# Fileset

[MSb2_SM.pdf](https://mdr.nims.go.jp/filesets/c21236e5-6c54-4ef8-aa79-ce5fe5e232d6/download)

## Creator

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

## Rights

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/)

## Other metadata

[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)

## Fulltext

Supplemental Material: Thermoelectric properties of marcasite-type compoundsMSb2 (M = Ta, Nb): A combined experimental and computational studyShamim Sk1, Naoki Sato1,,∗ and Takao Mori1,†1Research Center for Materials Nanoarchitectonics (MANA),National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanI. COMPUTATION DETAILSIn this Supplemental Material (SM), we provide theelectronic structure calculations using spin-orbit cou-pling (SOC) implemented in Quantum Espresso code[1]. Transport properties are calculated using BoltzTraPpackage [2]. A heavy k-mesh of size 20 × 40 × 20 is usedfor the transport calculations. The experimental trans-port properties are compared with the calculated resultsof non-SOC and SOC.II. RESULTS AND DISCUSSIONFig. S1(a) and (c) show the calculated band-structureof TaSb2 and NbSb2, respectively. A very small effectis observed by the inclusion of SOC. Fig. S1(b) and (d)exhibit the density of states (DOS) of said compounds,respectively using SOC. Fig. S2 represents the compar-ison of experimental Seebeck coefficient (S ) with calcu-lated one. For TaSb2, the non-SOC and SOC give thesimilar trend of S, while for NbSb2, the non-SOC givemore closer match of S with experiment as comparedto SOC. A significant change in the electrical conduc-tivity per relaxation time (σ/τ) are observed for bothcompounds by inclusion of SOC in Fig. S3. For TaSb2,the non-SOC electronic part of thermal conductivity (κe)provides closer match as compared to SOC as shown inFig. S4(a). Fig. S5 shows the power factor per re-laxation time as a function of chemical potential usingSOC. The maximum power factors for p-type conduc-tion are calculated as ∼1.01 and ∼1.12 mW m−1 K−2 at∼ −375 and ∼ −320 meV, respectively at 300 K. Thesevalues are found to be ∼1.41 and ∼1.53 mW m−1 K−2at ∼215 and ∼215 meV for n-type of TaSb2 and NbSb2,respectively at 300 K. Fig. S6(a) and (b) exhibits thecalculated direction-dependent S for TaSb2 and NbSb2,respectively.III. ACKNOWLEDGEMENTSThis work was supported by JST Mirai Program GrantNumber JPMJMI19A1.[1] P. Giannozzi et al., J. Phys. Condens. Matter 21, 395502(2009).[2] G. K. H. Madsen and D. J. Singh, Comput. Phys. Com-mun. 175, 67 (2006).∗ Electronic mail: SATO.Naoki@nims.go.jp † Electronic mail: MORI.Takao@nims.go.jp2Γ C C2 Γ M2 D2 A L2 Γ V2-2-1012Energy (eV)(a)12Non-SOCSOC0 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)12Non-SOCSOC0 1 2 3 4 5DOS (states/eV/f.u.)-2-1012(d)TotalNb_dSb_pFIG. S 1: (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 (0.26 0.260.5), A (0 0 0.5), L2 (0 0.5 0.5) and V2 (0 0.5 0).300 400 500 600 700Temperature (K)-40-30-20-10010S (µV K-1)(a)TaSb2_ExpTaSb2_Non-SOCTaSb2_SOC300 400 500 600 700Temperature (K)-40-30-20-10S (µV K-1)(b)NbSb2_ExpNbSb2_Non-SOCNbSb2_SOCFIG. S 2: Comparison of experimental and calculated Seebeck coefficients, S of (a) TaSb2 and (b) NbSb2.6912σ/τ (1019 Ω−1 m-1 s-1)(a)Non-SOCSOC300 400 500 600 700Temperature (K)01231/τ (1014s) Non-SOCSOC300 400 500 600 700Temperature (K)36912σ/τ (1019 Ω−1 m-1 s-1)(b)Non-SOCSOC300 400 500 600 700Temperature (K)01231/τ (1014s)Non-SOCSOCFIG. S 3: Calculated electrical conductivity divided by relaxation time, σ/τ of (a) TaSb2 and (b) NbSb2. Inset shows 1/τ asa function of temperature, which is estimated by comparing the calculated σ/τ with experimental σ.3300 400 500 600 700Temperature (K)036912κe (W m-1 K-1)(a)TaSb2_ExpTaSb2_Non-SOCTaSb2_SOC300 400 500 600 700Temperature (K)03691215κe (W m-1 K-1)(b)NbSb2_ExpNbSb2_Non-SOCNbSb2_SOCFIG. S 4: Comparison of experimental (estimated using Wiedemann-Franz law) and calculated electronic part of thermalconductivity, κe of (a) TaSb2 and (b) NbSb2.-1200 -800 -400 0 400 800 1200Chemical potential (meV)0102030405060S2 σ/τ (1014 µW K-2 cm-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)01020304050607080S2 σ/τ (1014 µW K-2 cm-1 s-1)n-typep-typeEF300 K1000 K(b)Exp.300 K400 K500 K600 K700 K800 K900 K1000 KFIG. S 5: Variation of power factor (S2σ) per relaxation time with chemical potential at different temperatures of (a) TaSb2and (b) NbSb2.300 400 500 600 700Temperature (K)-40-200S (µV K-1)(a)S_AverageSxxSyySzz300 400 500 600 700Temperature (K)-60-40-200S (µV K-1)(b)S_AverageSxxSyySzzFIG. S 6: Calculated direction-dependent Seebeck coefficient, S for (a) TaSb2 and (b) NbSb2, obtained using Non-SOC.