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Shamim Sk, [Naoki Sato](https://orcid.org/0000-0002-6429-0591), [Takao Mori](https://orcid.org/0000-0003-2682-1846)

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This is the Accepted Manuscript version of an article accepted for publication in Journal of Physics: Condensed Matter.  IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.  The Version of Record is available online at https://dx.doi.org/10.1088/1361-648X/adb409.[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

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[Thermoelectric properties of marcasite-type compounds MSb<sub>2</sub> (M = Ta, Nb): a combined experimental and computational study](https://mdr.nims.go.jp/datasets/8584c01a-0522-401c-bad4-f700863f2ac1)

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Thermoelectric properties of marcasite-typecompounds MSb2 (M = Ta, Nb): A combinedexperimental and computational studyShamim Sk, Naoki Sato∗ and Takao Mori∗Research Center for Materials Nanoarchitectonics (MANA), National Institutefor Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanE-mail: SATO.Naoki@nims.go.jp and MORI.Takao@nims.go.jp∗Corresponding authorAbstract. Here, we investigate the thermoelectric properties of the marcasite-type compounds MSb2 (M = Ta, Nb) in the temperature range of 310–730K. These compounds were synthesized by a solid-state reaction followed bythe spark plasma sintering process. The Rietveld refinement method confirmsthe monoclinic phase with space group C2/m for both compounds. Theobserved values of Seebeck coefficients exhibit non-monotonic behaviour inthe studied temperature range, with the maximum magnitude of −14.4 and−22.7 µV K−1 for TaSb2 and NbSb2, respectively at ∼444 K. The negativesign of S in the full temperature window signifies the n-type behaviour ofthese compounds. Both electrical and thermal conductivities show decreasingtrends with increasing temperature. The experimentally observed thermoelectricproperties are understood through the first-principles DFT and Boltzmanntransport equation. A pseudogap in the density of states around the Fermilevel characterizes the semimetallic behaviour of these compounds. The multi-band electron and hole pockets were found to be mainly responsible for thetemperature dependence of transport properties. The experimental power factorsare found to be ∼0.09 and ∼0.42 mW m−1 K−2 at 300 K for TaSb2 and NbSb2,respectively. We found that there is much room for improvement of powerfactor by tuning carrier concentration. The DFT-based calculations predict themaximum possible power factors at fairly high doping concentrations. The presentstudy suggests that the combined DFT and Boltzmann transport theory are foundto be reasonably good at explaining the experimental transport properties, andmoderate power factors are predicted.Keywords: Thermoelectric properties, density functional theory, electronic structure,electron and hole pockets, semi-classical Boltzmann theory, power factor.Thermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 21. IntroductionThe performance of thermoelectric (TE) materialsis evaluated by the dimensionless figure-of-merit,ZT = S2σTκ , where S is the Seebeck coefficient,σ is the electrical conductivity, κ is the thermalconductivity (which is the sum of electronic, κeand lattice thermal conductivity, κl), and T is theabsolute temperature. The value of ZT determinesthe conversion efficiency; the higher the ZT value,the better the TE performance. Finding materialshaving ZT higher than unity is still a challenging task,though the research in TE has made in progress formany decades [1–7]. Actually, efficient TE materialshave to pass through a typical tradeoff, which includesmaterials that are good electrical conductors but havepoor thermal conductivity. This implies that thetransport of charge carriers within the material shouldexperience weak electron scattering and strong phononscattering.Realizing high ZT has always been a challengingtask due to the strong correlation among the TEparameters through charge carriers [8, 9]. Till now,the state-of-the-art TE materials are Bi2Te3 [10, 11],Sb2Te3 [12]; PbTe [13, 14], SnTe [15]; and SiGe[16, 17] based compounds. Recently, the antimonideshave gained increased interest with high performancediscovered in Mg3Sb2-type materials for example [18–21]. The expression of ZT implies that there aretwo ways for boosting the TE performance: eitherby decreasing the lattice thermal conductivity withoutaffecting or less affecting the electronic properties[1, 22–24] or by improving the power factor (S2σ)[25–30].In recent decades, the TE properties of FeSb2were extensively studied because of ultra-high S ofup to −45000 µV K−1 at 12 K, resulting in thehighest power factor reported ever [31, 32]. But, dueto the large κ of FeSb2, the ZT is diminished withthe low value of 0.005 at 12 K [31, 32]. The FeSb2is a narrow-gap semiconductor with an orthorhombicmarcasite structure [31, 32]. The TE properties ofother marcasite-type compounds including XTe2 (X =Fe, Co, Ni) [33], FeX2 (X = Se, Te) [34], FeS2 [35],FeAs2 [36], RuSb2 [36, 37], etc, have been studied inthe last decades. Within the same family of marcasite-type compounds, the MSb2 (M = Ta, Nb) with amonoclinic crystal structure (Space group: C2/m,No. 12) has recently attracted remarkable attentionas Weyl semimetals exhibiting unusual magneto-transport properties [38–42]. As semimetals, thesematerials typically feature a small overlap of energybands and the absence of a band gap, which canlead to a high power factor. However, their TEproperties remain largely unexplored, particularly atelevated temperatures. For instance, Masuda et al.have studied the TE properties of TaSb2 compoundin the temperature range of 300–800 K [43]. Theysynthesized TaSb2 using solid-state reaction methodwith the spark plasma-sintering process and exploredthe temperature dependent S and σ [43]. Theexperimental measurements of S and σ of MSb2 (M= Ta, Nb) have been done by Failamani et al. [44]in the temperature range of 300–800 K. MSb2 (M= Ta, Nb) are prominent compensated semimetalsthat exhibit resistivity plateaus under magnetic fieldsand anisotropic quasi-parabolic magnetoresistance atlow temperatures [38, 45–49]. TaSb2, in particular,shows negative longitudinal magnetoresistance and anontrivial Berry phase at low temperatures [38, 47].Additionally, TaSb2 and NbSb2 are distinctive as weaktopological insulators in the absence of a magneticfield and can be categorized as type II Weyl materialswhen magnetic fields are applied [46,48]. Although thephysics of MSb2 (M = Ta, Nb) has been extensivelystudied, there is still a lack of theoretical understandingof the experimental TE properties of MSb2 (M = Ta,Nb) at elevated temperatures. In the present study, theTE properties of MSb2 (M = Ta, Nb) are investigatedusing both experimental and computational toolsat the high temperatures. The experimental TEproperties of said compounds are understood usingdensity functional theory (DFT)-based calculations,and we predict the possible maximum power factorswith a suitable amount of doping.In this work, we have synthesized marcasite-typecompounds MSb2 (M = Ta, Nb) using the combinedsolid-state reaction and spark plasma sintering process.All the TE properties are measured and analyzed.First-principle calculations and Boltzmann transportequations are utilized to understand the experimentalresults. The multi-band electron and hole pockets arefound to reasonably explain the experimental data.The maximum possible power factors for p-type andn-type of MSb2 (M = Ta, Nb) are also predicted usingthe DFT-based calculations.Thermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 32. Experimental and computational details2.1. SynthesisMSb2 (M = Ta, Nb) were synthesized using a combinedsolid state reaction (SSR) and spark plasma sintering(SPS) process. The high purity powder of Ta (99.99%),Nb (99.99%) and Sb (99.99%) from Sigma-Aldrich weretaken as starting materials. The desired amount ofmetal powder were ground in alumina mortar and coldpressed at 25 MPa to form pellets. Then the obtainedpellets were heated at 700 °C for 3 days in vacuum-sealed quartz tube. Although the target phase for bothcompounds were obtained in SSR, but the pellets weretoo brittle for the transport measurements. In orderto get dense pellets, we ground the SSR pellets anddid the SPS (SPS-1080, SPS Syntex Inc.) at 750 °Cfor 8 minutes. During the SPS, the constant uniaxialpressure of 50 MPa was applied to a graphite punchof 10 mm diameter under a partial argon atmosphere.The relative densities were calculated from the sampledensities determined by Archimedes principle, whichare found to be ∼95% and ∼94% for TaSb2 and NbSb2,respectively. The obtained pellets were cut into therequired dimensions for the transport measurements.2.2. CharacterizationX-ray diffraction (XRD) were taken (Smart Lab3,Rigaku) in 10–90° as shown in Fig. 1(a) and (b) forTaSb2 and NbSb2, respectively. Rietveld refinementmethod confirms the monoclinic phase with spacegroup C2/m (No. 12) for both compounds. Therefined lattice parameters and angles are shown inTable I. The impurity peak at 28.7° (Fig. 1(a)) mayarise from the surface oxide layer of Sb2O3 [43].2.3. Thermoelectric measurementThe simultaneous measurement of the electricalconductivity and Seebeck coefficient were performedusing ZEM-2 (ADVANCE RIKO) under partial heliumenvironment. The dimensions of TaSb2 and NbSb2were taken as 4.11×1.92×7.57 mm3 and 4.11×1.62×7.39 mm3, respectively. The thermal conductivity wasobtained using the formula: κ = D × Cp × ρ. The ρis the density of the sample. The D is the thermaldiffusivity, which is measured using the laser flashdiffusivity method implemented in LFA-467 Hyperflash (Netzsch) instrument. The heat capacity, Cp wasestimated using a standard sample (pyroceram-9060)in LFA-467. The circular pellets of TaSb2 and NbSb2with diameter of 10 mm and thickness of 1.3 mm and1.6 mm, respectively were used for the measurements.0200040006000Intensity (a.u.)(a)Bragg PositionsObservedCalculatedResidual20 40 60 802θ (Degree)0200040006000Intensity (a.u.)(b)Bragg PositionsObservedCalculatedResidualFigure 1: Measured room temperature X-ray diffractionpatterns and calculated ones by Rietveld method of (a)TaSb2 and (b) NbSb2. The peak at 28.7° indicated by anarrow in (a) is an impurity peak.Table 1: The experimental (obtained from the Rietveldrefinement) and calculated (obtained from DFT) latticeparameters and angles of TaSb2 and NbSb2. The unitsof lattice parameters and angles are in Å and in degree,respectively. Parentheses refer to the estimated standarddeviations.TaSb2 NbSb2Exp. Cal. Exp. Cal.a 10.22203(9) 10.14321 10.23722(1) 10.16523b 3.64461(9) 3.62423 3.63139(1) 3.59164c 8.29068(4) 8.22734 8.33121(8) 8.25354β 120.396(0) 120.534 120.026(4) 120.0132.4. Computational detailsThe ground state electronic structure calculationsare carried out within DFT [51]. The projectoraugmented-wave method is used as implementedin Quantum Espresso code [52]. The PERDEW-ZUNGER (LDA) [53] exchange-correlation (XC)functional is used for the calculation. The calculationsare done in relaxed structure. The optimized latticeparameters and angles are tabulated in Table I. Theforce convergence criteria for structure relaxation wasset to be 10−4 Ry/Bohr. Table II shows the relaxedatomic positions along with the experimental valuesfor both compounds. The structures relaxed usingDFT are closely matched with the experimental ones.Thermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 4Table 2: Fractional coordinates of atomic positions for relaxed structure of TaSb2 and NbSb2. The experimental valuesare also mentioned in the parentheses.TaSb2 x (exp) y (exp) z (exp) NbSb2 x (exp) y (exp) z (exp)Ta 0.150 (0.152) 0 (0) 0.188 (0.193) Nb 0.151 (0.152) 0 (0) 0.190 (0.194)Sb1 0.148 (0.143) 0 (0) 0.535 (0.532) Sb1 0.149 (0.145) 0 (0) 0.536 (0.531)Sb2 0.405 (0.401) 0 (0) 0.114 (0.111) Sb2 0.405 (0.402) 0 (0) 0.115 (0.111)The kinetic energy cut-off for wavefunctions is used as60 Ry. The kinetic energy cut-off for charge densityis set to be 8 times the kinetic energy cut-off forwavefunctions. The k -mesh grid was used as 7×15×7for both compounds. The energy convergence criteriawas set to be 10−8 Ry for the self-consistent fieldcalculation. The transport coefficients were calculatedusing the BoltzTraP2 package [54] interfaced withQuantum Espresso code [52]. For the transportproperties calculations, the electronic structures arecalculated applying the k-mesh of 30 × 60 × 30.The phonon dispersion is computed using densityfunctional perturbation theory (DFPT), implementedin Quantum Espresso code. The q-mesh size of 2×4×2is used for force calculation. The convergence criteriafor the calculations of forces is set as 10−14 Ry/Bohr.3. Results and discussion3.1. Experimental transport propertiesFig. 2(a) exhibits the experimentally measuredSeebeck coefficients (S ) of MSb2 (M = Ta, Nb) inthe temperature range of 310–730 K. The |S| for bothcompounds are found to increase up to ∼450 K, thendecreases till the highest temperature. The highestmagnitudes of S are found to be −14.4 and −22.7 µVK−1 for TaSb2 and NbSb2, respectively at∼444 K. Ourexperimental results align closely with the reporteddata [43,44]. For instance, Masuda et al. reported theS of TaSb2 as −12 µV K−1 at 500 K [43]. Similarly,Failamani et al. reported the S of TaSb2 and NbSb2as −14 and −21 µV K−1, respectively, at 500 K [44].The total S mainly comes from the contributions ofelectrons and holes. Under the two-carrier conductionmodel, the S can be expressed as S = Shσh+Seσeσh+σe[55],where Sh,e is the Seebeck coefficients of holes andelectrons and σh,e is the electrical conductivity of holesand electrons. The sign of the S is determined bythe major contribution coming from the electrons orholes, because electrons generally yield the negativeS, while holes give positive S. Therefore, the negativesign of S in Fig. 2(a) signifies the dominating n-typebehaviour of these compounds. The magnitude of Sfor NbSb2 is larger than that of TaSb2 in the fulltemperature window. The temperature dependence ofS shows a peak at around 444 K for both compounds,which suggests a compensation of p- and n-type chargecarriers [50]. The non-linear behaviour of S withtemperature for both compounds can be explained bythe calculated band-structure, which is discussed later.Fig. 2(b) shows the temperature dependence ofelectrical conductivities (σ) of TaSb2 and NbSb2. Theσ are found to be 0.88 ×106 and 0.95 ×106 W−1 m−1for TaSb2 and NbSb2, respectively at ∼310 K. Thenas the temperature increases, the σ decreases till thehighest temperature (∼730 K) with the correspondingvalues of 0.39 ×106 and 0.41 ×106 W−1 m−1 forTaSb2 and NbSb2, respectively. Our measured valuesof σ are accordance with the other experimentallyreported data [43, 44]. For example, Masuda et al.reported the σ of 1.0 ×106 W−1 m−1 for TaSb2 at300 K [43], while Failamani et al. reported valuesof 1.11 ×106 W−1 m−1 and 1.18 ×106 W−1 m−1 forTaSb2 and NbSb2, respectively, at room temperature[44]. The decrement behaviour of σ can be explainedby the simple formula: σ = ne2τm∗ , where, n, e, τand m∗ are the carrier concentration, the electroniccharge, the relaxation time and the effective mass ofcharge carriers, respectively. Generally, under theincrement of temperature, n increases, whereas τdecreases. Hence, among the opposite trend of n and τwith temperature, the dominating behaviour generallygives the temperature dependent trend of σ. Hence,Fig. 2(b) shows that the temperature dependent τis dominating over n in σ. In general, with increasein temperature, the σ of semiconductors increases,while σ of metals decreases. Hence, the temperaturedependent trend of σ of present compounds showthe metal-like behaviour. However, the electronicstructure calculations predict the semimetallic (inbetween semiconductor and metals) behaviour of thesecompounds, which is discussed later.Using the measured S and σ, the power factorsare calculated as shown in Fig. 2(c). The calculatedvalues of power factors are found to be ∼0.09 and∼0.42 mW m−1 K−2 at 300 K for TaSb2 and NbSb2,respectively. At 750 K, the power factors are calculatedas ∼0.03 and ∼0.08 mW m−1 K−2, respectively.The comparable power factors of other marcasite-typecompounds, including for CoTe2 as 0.33 mW m−1 K−2at 570 K [33], FeSe2 as 0.12 mW m−1 K−2 at 554 K [56]Thermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 5300 400 500 600 700Temperature (K)-30-25-20-15-10-5S (µV K-1)(a)TaSb2NbSb2300 400 500 600 700Temperature (K)0.40.60.81σ (106 Ω−1 m-1)TaSb2NbSb2(b)300 400 500 600 700 800Temperature (T)00.20.40.6S2σ (mW m-1 K-2)(c)TaSb2NbSb2300 400 500 600 700Temperature (K)691215κ (W m-1 K-1)TaSb2NbSb2(d)Figure 2: Temperature dependence of measured (a) Seebeck coefficient, S (b) electrical conductivity, σ (c) power factor,S2 σ and (d) thermal conductivity, κ of TaSb2 and NbSb2.Γ C C2 Γ M2 D2 A L2 Γ V2-2-1012Energy (eV)(a)120 1 2 3 4 5DOS (states/eV/f.u.)-2-1012(b)TotalTa_dSb_pΓ C C2 Γ M2 D2 A L2 Γ V2-2-1012Energy (eV)(c)120 1 2 3 4 5DOS (states/eV/f.u.)-2-1012(d)TotalNb_dSb_pFigure 3: (a) Band-structure and (b) density of states (DOS) of TaSb2; (c) band-structure and (d) DOS of NbSb2. Thecoordinates of the high symmetry k-points are: Γ (0 0 0), C (0.27 0.29 0), C2 (-0.29 0.7 0), M2 (-0.5 0.5 0.5), D2 (0.260.26 0.5), A (0 0 0.5), L2 (0 0.5 0.5) and V2 (0 0.5 0).have been reported. Usually, semimetals possess low Swith high σ. But recent studies have shown that theS of the semimetals can be tuned by magnetic field,strain, etc [57–59]. Semimetals having asymmetryin their electron and hole pockets could have highS [60, 61]. Semimetals with high (or fractionally low)electron (m∗e) and hole (m∗h) effective mass ratio resultsin high S [60, 62]. If the m∗e/m∗h ratio tends to 1, itsignifies a very low magnitude of the S. For instance,HgTe possesses a high m∗e/m∗h ratio of ≈ 0.1, whichresults in high negative S between -90 and -135 µV K−1at room temperature [60]. In our study, the m∗e/m∗hratio for TaSb2 is calculated as ∼1.2 (near to 1), whichresults in low magnitude of S.The thermal conductivities (κ) of TaSb2 andNbSb2 are measured in the temperature region 300–750 K as shown in Fig. 2(d). The κ are graduallydecreasing with the increment of temperature in thewhole temperature range. At 300 K, the κ arefound to be 13.7 and 12.2 W m−1 K−1, while theseare decreased to 9.6 and 8.2 W m−1 K−1 at 750K for TaSb2 and NbSb2, respectively. In the fulltemperature window, the values of κ for TaSb2 arehigher than the NbSb2. The total κ is a simple additionof electronic thermal conductivity (κe) and latticethermal conductivity (κL), i.e., κ = κe + κL. In thiswork, we have calculated the temperature dependenceof κe for both compounds. The experimental κe canbe estimated using the experimental σ via Wiedemann-Franz law: κe = LσT , L is Lorenz number. Then itwill be interesting to see how calculated κe explainsthe experimental κe, which is described later. As canbe seen from the Fig. 2(b), the σ of NbSb2 are higherthan that of TaSb2. Hence, larger values of κe areexpected for NbSb2 as compared to TaSb2 accordingto the Wiedemann-Franz law.3.2. Electronic structureTo understand the experimentally measured transportcoefficients, we have calculated the electronic structureof MSb2 (M = Ta, Nb). The band-structures for TaSb2and NbSb2 are calculated along the lines betweenhigh symmetry points (Γ–C–C2–Γ–M2–D2–A–L2–Γ–V2) in the first Brillouin zone, which are shown inFig. 3(a) and (c), respectively. The dashed red linecorresponding to zero energy defines the Fermi level,EF of the compounds. It is clear that the two bands(which are indexed by 1 and 2) around the EF areexpected to contribute to the transport properties ofthese compounds. In both Fig. 3(a) and (c), theoccupied band 1 crosses the EF at either side of the Γpoint and becomes unoccupied, while the unoccupiedband 2 crosses the EF in the M2–D2, A–L2 andThermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 6Γ–V2 directions and becomes occupied. This typeof mixing of occupied and unoccupied bands aroundthe EF predicts the semimetal-like character of thecompound, which is consistent with the other reportedworks [38, 39, 41, 63]. The electronic band-structure isthe key input for calculating any electronic transportproperties. In the present study, we have calculatedthe Seebeck coefficient, electrical conductivity andelectronic part of thermal conductivity for MSb2 (M= Ta, Nb). We will recall this part in the next sub-section during the discussion of calculated transportproperties. We have also investigated the effect of spin-orbit coupling (SOC) on band structures and transportproperties, and found that the effects were minor.All the results including SOC effects can be found inSupplemental Material (SM).Fig. 3(b) and (d) express the calculated totaland partial density of states (DOS) of TaSb2 andNbSb2, respectively. At EF , the values of DOS arecalculated as ∼0.34 and ∼0.47 states/eV/f.u. forTaSb2 and NbSb2, respectively. A pseudogap aroundthe EF characterizes the semimetallic behaviour ofthese compounds. In order to know the contributionsin transport properties from different atoms, we havecalculated the partial DOS of Ta, Nb and Sb as shownin the same figures. In the occupied band region,the contribution in the DOS comes from Ta(Nb)-dand Sb-p orbitals almost equally. In contrast, in theunoccupied band region, the dominant contributionin the DOS comes from Ta(Nb)-d orbitals, with thesmall contribution from Sb-p orbitals. In the energyrange of −1 to 0 eV in the occupied band regionof Fig. 3(b), the contributions of Ta-d and Sb-p inthe DOS are calculated as ∼60% and ∼40%, whilethese contributions are found to be ∼80% and ∼20%,respectively, in the energy range of 0 to 1 eV in theunoccupied band region.The effective mass (m∗) of electrons (m∗e) andholes (m∗h) are calculated using the formula: m∗ =~2/(d2E/dk2) under parabolic approximation [8].Table III lists the m∗ of bands 1 and 2 correspondingto different electron and hole pockets near the EF interms of electron’s mass (me) of TaSb2. These bandsare named as B1 and B2 in the table. The effectivemass ratio of m∗e/m∗h is calculated as ∼1.2, results insmall magnitude of S.The bulk modulus of TaSb2 and NbSb2 are alsocalculated. This is an elastic property of a material,which can be defined as: B = −V (P−P1)(V−V 1) , where V isthe equilibrium volume, and P is the correspondingpressure. The V 1 is the expanded/shrunk volume,and P1 is the corresponding pressure. The threecalculations are performed, including the equilibriumlattice constant, +1% (expanded volume) and −1%(shrunk volume). The final B is calculated by takingTable 3: Effective mass (m∗) of electrons (m∗e) and holes(m∗h) corresponding to bands 1 and 2 of TaSb2.Bands Directions m∗eB1 Γ–M2 5.45B2 C–C2 1.69B2 M2–D2 1.37B2 A–L2 6.49Bands Directions m∗hB1 Γ (C2–Γ–M2) 4.14B1 Γ–M2 5.26B1 Γ (L2–Γ–V2) 2.26051015202530Energy (meV)(a)Γ C C2 Γ M2 A Γ051015202530Energy (meV)(b)Figure 4: Phonon dispersion of (a) TaSb2 and (b) NbSb2.the average of expanded and shrunk one, which arefound to be ∼131 GPa and ∼125 GPa for TaSb2 andNbSb2, respectively. In Materials Project, the B arereported as 103 GPa and 98 GPa for TaSb2 (mp -11697 [64]) and NbSb2 (mp - 1969 [65]), respectively.However, the B of TaSb2 has been reported as 131.2± 3.4 by Zhou et al. [66], which gives close match withour calculation.3.3. Phonon dispersionPhonon dispersions of TaSb2 and NbSb2 are presentedin Fig. 4 along the high symmetry direction Γ–C–C2–Γ–M2–A–Γ. As the primitive unit cell of compoundscontains 12 atoms, the phonon dispersion associateswith 36 branches. Out of these branches, 3 are acousticThermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 7(plotted by red lines), and the remaining 33 are optical(plotted by black lines). All the branches give positiveenergies, signifying the mechanical stability of thecompound. Two of the optical branches of TaSb2having energy higher than 25 meV are well separatedfrom other branches. These two branches are nearlydegenerate at M2-point and either side of C2-pointaround 27 meV. Few optical branches of NbSb2 havingenergy higher than 21 meV are well separated fromother branches. The maximum phonon energies arecalculated as ∼29.0 meV and ∼32.5 meV for TaSb2and NbSb2, respectively.3.4. Calculated transport propertiesIn this sub-section, we discuss the calculated transportproperties, viz., the temperature dependence ofSeebeck coefficient (S ), electrical conductivity dividedby relaxation time (σ/τ) and electronic thermalconductivity divided by relaxation time (κe/τ) ascalculated using the BoltzTraP2 package [54] undersemi-classical Boltzmann theory. The BoltzTrap2is based on the combined constant relaxation timeapproximation (CRTA) and rigid band approximation(RBA). In CRTA, relaxation time (τ) is considered asa constant, but in principle τ is dependent on bothband index and wave vector direction. The RBA meansthat the band-structure is independent of temperatureand doping. Considering the CRTA, the σ/τ , S andκe/τ can be calculated using the following Boltzmanntransport equations (BTE):σ/τ = e2∫dε(− ∂f0∂ε)∑kv2kδ(ε− εk), (1)S =ekBτσ∫dε(− ∂f0∂ε)∑kv2kδ(ε− εk)[ε− µkBT], (2)κeτ= k2BT∫dε(−∂f0∂ε)∑kv2kδ(ε−εk)[ε− µkBT]2−στS2T, (3)where e, kB , ε, f0, k, v, µ are the chargecarrier, Boltzmann constant, the energy, the Fermi-Dirac distribution function, the wave vector, the groupvelocity, and the chemical potential, respectively. Thef0 takes care of the temperature dependency of thecompound. The marcasite-type TaSb2 and NbSb2possess anisotropic crystal structures. However, sincethe samples prepared in this study are polycrystallinewithout any preferred orientation, the physicalproperty measurements were conducted in only onedirection. Thus, when comparing the calculatedtransport properties with the experimental ones, weaveraged the calculated values over all directions. Thecalculated direction-dependent transport propertiesare shown in Fig. S6(a) and (b) in SupplementalMaterial. Addressing anisotropy using high-qualitysingle crystal is possible future work. Additionally,we acknowledge that CRTA simplifies the complexnature of TE transport by assuming a constantrelaxation time, which may not fully capture theanisotropic characteristics and off-stoichiometry ofthe materials. Anisotropic materials often displaydirection-dependent properties, while stoichiometricdeviations can introduce localized states and additionalscattering mechanisms that CRTA may not accuratelyaccount for. To improve the accuracy of theresults, it would be beneficial to consider energy-and direction-dependent scattering rates and potentialvariations in relaxation time due to off-stoichiometry.While this approach would provide a more detailedunderstanding of the TE transport, it is also time-consuming and computationally expensive, posingpractical challenges.At first, we discuss the S followed by σ/τand κe/τ . Initially, the S are calculated at EF(i.e., at µ = 0 eV), which are ∼1 and ∼20 µVK−1 at 310 K for TaSb2 and NbSb2, respectively.These positive values of S are far away from theexperimental negative values of ∼ −10 and ∼ −21 µVK−1 for TaSb2 and NbSb2, respectively at the sametemperature. At this point, it is important to notethat the calculations of S have been done on singlecrystalline stoichiometric compounds. But, it is verycommon to have off-stoichiometry in any synthesizedpolycrystalline samples. This off-stoichiometry maycome from many factors, including the purity of thestarting materials, inaccuracy in weighing the rawmaterials, inhomogeneous mixing during the synthesisprocess, evaporation of low melting element duringthe heat treatment etc. These factors are mainlyresponsible for the defects and/or disorders in thesamples which may affect the S of the sample.Here we do not consider any structural imperfectionsinfluencing the transport properties, such as changesin oxidation states, anti-site defects, and vacancies,although considering these factors can improve theprediction accuracy. In addition to this, the anisotropyoften matters when comparing the calculation of singlecrystal with the experimental polycrystalline one. Allthese factors can be addressed in the calculation byshifting the chemical potential (µ) of the compound.But, quantifying the exact value of µ is a challengingjob for any compound. For doing this, we havecalculated µ dependent S at different temperatures asshown in Fig. 5. Then, the µ has been chosen at 300 Kfor a better representation of experimental S. We foundthat at µ≈ 64 and 82 meV, the calculated T dependentS gives the best match with the experimental Tdependent S for TaSb2 and NbSb2 as shown in Fig.6 (a) and (b), respectively. This constant µ calculatedThermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 8-800 -400 0 400 800Chemical Potential (meV)-60-40-200204060S (µV K-1)300 K400 K500 K600 K700 K750 KFigure 5: Calculated Seebeck coefficient, S at the functionof chemical potential, µ at different temperatures of TaSb2.The solid vertical black line indicates the µ value, wheretransport properties are calculated.-40-30-20-10010S (µV K-1)(a)TaSb2_ExpTaSb2_Cal300 400 500 600 700Temperature (K)-40-30-20-10S (µV K-1)(b)NbSb2_ExpNbSb2_CalFigure 6: Comparison of experimental and calculatedSeebeck coefficients, S of (a) TaSb2 and (b) NbSb2.at 300 K is used to calculate the other transportproperties in the full temperature range.The T dependent S of TaSb2 and NbSb2 at µ ≈ 64and 82 meV, respectively can be understood throughelectron/hole pockets formed with the bands 1 and2 in the band-structure of Fig. 3(a) and (c). Theblack horizontal dotted lines above the EF indicatethe µ values, where the temperature dependent S arecalculated. For both compounds, it is clear that in S,the contributions of charge carriers mainly come fromthe hole pockets formed with band 1 at the vicinityof Γ and A points and in the Γ–M2 direction, andelectron pockets formed with the band 2 in the C–C2, C2–Γ, M2–D2, A–L2, Γ–V2 and Γ–M2 (band1) directions at µ ≈ 64 (82) meV. The presence ofdominating electron pockets over hole pockets gives thenegative S for both compounds. The low magnitude ofS can be understood from the calculated m∗e/m∗h ratioof ∼1.2 (near to 1) for TaSb2. The size of the holepockets at Γ point for TaSb2 (at 64 meV) is largerthan the hole pocket at Γ point for NbSb2 (at 82meV), which supports the less magnitude of the S forTaSb2 as compared to that of NbSb2. Noticeably, theexperimental |S| for both compounds increases up to∼450 K, then decreases till the highest temperature.As the S throughout the temperature range arenegative, the dominant contribution comes from theelectron pockets. After ∼450 K, the contribution ofmore hole pockets may result in decreasing of |S|.However, the calculated S are deviating from theexperimental S in the high temperature region. Atthis conjuncture, it is important to note that the Sis calculated using the ground-state band-structuresand constant µ of 300 K. But, the band-structureand µ are the temperature dependent quantities.Hence, considering the temperature dependence ofthese quantities are expected to improve the accuracyof calculated S at higher temperature, which will beour future work.Fig. 7 shows the σ/τ of TaSb2 and NbSb2calculated using Equation 1 as implemented inBoltzTraP2. Equation shows that the calculatedσ/τ depends on group velocity of an electron, ∂f0∂ε ,and number of available states at a given µ. Withan increase in temperature, the number of statesalways increases. Hence, the increasing nature of σ/τwith temperature (Fig. 7) is directly related to themore number of available states at high temperature.Initially, the charge carriers from band 1 at the vicinityof Γ point and in the Γ–M2 direction, and band2 in the C–C2, M2–D2, A–L2 and Γ–V2 directionsare participated in the transport (Fig 3(a)). As thetemperature increases, the more charge carriers fromband 1 at the vicinity of A point and in the M2–D2and Γ–V2 directions; the band 2 in C2–Γ directionare expected to contribute in the σ/τ . At hightemperature, more charge carriers from the differentelectron/hole pockets participate in the conduction,and hence σ/τ increases. The calculated temperaturedependent σ/τ is compared with the experimental σ(Fig. 2(b)) to extract the temperature dependentThermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 955.25.45.65.866.2σ/τ (1019 Ω−1 m-1 s-1)(a)300 400 500 600 700Temperature (K)0.511/τ (1014s)300 400 500 600 700Temperature (K)44.44.85.25.6σ/τ (1019 Ω−1 m-1 s-1)(b)300 400 500 600 700Temperature (K)0.511.51/τ (1014s)Figure 7: Calculated electrical conductivity divided byrelaxation time, σ/τ of (a) TaSb2 and (b) NbSb2. Insetshows 1/τ as a function of temperature, which is estimatedby comparing the calculated σ/τ with experimental σ.1/τ . Insets of Fig. 7 shows the extracted 1/τ in thetemperature range of 300–750 K. The values of τ arecalculated as ∼1.8 × 10−14 s and ∼2.5 × 10−14 s at300 K for TaSb2 and NbSb2, respectively. With theincrease in temperature, 1/τ increases monotonicallyand reaches the τ values of ∼0.66 × 10−14 s and∼0.82 × 10−14 s at 750 K, respectively. Thedecreasing nature of τ is due to the presence of morescattering centers at high temperature. For a realsystem, the calculation of τ is a challenging task dueto the involvement of many scattering mechanisms,including electron-electron scattering, electron-phononscattering, electron-defect scattering etc [8]. This isthe reason why we have chosen the simple methodto extract temperature dependent τ . This methodis previously utilized in literature [67]. It will beinteresting to see how this temperature dependent τexplains the other transport properties.The κe/τ for MSb2 (M = Ta, Nb) are calculatedusing Equation 3 implemented in BoltzTraP2. As theoutput of BoltzTraP2 is κe/τ , the κe is computed usingthe temperature dependent τ (inset of Fig. 7). Fig. 8shows the κe for TaSb2 and NbSb2 in the temperatureregion 300–750 K. The calculated κe is comparedwith the experimental κe in the same figure. The036912κe (W m-1 K-1)(a)TaSb2_ExpTaSb2_Cal300 400 500 600 700Temperature (K)036912κl (W m-1 K-1)(c)TaSb2_ExpNbSb2_Exp03691215κe (W m-1 K-1)(b)NbSb2_ExpNbSb2_CalFigure 8: Comparison of experimental (estimated usingWiedemann-Franz law) and calculated electronic part ofthermal conductivity, κe of (a) TaSb2 and (b) NbSb2. (c)Experimental lattice thermal conductivity calculated usingthe formula: κl = κ− κeexperimental κe is estimated using Wiedemann-Franzlaw: κe = LσT . Here, the temperature dependentexperimental σ (Fig. 2(b)) and the constant value ofL (∼2.45 × 10−8 W W K−2) are taken to estimatethe experimental κe. However, the L is temperaturedependent quantity, and the temperature dependencyof L is estimated from the calculated σ/τ and κe/τas shown in Fig. 9. The L at 300 K are foundto be ∼2.63 × 10−8 W W K−2 and ∼2.86 × 10−8W W K−2 for TaSb2 and NbSb2, respectively. TheL increases as the temperature increases. Fig. 8(c)illustrates the experimental κl, which is obtained bysubtracting the experimental κe (estimated using theThermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 10300 400 500 600 700Temperature (K)22.533.54L (10-8 W Ω Κ−2)TaSb2NbSb2Figure 9: Temperature dependent Lorenz number, L,estimated from the calculated σ/τ and κe/τ .Wiedemann-Franz law) from the total experimental κ.As the temperature rises, there is a notable decreasein κl for both compounds. Specifically, at 300 K,the calculated κl values are 7.1 and 4.9 W m−1 K−1,while these values decrease to 2.7 and 0.9 W m−1K−1 at 750 K for TaSb2 and NbSb2, respectively.This trend indicates that at lower temperatures, bothelectrons and phonons contribute almost equally tothe overall κ. However, as the temperature increases,the contribution of phonons to the κ diminishessignificantly, making the electronic contribution muchmore dominant in the heat transfer process. Moreover,from Fig. 8 (a) and (b), it is observed that thecalculated κe gives quite good agreement with theexperimental κe. With an increase in temperature,κe increases due to contributions of more chargecarriers from the different electron/hole pockets. Thefigure shows that there is a small deviation at hightemperature region. At this point, it is importantto note that the calculations have been done usingground-state band-structure and constant µ values,as we mentioned earlier. Considering temperaturedependency of all these factors may improve thereproducibility at high temperature, which demandsextra computational costs.3.5. Power factorFinally, the chemical potential dependence of thepower factor divided by relaxation time of MSb2 (M= Ta, Nb) is calculated in the temperature range of300–1000 K as shown in Fig. 10. The red verticaldashed line at zero eV indicates the Fermi level of thecompound. The black vertical solid line at ∼64 and∼82 meV of TaSb2 and NbSb2, respectively indicatesthe µ value, at which the transport properties arecalculated to explain the experimental results. Usingthe temperature dependent τ (inset of Fig. 7), thechemical potential dependence of the power factor iscalculated in the temperature range of 300–700 K asshown in Fig. 11. The maximum possible power factorsare also calculated for p-type and n-type of thesecompounds. The maximum power factors for p-typeconduction are calculated as ∼1.14 and ∼1.74 mWm−1 K−2 at ∼ −375 and ∼ −320 meV, respectivelyat 300 K. These values are found to be ∼1.16 and∼1.80 mW m−1 K−2 at ∼215 and ∼215 meV for n-type of TaSb2 and NbSb2, respectively at 300 K. Thep-type and n-type are confirmed from the sign of S atthe corresponding µ values of Fig. 5. The τ valuesare taken from the previous calculations (Inset of Fig.7). The carrier concentrations corresponding to themaximum power factors for p-type of TaSb2 and NbSb2are calculated as ∼2.56 × 1021 and ∼2.60 × 1021cm−3, respectively, whereas for the n-type conductionof TaSb2 and NbSb2 these values are found to be∼1.42 × 1021 and ∼1.58 × 1021 cm−3, respectively.The predicted power factors at 300 K in this studyare comparable with the power factors of ∼1–2 mWm−1 K−2 for Bi2Te3 parent compound [68–70], thoughthe power factors of BiTe-based doped compounds arereported as ∼4–7 mW m−1 K−2 in many literatures[71–74] at/around the room temperature. However,the power factor of many semimetals is reportedinsensitive to doping concentration [75]. In contrast,the enhancement of the power factor of rare-earthdoped semimetal HfTe5 is reported by Lowhorn etal [76]. The improvement of the power factors of somesemimetallic Heusler alloys are reported by tuning thedoping concentration [77, 78]. Moreover, a rigorouseffort is required to synthesize the suitable p and n-type doping of MSb2 (M = Ta, Nb) to validate thecomputational prediction.4. ConclusionsThe thermoelectric properties of MSb2 (M = Ta, Nb)are studied in the present study. These compoundswere prepared by a combined solid-state reaction anda spark plasma sintering process. The monoclinicphase with space group C2/m is confirmed forboth compounds through Rietveld refinement. Thenegative sign of the Seebeck coefficient indicates then-type behaviour of these compounds. The DFT-based electronic structure calculations were carried outin order to understand the experimentally observedthermoelectric properties. The semimetallic behaviourof these compounds was confirmed from the band-structure and density of states calculations. Themulti-band electron and hole pockets are foundreasonably good in explaining the experimental results.Further study of computational calculations gives themaximum possible power factors of ∼1.14 and ∼1.74Thermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 11-1200 -800 -400 0 400 800 1200Chemical potential (meV)00.511.522.53S2 σ/τ (1014mW K-2 m-1 s-1)n-typep-typeEF300 K1000 KExp. (a)300 K400 K500 K600 K700 K800 K900 K1000 K-1200 -800 -400 0 400 800 1200Chemical potential (meV)00.511.522.533.5S2 σ/τ (1014mW K-2 m-1 s-1)n-typep-typeEF300 K1000 KExp.(b)300 K400 K500 K600 K700 K800 K900 K1000 KFigure 10: Variation of power factor (S2σ) per relaxation time with chemical potential at different temperatures of (a)TaSb2 and (b) NbSb2.-1200 -800 -400 0 400 800 1200Chemical potential (meV)00.40.81.21.6S2 σ (mW K-2 m-1)n-typep-typeEFExp. (a)300 K400 K500 K600 K700 K-1200 -800 -400 0 400 800 1200Chemical potential (meV)00.511.522.5S2 σ (mW K-2 m-1)n-typep-typeEFExp.(b)300 K400 K500 K600 K700 KFigure 11: Variation of power factor (S2σ) with chemical potential at different temperatures of (a) TaSb2 and (b) NbSb2.mW m−1 K−2 for p-type conduction of TaSb2 andNbSb2, respectively at 300 K, while these valuesare found to be ∼1.16 and ∼1.80 mW m−1 K−2at 300 K for n-type conduction, respectively withthe corresponding concentrations. According to thecalculations, a relatively high power factor can beachieved, but since the required carrier concentrationis high, it should be noted that the rigid bandapproximation is properly maintained. In conclusion,the combined DFT and Boltzmann transport theoryare found to be reasonably good at addressingthe experimental transport properties, and moderatepower factors can be obtained if these compounds aresynthesized with the proper doping concentration.Supplemental materialSee the Supplemental Material (SM) for the electronicstructure and transport calculations using spin-orbitcoupling (SOC).Data availability statementThe data that support the findings of this studyare available within the article and supplementarymaterial.AcknowledgmentsThis work was supported by JST Mirai Program GrantNumber JPMJMI19A1.References[1] G. J. Snyder and E. S. Toberer, Nat. Mater. 7, 105 (2008).[2] J. R. Sootsman, D. Y. Chung and M. G. Kanatzidis, Angew.Chem. Int. Ed. 48, 8616 (2009).[3] D. Zhao and G. Tan, Appl. Therm. Eng 66, 15 (2014).[4] T. Mori, Small 13, 1702013 (2017).[5] S. Shittu, G. Li, X. Zhao and X. Ma, Appl. Energy 268,115075 (2020).[6] T. Hendricks, T. Caillat and Takao Mori, Energies 15, 7307(2022).[7] M. d’Angelo, C. Galassi and N. Lecis, Energies 16, 6409(2023).[8] N. W. Ashcroft and N. D. Mermin, Solid State Physics,edited by D. G. Crane, (Saunders College Publishing,New York, 1976), Vol. 239.[9] S. Sk, P. Devi, S. Singh and S. K. Pandey, Mater. Res.Express 6, 026302 (2018).[10] W. M. Yim and F. D. Rosi, Solid State Electron. 15, 1121(1972).[11] O. Yamashita, S. Tomiyoshi and K. Makita, J. Appl. Phys.93, 368 (2003).[12] D. K. Ko, Y. Kang and C. B. Murray, Nano Lett. 11, 2841(2011).[13] K. Biswas, J. Q. He, I. D. Blum, C. I. Wu, T. P. Hogan, D.Thermoelectric properties of marcasite-type compounds MSb2 (M = Ta, Nb) 12N. Seidman, V. P. Dravid and M. G. Kanatzidis, Nature489, 414 (2012).[14] Y. Xiao and L. D. Zhao, npj Quantum Mater. 3, 55 (2018).[15] M. Hong, Y. Wang, S. Xu, X. Shi, L. Chen, J. Zou and Z.G. Chen, Nano Energy 60, 1 (2019).[16] G. Joshi et al., Nano Lett. 8, 4670 (2008).[17] R. Basu and A. Singh, Mater. Today Phys. 21, 100468(2021).[18] H. Tamaki, H. K. Sato and T. Kanno, Adv. Mater. 28,10182 (2016).[19] Z. Liu et al., Joule 5, 1196 (2021).[20] Z. Liu, W. Gao, H. Oshima, K. Nagase, C. H. Lee, and T.Mori, Nat. Commun. 13, 1120 (2022).[21] L. Wang et al., Adv. Energy Mater. 13, 2370143 (2023).[22] N. Wang, H. Chen, H. He, W. Norimatsu, M. Kusunoki andK. Koumoto, Sci. Rep. 3, 3 (2013).[23] X. Shi, A. Wu, W. Liu, R. Moshwan, Y. Wang, Z. G. Chenand J. Zou, ACS Nano 12, 11417 (2018).[24] A. U. Khan et al., Nano Energy 31, 152 (2017)[25] G. Mahan and J. Sofo, Proc. Nat. Acad. Sci. 93, 7436(1996).[26] F. Ahmed, N. Tsujii and T. Mori, J. mater. Chem. A 5,7545 (2017).[27] Z. Liu, W. Gao, W. Zhang, N. Sato, Q. Guo and T. Mori,Adv. Energy Mater. 10, 2002588 (2020).[28] C. Bourges, N. Sato, T. Baba, T. Baba, I. Ohkubo, N. Tsujiiand T. Mori RSC Advances. 10, 21129 (2020).[29] F. Garmroudi et al., Mater. Today Phys. 27, 100742 (2022).[30] W. Zhang, J. -F. Halet and T. Mori, Npj Comput. Mater.9, 137 (2023).[31] A. Bentien, S. Johnsen, G. K. M. Madsen, B. B. Iversenand F. Steglich, EPL 80, 17008 (2007).[32] P. Sun, N. Oeschler, S. Johnsen, B. B. Iversen and F.Steglich, Dalton Trans 39, 1012 (2010).[33] Z. Bai, Y. Ji and B. Qin, J Mater Sci: Mater Electron 34,461 (2023).[34] V. K. Gudelli, V. Kanchana, G. Vaitheeswaran, M. C.Valsakumar and S. D. Mahanti, RSC Adv. 4, 9424(2014).[35] V. K. Gudelli, V. Kanchana, S. Appalakondaiah, G.Vaitheeswaran and M. C. Valsakumar, J. Phys. Chem.C 117, 21120 (2013).[36] P. Sun, N. Oeschler, S. Johnsen, B. B. Iversen and F.Steglich, Appl. Phys. Express 2, 091102 (2009).[37] P. Sun, N. Oeschler, S. Johnsen, B. B. Iversen, and F.Steglich, J. Phys. Conf. Ser 150, 012049 (2009).[38] Y. Li, L. Li, J. Wang, T. Wang, X. Xu, C. Xi, C. Cao andJ. Dai, Phys. Rev. B 94, 121115 (2016).[39] A. Pariari, R. Singha, S. Roy, B. Satpati and P. Mandal,Sci. Rep. 8, 10527 (2018).[40] P. Kumar, Sudesh and S. Patnaik, J. Phys. Commun. 3,115007 (2019).[41] P. Li, P. Qiu, Q. Xu, J. Luo, Y. Xiong, J. Xiao, N. Aryal, Q.Li, L. Chen and X. Shi, Nat. Commun. 13, 7612 (2022).[42] P. Li, P. Qiu,J. Xiao, T. Deng, L. Chen and X. Shi, EnergyEnviron. Sci. 16, 3753 (2023).[43] I. Masuda, H. Miyazaki, M. Yoshimura, H. Ishii and Y.Nishino, Phys. Status Solidi B 259, 2100571 (2022).[44] F. Failamani et al., Intermetallics 65, 94 (2015).[45] K. F. Wang, D. Graf, L. J. Li, and L. M. Wang, Petrovic,C. Sci. Rep. 4, 7328 (2015).[46] C. Xu, J. Chen, G. -X. Zhi, Y. Li, J. Dai and C. Cao, Phys.Rev. B 93, 195106 (2016).[47] X. Y. Liu et al., Chin. Phys. Lett. 34, 127501 (2017).[48] D. Gresch, Q. S. Wu, G. W. Winkler and A. A. Soluyanov,New J. Phys. 19, 035001 (2017).[49] L. Guo et al., J. Appl. Phys. 123, 155103 (2018).[50] C. Gayner and Y. Amouyal, Adv. Funct. Mater. 30(18),1901789 (2020).[51] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).[52] P. Giannozzi et al., J. Phys. Condens. Matter 21, 395502(2009).[53] J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).[54] G. K. H. Madsen, J. Carrete and M. J. Verstraete, Comput.Phys. Commun. 231, 140 (2018).[55] A. F. Ioffe, Physics of Semiconductors (Infosearch Limited,London, 1960).[56] G. Li et al., Chem. Mater. 27, 8220 (2015).[57] K. Kaur, S. Dhimanb and R. Kumar, Physics Letters A,381(4), 339 (2017).[58] B. Skinner and L. Fu, Science Advances, 4, 2621 (2018).[59] Y. Pan et al., Adv. Mater., 33(7), 2003168 (2021).[60] M. Markov, X. Hu, H. C. Liu, N. Liu, S. J. Poon, K.Esfarjani, and M. Zebarjadi, Sci. Rep. 8(1), 9876 (2018).[61] J. Mao, H. Zhu, Z. Ding, Z. Liu, G. A. Gamage, G. Chenand Z. Ren, Science 365 498 (2019).[62] M. Markov et al., Phys. Rev. Materials 3, 095401 (2019).[63] S. E. Lee M. J. Oh, S. Ji, J. Kim, J. H. Jun, W. Kang,Younjung Jo and M. H. Jung Proc. Natl Acad. Sci. USA118, e2023027118 (2021).[64] The Materials Project, Materials Data on TaSb2 by Mate-rials Project, United States, 2015, doi:10.17188/1188289.[65] Data retrieved from the Materials Project for NbSb2 (mp-1969) from database version v2023.11.1.[66] Y. Zhou et al., J. Solid State Chem. 265, 359 (2018).[67] S. Sk, N. Shahi and S. K. Pandey, J. Phys.: Condens.Matter 34, 265901 (2022).[68] J. F. Li and J. Liu, Phys. Stat. Sol. (a) 203, 3768 (2006).[69] L. D. Zhao, B. P. Zhang, W. S. Liu and J. F. Li, J. Appl.Phys. 105, 023704 (2009).[70] J. Fu, S. Song, X. Zhang, F. Cao, L. Zhou, X. Li and H.Zhang, Crys. Eng. Comm 14, 2159 (2012).[71] O. Yamashita, S. Tomiyoshi and K. Makita, J. Appl. Phys.93, 368 (2003).[72] O. Yamashita and S. Tomiyoshi, J. Appl. Phys. 95, 6277(2004).[73] B. Poudel et al., Science 320, 634 (2008).[74] K. Park et al., J. Am. Chem. Soc. 138, 14458 (2016).[75] M. Markov, S. E. Rezaei, S. N. Sadeghi, K. Esfarjani andM. Zebarjadi, Phys. Rev. Materials 3, 095401 (2019).[76] N. D. Lowhorn, T. M. Tritt, E. E. Abbott and J. W. Kolis,Appl. Phys. Lett. 88, 022101 (2006).[77] F. Garmroudi et al., Materials Today Physics 27, 100742(2022).[78] Y. Xia, S. Bhattacharya, A. L. Pope, S. J. Poon and T. M.Tritt, J. Appl. Phys. 88, 1953 (2000). Introduction Experimental and computational details Synthesis Characterization Thermoelectric measurement Computational details Results and discussion Experimental transport properties Electronic structure Phonon dispersion Calculated transport properties Power factor Conclusions