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Fumiya Matsunaga, [Yoshihiko Okamoto](https://orcid.org/0000-0003-4468-0522), [Yasunori Yokoyama](https://orcid.org/0000-0002-6884-9022), [Kanji Takehana](https://orcid.org/0000-0001-6386-1746), [Yasutaka Imanaka](https://orcid.org/0000-0003-2804-4438), Yuto Nakamura, [Hideo Kishida](https://orcid.org/0000-0002-6369-2660), Shoya Kawano, [Kazuyuki Matsuhira](https://orcid.org/0000-0001-9185-0016), [Koshi Takenaka](https://orcid.org/0000-0003-3206-1919)

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[Anisotropic optical conductivity accompanied by a small energy gap in the one-dimensional thermoelectric telluride <math>  <mrow>    <msub>      <mi>Ta</mi>      <mn>4</mn>    </msub>    <msub>      <mi>SiTe</mi>      <mn>4</mn>    </msub>  </mrow></math>](https://mdr.nims.go.jp/datasets/2716cb2d-6a48-44f2-8030-907a6d835eb2)

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Anisotropic optical conductivity accompanied by a small energy gap in the one-dimensional thermoelectric telluride ${\rm{T}}{{{\rm{a}}}_4}{\rm{SiT}}{{{\rm{e}}}_4}$PHYSICAL REVIEW B 109, L161105 (2024)LetterAnisotropic optical conductivity accompanied by a small energy gap in the one-dimensionalthermoelectric telluride Ta4SiTe4Fumiya Matsunaga,1 Yoshihiko Okamoto ,1,2,* Yasunori Yokoyama ,1 Kanji Takehana,3 Yasutaka Imanaka ,3Yuto Nakamura,1 Hideo Kishida ,1 Shoya Kawano,4 Kazuyuki Matsuhira ,4 and Koshi Takenaka 11Department of Applied Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464–8603, Japan2Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa 277–8581, Japan3National Institute for Materials Science (NIMS), Sakura 3–13, Tsukuba 305-0003, Japan4Graduate School of Engineering, Kyushu Institute of Technology, Kitakyushu 804–8550, Japan(Received 8 September 2023; revised 31 January 2024; accepted 19 March 2024; published 8 April 2024)We investigated the optical properties of single crystals of one-dimensional van der Waals crystal Ta4SiTe4,which exhibited high thermoelectric performance below room temperature. Optical conductivity estimated fromreflectivity spectra indicates the presence of a small energy gap of 0.1–0.15 eV at the Fermi energy. At the lowestenergy, optical conductivity along the Ta4SiTe4 chain is an order of magnitude higher than that perpendicular tothis direction, reflecting anisotropic electron conduction in Ta4SiTe4. These results suggest that the coexistenceof a small band gap and moderate anisotropy in electron conduction is a promising strategy for developinghigh-performance thermoelectric materials for low-temperature applications.DOI: 10.1103/PhysRevB.109.L161105There are great expectations for thermoelectric energy con-version between thermal and electrical energies, which canbe used for energy harvesting and local cooling. Currently,thermoelectric energy conversion has been practically usedin Peltier cooling at around room temperature using Bi2Te3-based materials, and in radioisotope thermoelectric generatorsusing PbTe- or SiGe-based materials. A new material thatexhibits much higher performance at room temperature wouldopen an avenue for the utility of energy harvesting, whichobtains electrical energy from the surrounding temperaturedifferences. In addition, a new material that exhibits highperformance below −100 °C, where Bi2Te3-based materialscannot be used, would lead to Peltier cooling and precisiontemperature control at low temperatures. Recently, the devel-opment of new materials for high-temperature applicationshas been remarkable. PbTe with hierarchical architectures,AgPbmSbTe2+m, and SnSe have been reported to exhibit con-siderably low thermal conductivity κ , resulting in a largedimensionless figure of merit ZT = S2T/ρκ exceeding 2 athigh temperatures, where S, ρ, and T are Seebeck coefficient,electrical resistivity, and temperature, respectively [1–4]. Incontrast, there were few candidate materials, such as Bi1−xSbxand CsBi4Te6, for low-temperature applications [5–7].Thus, at low temperatures, a reduction in κ alone is notsufficient to achieve high thermoelectric performance, but anincrease in S and a reduction in ρ are also essential.Recently, one-dimensional van der Waals crystal Ta4SiTe4and its chemically substituted samples were reported to ex-hibit a significantly large |S| with sufficiently small ρ forthermoelectric materials over wide temperatures from 50 K*yokamoto@issp.u-tokyo.ac.jpto room temperature [8]. Ta4SiTe4 has a strongly one-dimensional crystal structure consisting of Ta4SiTe4 chainsloosely bonded by van der Waals interactions between Teatoms, as shown in Fig. 1(a) [9,10]. This crystal structurehas the orthorhombic Pbam symmetry, but is almost isotropicwithin the ab plane. The Ta4SiTe4 chains are parallel to thec axis, forming an almost perfect triangular lattice in the abplane, where the distances between neighboring chains differby only 0.1%. Whisker crystals with a length of several mil-limeters and a maximum thickness of 10 µm were synthesizedby the crystal growth in the vapor phase, and ρ and S alongthe whisker, //c, were measured [8]. Furthermore, 0.1–0.2%Mo-doped whiskers exhibited a large negative Seebeck co-efficient of |S| ∼ 300 µV K−1 and a small ρ = 1 m� cmat 220–280 K, resulting in a huge power factor P = S2/ρof 170 µW cm−1 K−2. This P is more than four times theroom-temperature value for Bi2Te3-based practical materials.Since the above report, research on this system as athermoelectric material has increased. The whisker crys-tals of chemically doped Nb4SiTe4, which is a 4d analogof Ta4SiTe4, and the solid solution between Ta4SiTe4 andNb4SiTe4 also showed a large P exceeding those of prac-tical materials [11,12]. Moreover, p-type whisker crystalswere obtained by Ti doping at Ta sites [13]. The powerfactor of the p-type whiskers reached a maximum value of60 µW cm−1 K−2 and exceeded the practical level between100 K and room temperature. Furthermore, the thermoelectricproperties of sintered Ta4SiTe4 samples prepared by the cold-press method and a flexible composite of Ta4SiTe4 whiskersand an organic conductor were investigated [14,15].However, the physical background behind the realizationof a huge P below room temperature in this system has notyet been clarified experimentally. First-principles calculationsshowed that Ta4SiTe4 and Nb4SiTe4 have a one-dimensional2469-9950/2024/109(16)/L161105(6) L161105-1 ©2024 American Physical Societyhttps://orcid.org/0000-0003-4468-0522https://orcid.org/0000-0002-6884-9022https://orcid.org/0000-0003-2804-4438https://orcid.org/0000-0002-6369-2660https://orcid.org/0000-0001-9185-0016https://orcid.org/0000-0003-3206-1919https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevB.109.L161105&domain=pdf&date_stamp=2024-04-08https://doi.org/10.1103/PhysRevB.109.L161105FUMIYA MATSUNAGA et al. PHYSICAL REVIEW B 109, L161105 (2024)FIG. 1. (a) Crystal structure of Ta4SiTe4. The orthorhombic unitcell is indicated by solid lines. (b) A single crystal of Ta4SiTe4.(c) A typical crystal surface used in optical reflectivity measure-ments. (d) Seebeck coefficient and electrical resistivity of a Ta4SiTe4single crystal.band structure, in which a small band gap opens at the Diracpoint owing to strong spin-orbit coupling [8,10,16]. Naturally,this characteristic band structure plays an important role inachieving huge P at low temperatures. However, there havebeen few experimental studies on the electronic state andthe correlation between the electronic state and thermoelec-tric properties of this system. Only the magnetoresistancemeasured along the chain direction and magnetic suscepti-bility of a nonoriented sample have been reported thus far[17–19]. The whisker morphology of the synthesized sam-ples hampered the experimental studies. In this Letter, wereport the reflectivity spectra of Ta4SiTe4 single crystals mea-sured over a wide energy range using linearly polarized lightoscillating either parallel or perpendicular to the Ta4SiTe4chains, which enables us to obtain information on the one-dimensional electronic anisotropy. The optical conductivityσ (ω) estimated from the reflectivity data showed two char-acteristic features that are closely related to the thermoelectricproperties of Ta4SiTe4. One is a small energy gap of 0.1–0.15eV-opening at the Fermi energy EF. The other is an anisotropyin the low-energy region, where σ (ω) parallel to the Ta4SiTe4chains is an order of magnitude higher than that perpendicularto them.Single crystals of Ta4SiTe4 were synthesized by crystalgrowth in the vapor phase. A mixture with a 2:1:2 molar ratioof Ta (Rare Metallic, 99.9%), Si (Kojundo Chemical Labora-tory, �99.9%), and Te (Rare Metallic, 99.999%) powders wassealed in an evacuated quartz tube with 10–20 mg of TeCl4powder. The tube was heated to and kept at 873 K for 24 h and1423 K for 96 h, and then furnace cooled to room temperature.We fabricated several hundred tubes to obtain single crystalsfor the reflectivity measurements, because the single crystalslarge enough were rarely obtained. Single crystals with amaximum width of 100 µm or more and a length of severalmillimeters were used for the reflectivity measurements de-scribed below. A typical example is presented in Fig. 1(b). Theobtained single crystals exhibited almost the same Seebeckcoefficient and slightly higher electrical resistivity as those inthe whisker crystals reported in a previous study [8], as shownin Fig. 1(d).Normal incident reflectivity measurements were performedon the as-grown shiny surface at room temperature, us-ing Fourier-type interferometers (0.02–0.06 eV, DA-8, ABBBomen and 0.05–2.2 eV, FT/IR6600 IRT-5200) and a gratingspectrometer (2–4 eV, MSV-5200) [20]. A typical surfaceused for the measurements is shown in Fig. 1(c). The re-flectivity spectra were measured using linearly polarized lightoscillating parallel or perpendicular to the Ta4SiTe4 chains,that is, along the c axis. A Ta4SiTe4 single crystal can eas-ily bend and break under stress, reflecting the nature of theone-dimensional van der Waals crystals. This study used sin-gle crystals that were immediately after taken out from anevacuated quartz tube, which were confirmed to be free ofcleavage and twisting. The crystal size was sufficient for op-tical measurements using microscopes designed for infraredand visible-ultraviolet spectrometers [20]. An evaporated Auor Ag film on a glass plate was used as a reference mirror.Reflectivity measurements in the visible- to visible-ultravioletregion were performed using synchrotron radiation at theBL3B beamline of the ultraviolet synchrotron orbital radia-tion facility (UVSOR), Institute for Molecular Science, Aichi,Japan. The spectrum was confirmed to be independent of itslocation within the spatial resolution. For quantitative dis-cussion, the optical conductivity σ (ω) was deduced fromthe reflectivity R(ω) by the Kramers-Kronig transformation.This transformation requires appropriate extrapolation. Anextrapolation below 0.02 eV was made according to theHagen-Rubens equation and one above 30 eV assuming R ∝ω−4. Parameters in the Hagen-Rubens extrapolations σ (0)HRwere 180 and 38 �−1 cm−1 for the R(ω) spectra taken paralleland perpendicular to the c axis, respectively.First-principles density-functional calculations were per-formed on Ta4SiTe4 using the QUANTUM ESPRESSO code[21,22]. The calculations used norm-conserving pseudopo-tentials from the optimized norm-conserving Vanderbiltpseudopotential library [23] sourced from PSEUDODOJO [24].The exchange-correlation function was treated within thegeneralized gradient approximation in the Perdew-Burke-Ernzerhof formalism [25]. The plane-wave energy cutofffor the wave functions was set to 92 Ry. Brillouin-zoneintegration was performed using a 4 × 2 × 9k-point mesh.Electronic occupations were smeared with a Gaussian widthof 0.002 Ry. In these calculations, the spin-orbit coupling wasexplicitly considered. The results of the density-functionalcalculations were used to calculate the optical conductivityspectra using the RESPACK code [26,27]. In RESPACK, the op-tical conductivity is derived from a dielectric function basedon a random-phase approximation. The energy cutoff of thedielectric function was set to 3 Ry. The integral over theL161105-2ANISOTROPIC OPTICAL CONDUCTIVITY ACCOMPANIED … PHYSICAL REVIEW B 109, L161105 (2024)1.00.80.60.40.20Reflectivity43210Photon Energy (eV)1.00.50.0Reflectivity0.150.100.050Photon Energy(eV)E // cE // cTa4SiTe4E ⊥ cE ⊥ cFIG. 2. Optical reflectivity spectra of a Ta4SiTe4 single crystalfor polarization parallel and perpendicular to the c axis measuredat room temperature. The inset shows the enlarged spectra below0.15 eV. The dotted lines are extrapolations using the Hagen-Rubensformula.Brillouin zone was calculated using the generalized tetrahe-dron technique with a smearing of 0.01 eV.Figure 2 shows the reflectivity spectra of a Ta4SiTe4 singlecrystal measured at room temperature using linearly polarizedlight oscillating parallel to the c axis (the electric field E isparallel to the c axis, i.e., E//c) and perpendicularly to the caxis (E⊥c). The reflectivity for E//c, R//(ω), shows a peakat approximately 1.4 eV and a strong increase below 0.7 eV.The latter increase most likely corresponds to the plasma edgeof the metals. However, R//(ω) is considerably suppressedand decreased below 0.3 and 0.17 eV, respectively, in themidinfrared region, followed by a sharp increase below 0.03eV. This complex spectral shape below the edge at 0.4 eVsuggests that Ta4SiTe4 is not a simple metal with Fermi sur-faces, but has a complex structure in its band structure near EF,as will be discussed later. The E⊥c reflectivity, R⊥(ω), alsoshowed a decrease below 0.17 eV and a sharp increase below0.03 eV, similarly to R//(ω). However, the R⊥(ω) values arelower than R//(ω) in the whole energies, and the increase inR⊥(ω) below 0.4 eV is significantly weaker than that in R//(ω)below 0.7 eV, probably reflecting an anisotropy in electricalconduction.The optical conductivity spectra of Ta4SiTe4 at roomtemperature obtained by performing the Kramers-Kronigtransformation of the extrapolated reflectivity spectra areshown in Fig. 3(a). The optical conductivity for E//c, σ//(ω),exhibits peaks at 2.5, 1.9, 1.3, and 0.2 eV. The first three peaksin the near-infrared to visible region most likely correspond tothe interband transitions. The last peak at 0.2 eV correspondsto the band gap at EF, which will be discussed in detail below.In contrast, the optical conductivity for E⊥c, σ⊥(ω), also hasa small peak at approximately 0.2 eV, but does not show aclear peak owing to the interband transition. These behav-iors are good agreement with the theoretical result shown inFig. 3(b). The theoretical spectrum for E//c has four prominentpeaks at 2.5, 2.0, 1.4, and 0.4 eV, which correspond to thoseobserved in the experimental spectrum shown in Fig. 3(a).543210Conductivity (103 Ω-1 cm-1)(a) Ta4SiTe4E // cE ⊥ c50403020100Neff403020100Photon Energy (eV)E // cE ⊥ c642043210Photon Energy (eV)(b)E // cE // aE // bFIG. 3. (a) Optical conductivity spectra of a Ta4SiTe4 singlecrystal parallel and perpendicular to the c axis at room temperature.The inset shows the effective number of electrons per formula unit.(b) Calculated optical conductivity spectra of Ta4SiTe4 parallel tothe a-, b-, and c axes.The theoretical spectra of E//a and E//b are also consistentwith the experimental σ⊥(ω). The theoretical spectra of E//aand E//b are almost identical, which is natural consideringthe almost isotropic crystal structure within the ab plane, asdiscussed above, and have no significant structure other thana strong decrease below 0.2–0.4 eV. The experimental σ (ω)of Ta4SiTe4 also satisfies the summation rule. The inset ofFig. 3(a) shows the effective electron number per formulaunit, Neff , which is calculated as Neff = 2m0Vπe2 ∫ω0 σ (ω′)dω′,where m0 and V are the bare electron mass and the volumeper formula unit, respectively. At sufficiently high energies,Neff values for both E//c and E⊥c converge to 48, which is thenumber of valence electrons in the formula unit of Ta4SiTe4.These results indicate that the spectral analysis performed inthis study, including extrapolation, is appropriate.Subsequently, the low-energy σ (ω) of Ta4SiTe4, which isclosely related to its thermoelectric properties, is discussed.As shown in Fig. 4(a), σ//(ω) strongly increases fromlow values above 0.1 eV with increasing ω. The σ⊥(ω)also increases above 0.15 eV, even though the changeis weaker than that for E//c. The direct-independentincreases of σ (ω) above 0.1–0.15 eV indicate thepresence of a small energy gap of 0.1–0.15 eV at EF.The presence of such a small energy gap was impliedby the Arrhenius plot of the electrical conductivity ofthe Ti-doped whiskers, where the carrier density wasreduced by Ti doping [13]. A small band gap was alsoL161105-3FUMIYA MATSUNAGA et al. PHYSICAL REVIEW B 109, L161105 (2024)432100.20.1 (eV)(b) Conductivity (102 Ω-1 cm-1)E // cE ⊥ c043210Conductivity (103 Ω-1 cm-1)0.40.20Photon Energy (a) Ta4SiTe4E // cE ⊥ cFIG. 4. Low-energy optical conductivity spectra of a Ta4SiTe4single crystal parallel and perpendicular to the c axis at room tem-perature. (a) and (b) show the optical conductivity spectra below 0.5and 0.2 eV, respectively.noted in first-principles calculations [8,16]. First-principlescalculations without spin-orbit coupling showed thatTa4SiTe4 is a Dirac semimetal with band-crossing pointsat EF. When spin-orbit coupling is switched on, a small bandgap of ∼0.1 eV opens at EF. The strong increase in σ (ω)above 0.1–0.15 eV is a direct observation of a spin-orbit gapopening at EF in Ta4SiTe4.In the topological semimetals with Dirac-like band disper-sion in the vicinity of the EF, a flat region often appears inthe wide midinfrared energy region of the optical conduc-tivity spectra [28,29]. They also show a Drude peak with asignificantly narrow energy width owing to the presence ofextremely light carriers. In contrast, a flat region does notexist in the optical conductivity spectra of Ta4SiTe4, probablybecause such a flat region is masked by the spin-orbit gapof 0.1–0.15-eV opening at EF. The narrow Drude peak maycorrespond to a sharp increase in the optical conductivity inthe lowest-energy region, which will be discussed later, buteven lower-energy and lower-temperature measurements areneeded to confirm it.The existence of a small energy gap at EF is closely relatedto the high thermoelectric performance at low temperaturesof Ta4SiTe4. According to the 10 kBT rule for thermoelectricmaterials, a relationship � ∼ 10kBTmax exists between thesize of the band gap � and the optimum temperature for athermoelectric material Tmax in semiconductor thermoelectricmaterials [30]. In fact, Bi2Te3, PbTe, and SiGe, with bandgaps of 0.3, 0.5, and 0.7 eV have Tmax of approximately 300,500–700, and 1000 K, respectively [21]. The observed � ∼0.1 eV in Ta4SiTe4 suggests high thermoelectric performanceat approximately 100 K in this material. However, it is difficultfor a material to have such a significantly small � at EF, whichis one of the reasons why thermoelectric conversion has notbeen utilized at low temperatures. For example, CsBi4Te6,which exhibits optimum performance at approximately 200 K,has a small � due to the sparse existence of Bi–Bi bonds in itscrystal structure [31]. In Ta4SiTe4, a spin-orbit gap openingat the Dirac point results in a small �. The realization ofa significantly small band gap can serve as a guideline forfinding a promising material for low-temperature applicationsthat is yet to be utilized. This discussion indicates that thespin-orbit gap is a promising approach.Below 0.05 eV, σ (ω) of Ta4SiTe4 for both E//c and E⊥cgradually increases toward the lowest energy, as shown inFig. 4(b), which is probably the Drude peak associated withthe itinerant electrons. As a result, σ//(ω) at the lowest energyof 0.02 eV is equal to 160 �−1 cm−1, which is approximatelyone-sixth of the dc electrical conductivity of 1000 �−1 cm−1measured using a whisker crystal [8]. Although the origin ofthis discrepancy is not fully understood, σ (ω) may continueto increase below 0.02 eV toward h̄ω = 0, resulting in asmaller discrepancy between σ (0) and the dc conductivity.In this case, the increase in σ (ω) toward h̄ω = 0 indicatesthe presence of a small amount of strongly light-conductingcarriers.Although the quantitative estimate of the lowest-energyσ (ω) remains ambiguous, as discussed above, σ⊥(ω) =20 �−1 cm−1 at h̄ω = 0.02 eV is one-eighth of σ//(ω), asshown in Fig. 4(b), suggesting the presence of an anisotropyof one order of magnitude in the electrical conduction ofTa4SiTe4. Although this anisotropy appears weak, consider-ing that Ta4SiTe4 is a one-dimensional van der Waals crystal,this result demonstrates the presence of anisotropic electronconduction in Ta4SiTe4.The observed weak one-dimensional anisotropy, i.e., oneorder of magnitude higher σ// than σ⊥, may play an im-portant role in realizing high thermoelectric performance inTa4SiTe4. Hicks and Dresselhaus theoretically indicated thatsystems with one-dimensional electron conduction can ex-hibit considerably higher thermoelectric performance thanthree-dimensional systems by considering the confinementof electrons in nanosized quantum wires [32]. This ef-fect is expected to work similarly for bulk materials withone-dimensional anisotropy of electron conduction, as dis-cussed for CsBi4Te6 [6,7,31]. However, one-dimensionalelectron conduction is weak against disorder. External fac-tors such as lattice defects have a significant negative effecton one-dimensional electron conduction due to Andersonlocalization. In contrast, electron conduction in Ta4SiTe4is robust against disorder. For example, the whisker sam-ples of Ta4SiTe4-Nb4SiTe4 solid solution show similar orsmaller ρ than that of the end members [12]. The moderateone-dimensional anisotropy in Ta4SiTe4 plays an importantrole in realizing the robustness of electron conduction inTa4SiTe4, which results in high thermoelectric performancein this system. Recently, materials with one-dimensionalcrystal structure were found to exhibit high thermoelectricperformance below room temperature [33–36], implying theimportance of anisotropic electrical conduction.In conclusion, we measured the reflectivity of synthesizedsingle crystals of a one-dimensional van der Waals crystalTa4SiTe4 that show high thermoelectric performance at lowtemperatures over a wide energy range. The optical conduc-tivity data estimated from the reflectivity spectra indicated thepresence of a small band gap of 0.1–0.15 eV at EF, corre-sponding to the spin-orbit gap predicted in the first-principlescalculations. At the lowest measured energy, σ//(ω) is one or-der of magnitude higher than σ⊥(ω), indicating the presence ofmoderate anisotropy in the electrical conduction of Ta4SiTe4.L161105-4ANISOTROPIC OPTICAL CONDUCTIVITY ACCOMPANIED … PHYSICAL REVIEW B 109, L161105 (2024)This significantly small band gap and the weak but robustone-dimensional anisotropy in electrical conduction play keyroles in the high thermoelectric performance, particularly theobserved gigantic power factor in Ta4SiTe4 below room tem-perature. The coexistence of these two factors in a materialis a promising strategy for developing practical materials forlow-temperature applications.We are grateful to Y. Yoshikawa and Y. Abe for theirhelp with single-crystal growth and K. Nakamura for hishelp with the first-principles calculations. Part of this workwas performed at the BL3B of the UVSOR SynchrotronFacility, Institute for Molecular Science (IMS program 21–637). This work was partly supported by JSPS KAKENHI(Grants No. 19H05823, No. 20H00346, No. 20H02603, No.22H04953, No. 23H01831, and No. 23H04871), JST ASPIRE(Grant No. JPMJAP2314), and the Research Foundation forthe Electrotechnology of Chubu. Part of the computation wasperformed at the Supercomputer Center, Institute for SolidState Physics, the University of Tokyo, Japan.[1] K. Biswas, J. He, I. D. Blum, C.-I. Wu, T. P. Hogan, D. N.Seidman, V. P. Dravide, and M. G. Kanatzidis, Nature (London)489, 414 (2012).[2] K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T.Hogan, E. K. Polychroniadis, and M. G. Kanatzidis, Science303, 818 (2004).[3] L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C.Wolverton, V. P. Dravid, and M. G. Kanatzidis, Nature (London)508, 373 (2014).[4] C. Chang, M. Wu, D. He, Y. Pei, C.-F. Wu, X. Wu, H. Yu, F.Zhu, K. Wang, Y. Chen, L. Huang, J.-F. Li, J. He, and L.-D.Zhao, Science 360, 778 (2018).[5] W. M. Yim and A. 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