSb is significantly higher than that of PbTe at 300 K^{8,38,39}.
Next, we illustrate the ultrahigh PFs of Li_{2}TlBi and Li_{2}InBi by comparing to FeNbSb. Despite the fact that S is generally much higher in FeNbSb (see Supplementary Figs. 5 and 6) due to its larger band gap of 0.54 eV compared to 0.18 eV (Li_{2}TlBi) and 0.15 eV (Li_{2}InBi), the S of Li_{2}TlBi and Li_{2}InBi is comparable with that of FeNbSb at optimal carrier concentration, particularly at 300 K, as shown in Fig. 5a. The strong bipolar effect further suppresses S of Li_{2}TlBi and Li_{2}InBi at higher temperatures. However, owing to the smaller band effective mass \(\left( {m_{\mathrm{b}}^ \ast } \right)\) and high valley degeneracy (N_{v}), both Li_{2}TlBi and Li_{2}InBi have significantly higher σ than FeNbSb from 300 to 500 K with a carrier concentration about one order of magnitudue lower than FeNbSb (see Supplementary Figs. 5 and 6). As a consequence, Li_{2}TlBi (Li_{2}InBi) achieves exceptional PFs of 30.4/20.1 (26.3/19.0) mW m^{−1} K^{−2} at 200/300 K, nearly twice that of FeNbSb at 300 K. The outperformance of Li_{2}TlBi and Li_{2}InBi over FeNbSb is due to a comparable S and a higher σ at the optimized carrier concentrations, supporting our previous discussion.
Phonon transport
The Li_{2}TlBi (Li_{2}InBi) primitive cell contains four atoms and therefore 12 phonon branches. The mode decomposition in the zone center (Γ point) is 3T_{1u} ⊕ 1T_{2g}. As shown in Fig. 6, the lowfrequency phonon modes are mainly from the stereochemically inert lonepair Tl^{+} cation instead of the heaviest atom Bi, which is consistent with the weaker bonding between Tl atom and its neighbors. As expected, the light lithium atom has much higher phonon frequencies 200 ~ 250 cm^{−1} and its phonon bands are completely separated from Tl and Bi. It is worth noting that these compounds possess two main differences from the previously reported alkali metal based rattling (R) Heusler^{15}: (i) higher acoustic phonon frequencies, and (ii) higher frequency of crossing bands between acoustic and optical modes, meaning Tl (In) atom has a slightly stronger interaction with its neighbors than RHeusler compounds.
The lattice thermal conductivity κ_{L} is calculated by using firstprinciples compressive sensing lattice dynamics (CSLD) and solving the linear Boltzmann transport equation (see Methods for details) and the results are shown in Fig. 7. Owing to the cubic symmetry, κ_{L} of Li_{2}TlBi and Li_{2}InBi are isotropic (\(\kappa _{\mathrm{L}}^{xx}\) = \(\kappa _{\mathrm{L}}^{yy}\) = \(\kappa _{\mathrm{L}}^{zz}\) = κ_{L}) and the calculated κ_{L} are 2.36 (1.55) Wm^{−1} K^{−1} at 300 K and 0.55 (0.52) Wm^{−1} K^{−1} at 900 K for Li_{2}TlBi (Li_{2}InBi), which are much lower than most FH and HH (≥7 Wm^{−1} K^{−1}^{40}) compounds without doping or nanostructuring and also lower than PbTe (2.74 at 300 K and 0.91 Wm^{−1} K^{−1} at 900 K at the same computational level).
Similar to PbTe, Li_{2}InBi, and Li_{2}TlBi have lowlying transverse optical modes (TO), as shown in Supplementary Figs. 7 and 8, further confirming the presence of the resonant bonding^{29}, as expected from earlier electronic structures analysis. The longrange interaction caused by the resonant bonding leads to strong anharmonic scattering and large phase space for threephonon scattering processes and, therefore, significantly suppresses lattice thermal transport^{29}. Moreover, the weak Tl–Bi (In–Bi) bonding resulting from the large bonding distance between Tl and Bi (In and Bi) gives rise to low group velocities. Finally, the highfrequency optical modes associated with the Li atoms provide extra scattering channels for lowlying acoustic modes.
The mechanism of the strong scattering of heat carrying acoustic phonon modes can be directly understood from phonon–phonon interactions. We show the phonon–phonon scattering rates in the absorption (Γ^{+}: λ + λ′ → λ″) and emission (Γ^{−}: λ″ → λ + λ′) processes in Fig. 7. The lowfrequency acoustic phonons are mainly scattered by the lowfrequency optical modes in the absorption process, while the optical modes decompose largely into low energy acoustic modes in the emission process. This scattering picture is similar to the alkali metal based RHeusler compounds^{15}.
Discussion
Using our calculated κ_{L}, S, σ, and κ_{e} within DFT framework by explicitly including electron–phonon and phonon–phonon interactions, the maximum figure of merit zT of Li_{2}TlBi and Li_{2}InBi are estimated to be 2.0 and 1.4 at 300 K for hole doping (ptype), respectively, which implies that Li_{2}TlBi is the TE material with the highest zT at room temperature. Note that our calculated κ_{L} might be overestimated due to neglect of the phonon–phonon interaction beyond the thirdorder and phonon scattering by defects and grain boundaries. Furthermore, the zT of these FH materials could be further enhanced by suppressing heat transport through nanostructuring precipitates and optimizing grain size as commonly used in other Heusler compounds if the optimized carrier concentration can still be achieved. The optimized hole concentrations within the rigid band approximation for the maximum zT at room temperature are 1.3 × 10^{19} and 1.6 × 10^{19} cm^{−3}, respectively, for Li_{2}TlBi and Li_{2}InBi (see Supplementary Figs. 5 and 6), which is close to those for PbTe at room temperature^{38,39} but one order of magnitude lower than in FeNbSb^{36}. Since Li_{2}TlBi has a better electronic structure than PbTe, the maximum zT at the same carrier concentration and room temperature is also higher^{39}.
For experiments, it is important to ascertain thermodynamic limit to the achievable dopant concentration. To estimate the defect solubility of forming ptype semiconductor, neutral defects of Li and Tl vacancy were considered. The calculated vacancy formation energy (E_{d}) of Li (Tl) in Li_{2}TlBi is 0.29 (0.31) eV per vacancy in Li (Tl) poor condition. These values are comparable with that of the Na doped PbTe (0.27 eV per defect)^{41}, where the hole concentration can reach 10^{20} cm^{−3} at room temperature^{42,43}. These values strongly suggest that the required hole concentrations for maximizing zT are achievable in Li_{2}TlBi.
Owing to the small band gap, the maximum zT values of Li_{2}TlBi and Li_{2}InBi are at room temperature, see Fig. 5. The drop down of the zT at higher temperature is mainly due to the decreased PF by the bipolar effect, stemming from their small band gaps since we assume that the band gap does not change with temperature. If their band gaps widen with elevated temperature as observed in PbTe, the maximum zT will be achieved at higher temperature. We also note that the electron doped (ntype) Li_{2}TlBi and Li_{2}InBi have high zT at room temperature as well, due to the high conduction band degeneracy (at Σ line and L point) and low lattice thermal conductivity. A material with high zT for both hole and electron doping is important for fabricating TE devices. Therefore, Li_{2}TlBi and Li_{2}InBi are promising materials for room temperature thermoelectric applications.
In summary, we discover two promising roomtemperature TE materials, Li_{2}TlBi and Li_{2}InBi FHs, by high throughput stability screening and TE material design strategy of creating the analogs with isovalent electronic structures to PbTe with much expanded lattices. We demonstrate that Li_{2}TlBi and Li_{2}InBi possess intrinsic high PFs and low κ_{L} by using the stateoftheart computational methods which combines the electron Boltzmann transport theory with ab initio carrier relaxationtime from electron–phonon coupling and phonon transport theory with phonon lifetime from firstprinciples CSLD. The high TE performance of the ptype Li_{2}TlBi and Li_{2}InBi at room temperature are mainly due to the high N_{v} induced by the extended lattice and the low κ_{L} caused by the resonant bonding as observed in PbTe and weak bonding interactions of the extended lattice, respectively. Our TE material design strategy enhances the band degeneracy and suppresses lattice thermal conductivity of the PbTetype materials simultaneously. It is also straightforward to be extended to design or discover other TE materials.
Methods
DFT calculation details
In this study, most DFT calculations are performed using the Vienna Ab initio Simulation Package (VASP)^{44,45}. The projector augmented wave (PAW^{46,47}) pseudo potential, plane wave basis set, and Perdew–Burke–Ernzerhof (PBE^{48}) exchangecorrelation functional were used. The qmpy^{18} framework and the Open Quantum Material Database (OQMD)^{18} was used for convex hull construction. The band gap was computed by means of the screened hybrid functional HSE06^{49}, including spin–orbit coupling (SOC).
Crystal structure prediction
The lowest energy structure of Li_{2}YBi were confirmed by prototype structure screening^{15} and crystal structure searching using the particle swarm optimization method as implemented in the CALYPSO code^{21,22}.
Free energy calculations
The lattice dynamic stability and vibrational entropy were computed by performing frozen phonon calculation as implemented in phonopy package^{50}. The disordered competing phases were simulated using the special quasirandom structures (SQS) as implemented in the alloy theoretic automated toolkit (ATAT)^{51}. Vibrational entropies of the ordered phases and SQSs of the disordered phases are calculated by using phonopy package^{50}. Configuration entropy is included if the competing phases have atom disorder. The calculated results are shown in the Supplementary Table 2.
Phonon and electron transport calculations
The CSLD^{52} technique was employed to obtain the thirdorder force constants, which were used to iteratively solve the linearized phonon Boltzmann transport equation with the ShengBTE package^{53}. The carrier lifetime due to electron–phonon coupling was computed by using Quantum Espresso and Electron–phonon Wannier (EPW) codes with SOC included^{35,54,55,56}. Thermoelectric properties including Seebeck coefficient (S), electrical conductivity (σ), and electronic thermal conductivity (κ_{e}) were computed using BoltzTrap code^{57} with the adjusted band gap from HSE06 calculations and moderesolved carrier lifetime from EPW.
Data availability
All data are available from the corresponding authors upon reasonable request. All codes used in this work are either publicly available or available from the authors upon reasonable request.
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Acknowledgements
J.H. and C.W. (stabilities and electronic structures calculations) acknowledge support by the U.S. Department of Energy, Office of Science and Office of Basic Energy Sciences, under Award No. DESC0014520. Y.X. (lattice thermal conductivity and electron transport calculations), S.S.N. (electronic structure analysis), and V.O. (electronic structure analysis) were supported by US Department of Energy, Office of Science, Basic Energy Sciences, under grant DEFG0207ER46433. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC0205CH11231.
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The research was conceived and designed by J.H., V.O., and C.W. High throughput DFT screening, stabilities, and electronic structure calculations were carried out by J.H. Thermoelectric properties calculations were conducted by Y.X. Analysis of the data was performed by J.H., S.S.N., and Y.X. All authors discussed the results contributed to writing the manuscript.
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He, J., Xia, Y., Naghavi, S.S. et al. Designing chemical analogs to PbTe with intrinsic high band degeneracy and low lattice thermal conductivity. Nat Commun 10, 719 (2019). https://doi.org/10.1038/s41467019085421
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DOI: https://doi.org/10.1038/s41467019085421
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