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Asato Seshita, Hirotaka Okabe, Riad Kasem, Yuto Watanabe, Jumpei G. Nakamura, Shoichiro Nishimura, [Kensei Terashima](https://orcid.org/0000-0003-0375-3043), [Ryo Matsumoto](https://orcid.org/0000-0001-6294-5403), [Yoshihiko Takano](https://orcid.org/0000-0002-1541-6928), Aichi Yamashita, Masaki Fujita, Yoshikazu Mizuguchi

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[Investigation of Superconducting Gap of High‑Entropy Telluride AgInSnPbBiTe5](https://mdr.nims.go.jp/datasets/efd4ebbe-c187-4f99-9e50-7ce19bcc59ee)

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1  Investigation of superconducting gap of high-entropy telluride AgInSnPbBiTe5  Asato Seshita1, Hirotaka Okabe2,3, Riad Kasem1, Yuto Watanabe1, Jumpei G. Nakamura2,4, Shoichiro Nishimura2,4, Kensei Terashima5, Ryo Matsumoto5, Yoshihiko Takano5, Aichi Yamashita1, Masaki Fujita3, Yoshikazu Mizuguchi1*  1 Department of Physics, Tokyo Metropolitan University, Hachioji 192-0397, Japan 2 Muon Science Division, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan 3 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan  4 Materials and Life Science Division, J-PARC Center, Tokai 319-1106, Japan 5 National Institute for Materials Science, Tsukuba 305-0047, Japan  *mizugu@tmu.ac.jp  Abstract We performed transverse-field muon spin relaxation/rotation (TF-μSR) on a high-entropy-type (HE-type) superconductor AgInSnPbBiTe5. The emergence of bulk superconducting states was confirmed from magnetic susceptibility, specific heat, and μSR. The superconducting gap 2Δ(0) estimated from μSR was clearly larger than that expected from conventional weak-coupling phonon-mediated model, suggesting the strong-coupling nature of superconductivity. In addition, a long penetration depth of 3.21(7) μm was obtained. The strong-coupling nature of superconductivity and the long penetration depth are similar to the trends observed in the other HE-type superconductors (HE alloys and transition-metal zirconides), which may be universal feature of HE-type superconductors.    Keywords: Superconductivity, superconducting gap, μSR, metal telluride, high-pressure synthesis  Statements and Declarations The authors declare no competing interests.   Data availability statement All the data presented in the paper can be provided from the corresponding author by a reasonable request.   mailto:*mizugu@tmu.ac.jp2  1. Introduction Recently, high-entropy (HE) materials, which are highly-disordered materials possessing multiple-element solution resulting in high configurational entropy, have been actively studied. The simplest HE materials are HE alloys (HEAs), which alloys typically containing five or more elements solving in a crystallographic site with a concentration of 5–35 at% [1–3]. The above-described criterion for element solution satisfies a high value of configurational entropy of mixing (ΔSmix), exceeding 1.5R, where R is gas constant. ΔSmix is defined as ΔSmix = −RΣicilnci, where ci is composition of the component i. HEAs and similar HE compounds, where one or more crystallographic sites of compounds are substituted by multiple elements, possess merit on the engineering aspects. For example, HEAs exhibit improved mechanical properties and stability or high performance in high temperature and/or extreme conditions [1,2]. Furthermore, superior catalytic and thermoelectric properties have been observed [4–9]. As well as the application merit, the highly disordered local structures and nearly-random bonding should be important issues in the field of materials science. Actually, HE superconductors with various types of crystal structures and constituent elements have been developed [10–23], and some of the HE superconductors exhibit robustness of superconductivity against applied external pressure [24,25]. In Ref. 26, we reported on the glassy atomic vibration and blurry electronic band structure in a AgInSnPbBiTe5 superconductor, and the origin of the unconventional pressure dependence of transition temperature (Tc) is discussed with the anomalous glassy phonon and electronic states. In this paper, we study the superconducting properties of a HE-type metal telluride AgInSnPbBiTe5 with a NaCl-type structure (space group: Fm-3m, #225) using muon spin relaxation/rotation (μSR), which is a powerful tool for discussing superconducting gap [27]. As shown in Fig. 1(a), the metal site is in the HEA configuration with the solution of five different metals. From the temperature evolution of magnetic penetration depth (λ), the superconducting gap and pairing symmetry can be discussed. Several μSR studies on superconducting properties of HEAs and HE compounds revealed that the HE superconductors [28,29] tend to show a value of 2Δ(0)/kBTc greater than 3.53 expected from the Bardeen-Cooper-Schrieffer (BCS) phonon-mediated weak-coupling model; Δ(0) and kB are a superconducting gap at 0 K and the Boltzmann constant, respectively [30]. The examples of 2Δ(0)/kBTc estimated using μSR are summarized in Fig. S1. Furthermore, there was a clear trend that the increase in ΔSmix results in an increase in 2Δ(0)/kBTc for transition-metal (Tr) zirconides TrZr2 [29], and the Tc of HE-type samples deviates from the conventional line in the Uemura plot [28,29]. If another example of strong (or moderate) coupling characteristics of superconductivity in HE materials, universal features of HE superconductors would be obtained, and that will be useful for clarifying the essential effects of HE-alloying on superconducting states. Here, we show the strong-coupling nature of the AgInSnPbBiTe5 superconductor.   2. Experimental methods Polycrystalline powders of AgInSnPbBiTe5 were firstly prepared by solid-state reaction in an 3  evacuated quartz tube. High-pressure annealing of the prepared precursor powders was performed to obtain single-phase polycrystalline samples of AgInSnPbBiTe5 using a cubic-anvil-type press system (CT factory). High-pressure annealing conditions were 3 GPa and 500ºC for 30 min. The details of sample preparation are reported in Refs. 20, 23, and 25. Powder X-ray diffraction (XRD) was performed using a MiniFlex600 (RIGAKU) diffractometer with Cu Kα radiation and a D/teX-Ultra detector by a conventional θ-2θ method. The crystal-structure parameters were refined using the Rietveld method with RIETAN-FP software [31], and the crystal structure was visualized using VESTA software [32]. The chemical composition of the selected sample was examined by energy-dispersive X-ray spectroscopy (EDX) on a scanning electron microscope TM-3030 (Hitachi Hightech) equipped with an EDX-SwiftED analyzer (Oxford). The EDX analysis was performed at five different points. To investigate the superconducting properties of AgInSnPbBiTe5, the temperature dependence of magnetic susceptibility (4πχ) was measured using a superconducting quantum interference device (SQUID) with a Magnetic Property Measurement System (MPMS, Quantum Design) after both zero-field cooling (ZFC) and field cooling (FC) occurred. Specific heat (C) measurements were performed using the thermal relaxation method with a Physical Property Measurement System (PPMS Dynacool, Quantum Design). The sample was fixed on a sample stage with the Apiezon N grease. Transverse field (TF) μSR measurements were performed using an ARTEMIS spectrometer installed on S1 area in MLF, J-PARC (proposal No.: 2024A0076). The measurements were performed under a TF of H = 246 Oe using a 3He cryostat.   3. Results and discussion 3.1 Sample characterization Powder XRD pattern for AgInSnPbBiTe5 is shown in Fig. 1(b). Although the tiny diffraction peak of BN (R3m, #160), which was used in the high-pressure annealing, was detected (see Fig. S1 for the Rietveld fitting), the other peaks were assigned to the NaCl-type phase with no peak splitting, indicating that homogeneous AgInSnPbBiTe5 was successfully synthesized. The lattice constant is estimated as 6.25405(5) Å. No compositional segregation was detected by EDX mapping (Fig. 1(c)). The average chemical composition of the obtained sample is estimated as Ag1.01In1.00Sn1.00Pb0.88Bi1.14Te4.96. The estimated ΔSmix for the M site using average chemical composition is 1.61R.   3.2 Magnetic susceptibility and specific heat Figure 2(a) shows the temperature dependence of 4πχ of AgInSnPbBiTe5. The 4πχ data is corrected by assuming the demagnetization effect. Large diamagnetic signals corresponding to the emergence of superconducting states are observed below 2.5 K, and the estimated Tc was 2.44 K; Tc was estimated as the 4  crossing point of two lines as shown in the inset of Fig. 2(a).  Figure 2(b) shows the temperature dependences of C under magnetic fields of μ0H = 0.0–1.0 T. Clear jumps were observed at μ0H ≤ 0.6 T, suggesting the emergence of bulk superconductivity. As shown in Fig. 2(c), the estimated Tcs were plotted, and the upper critical field at 0 K (μ0Hc2(0)) was estimated as 0.74 T by assuming the Werthamer-Helfand-Hohenberg model [33]. The low-temperature specific heat can be described as C/T = γ + βT2 + δT4, where γ, β, and δ represent contributions of electron, lattice, and anharmonicity term of the lattice, respectively. The values of γ, β, and δ were estimated as 2.6(2) mJ mol−1 K−2, 0.70(6) mJ mol −1 K−4, and 0.043(5) mJ mol−1 K−6, respectively, from fitting the data for μ0H = 1.0 T. The Debye temperature ΘD of 177 K was calculated from β = 12π4NR/5ΘD3, where N is the number of atoms in the formula unit. To examine the magnitude of electronic specific heat jump (ΔCele), the temperature dependence of Cele/T is plotted by subtracting the lattice contribution (βT2 + δT4) as shown in Fig. 2(d). Tc and ΔCele at Tc were estimated by considering the entropy balance, and the estimated values are Tc = 2.44 and ΔCele = 1.14γTc. The ΔCele of AgInSnPbBiTe5 is slightly smaller than 1.43γTc, which is expected from the BCS theory with a weak-coupling superconductor, but the comparable ΔCele proves the emergence of bulk superconductivity.  3.3 TF-μSR To obtain information on the superconducting gap information, TF-μSR measurement has been performed. Magnetic field of H = 246 Oe, which is in between the lower critical field at 0 K(μ0Hc1(0)) and the μ0Hc2(0), was applied above the Tc, followed by sample cooling to 0.69 K. Figure 3 shows the TF-μSR asymmetry spectrum at 0.69 K for AgInSnPbBiTe5. The spectrum exhibits damping oscillation, indicating that the sample falls into the flux-line-lattice state to exert strongly inhomogeneous internal field to implanted muons. The TF-μSR signal is best fitted with the following model function [28]: 𝐴(𝑡) = 𝐴exp (−12𝜎2𝑡2) cos(𝛾𝜇𝐵𝑡 + 𝜙) +∑𝐴BG𝑛exp (−12𝜎BG𝑛2𝑡2) cos(𝛾𝜇𝐵BG𝑛𝑡 + 𝜙)2𝑛=1, where A and ABGn are the asymmetry contributions from sample and sample holder, σ and σBGn are relaxation rate contributions from sample and sample holder, γμ is muon gyromagnetic ratio, B and BBGn are mean field contributions from sample and sample holder, and  is the initial phase offset. To accurately examine the small σ, fitting was performed with long time range spectrum (up to 15 μs). The σ includes both the temperature-independent depolarization σN, which comes from the static field arising due to the nuclear magnetic moment, and the contribution of the field variation from the flux-line-lattice, given as σ2 = σN2 + σFLL2. For a triangular lattice, the temperature dependence of the magnetic penetration depth λ(T) can be expressed by 𝜎FLL(𝑇)2𝛾𝜇2 =0.00371𝜙02𝜆4(𝑇), where γμ/2π = 135.5 MHz/T is the muon gyromagnetic ratio, and 0 is a flux quantum. The temperature dependence of λ−2 is shown in Fig. 4. To examine the λ(0) and Δ(0), the data was fitted with a superconducting gap function. Assuming an isotropic s-wave gap, the temperature 5  dependent relation between the λ(0) and Δ(0) can be described as 𝜆(0)2𝜆(𝑇)2=𝛥(𝑇)𝛥(0)tanh [𝛥(𝑇)2𝑘B𝑇], which is relation derived within the BCS scheme, i.e. 2Δ(0) = 3.53kBTc and in the dirty limit [29]. Here, we obtained Tc of 1.88 K from the fitting. The lower Tc than that shown in Fig. 2 is due to the strain-release effect and applied magnetic field. In AgInSnPbBiTe5, the flesh sample shows Tc close to 2.5 K as shown in Fig. 2, but after several weeks, the high-pressure-annealing strain is released, and Tc decreases to about 2 K (See Fig. S2 for the susceptibility data taken after 3 months from the high-pressure synthesis). The current μSR measurements were performed after 16 days from the high-pressure annealing. The solid line in Fig. 4 is the fit, and the long λ(0) of 3.21(7) μm and large 2Δ(0)/kBTc of 10(2) are obtained. This large 2Δ(0) clearly larger than the BCS value suggests that the AgInSnPbBiTe5 is possibly possessing strong-coupling nature of superconductivity. The examples of large 2Δ/kBTc in Fe- and Cr-based samples are summarized in Table S1. The estimated 2Δ/kBTc in the current sample is close to the largest value in the Fe-based superconductors. The large penetration depth would be caused by highly inhomogeneous atomic alignments in HE-type material, and such inhomogeneity would influence the homogeneous formation of the superconducting gap, which has been observed in other HE-type superconductors examined by μSR [29]. Therefore, the trend that HE-type superconductors have a strong-coupling nature would be the universal features when the HE configuration of the atoms largely affect the electronic and phonon characteristics and superconducting gap characterization. To confirm the universality, further experimental and theoretical studies are needed. In particular, for AgInSnPbBiTe5, low-temperature C measurements using a 3He or dilution system will be needed to examine superconducting gap.  4. Summary We synthesized polycrystalline samples of AgInSnPbBiTe5, which is a HE-type superconductor, using high-pressure annealing. From the powder XRD and EDX mapping, homogeneous single-phase quality of the obtained samples was confirmed. Bulk nature of superconductivity was confirmed using magnetic susceptibility and specific heat measurements. TF-μSR was performed on AgInSnPbBiTe5 under TF of H = 246 Oe. The emergence of bulk superconducting states was confirmed from μSR, and the estimated 2Δ(0)/ kBTc of 10 suggested the strong-coupling nature of superconductivity. The trend that the HE-type samples exhibit strong-coupling nature of superconductivity would be a universal feature, which will create new research field of physics for highly disordered superconductors.  Acknowledgements The authors thank E. Kenny, Y. Ikeda, and A. Bhattacharyya for discussion on the results. This project was partly supported by TMU Research Project for Emergent Future Society.  6   References 1. M. H. Tsai and J. W. Yeh, Mater. Res. Lett. 2, 107 (2014). 2. J. W. Yeh, S. K. Chen, S. J. Lin, J. Y. Gan, T. S. Chin, T. T. Shun, C. H. Tsau, S. Y. Chang, Adv. Energy Mater.  6, 299 (2004). 3. H. Inui, K. Kishida, Z. Chen, Mater. Trans. 63, 394 (2022). 4. D. Wu, K. Kusada, T. Yamamoto, T. Toriyama, S. Matsumura, I. Gueye, O. Seo, J. Kim, S. Hiroi, O. Sakata, S. Kawaguchi, Y. Kubota, H. Kitagawa, On the electronic structure and hydrogen evolution reaction activity of platinum group metal-based high-entropyalloy nanoparticles. Chem. Sci. 11, 12731–12736 (2020). 5. Y. Sun, S. Dai, Sci. Adv. 7, eabg1600 (2021). 6. B. Jiang, Y. Yu, J. Cui, X. Liu, L. Xie, J. Liao, Q. Zhang, Y. Huang, S. Ning, B. Jia, B. Zhu, S. Bai, L. Chen, S. J. Pennycook and J. He, Science, 371, 830–834 (2021). 7. A. Yamashita, Y. Goto, A. Miura, C. Moriyoshi, Y. Kuroiwa and Y. Mizuguchi, Mater. Res. Lett. 9, 366–372 (2021). 8. B. Jiang, W. Wang, S. Liu, Y. Wang, C. Wang, Y. Chen, L. Xie, M. Huang, J. He, Science 377, 208-213 (2022). 9. A. Seshita, A. Yamashita, T. Fujita, T. Katase, A. Miura, Y. Nakahira, C. Moriyoshi, Y. Kuroiwa, Y. Mizuguchi, J. Alloys Compd. 1004, 175679 (2024). 10. P. Koželj, S. Vrtnik, A. Jelen, S. Jazbec, Z. Jagličić, S. Maiti, M. Feuerbacher, W. Steurer, J. Dolinšek, Phys. Rev. Lett. 113, 107001 (2014). 11. L. Sun, R. J. Cava, Phys. Rev. Materials 3, 090301 (2019). 12. J. Kitagawa, S. Hamamoto, N. Ishizu, Metals 10, 1078 (2020). 13. J. Kitagawa, K. Hoshi, Y. Kawasaki, R. Koga, Y. Mizuguchi, T. Nishizaki, J. Alloys Compd. 924, 166473 (2022). 7  14. N. Ishizu, J. Kitagawa, Results in Physics 13, 102275 (2019). 15. R. Sogabe, Y. Goto, Y. Mizuguchi, Appl. Phys. Express 11, 053102 (2018). 16. Y. Fujita, K. Kinami, Y. Hanada, M. Nagao, A. Miura, S. Hirai, Y. Maruyama, S. Watauchi, Y. Takano, I. Tanaka, ACS Omega 5, 16819 (2020). 17. Y. Shukunami, A. Yamashita, Y. Goto, Y. Mizuguchi, Physica C 572, 1353623 (2020). 18. K. Wang, Q. Hou, A. Pal, H. Wu, J. Si, J. Chen, S. Yu, Y. Chen, W. Lv, J. Y. Ge, S. Cao, J. Zhang, Z. Feng, J. Supercond. Nov. Magn. 34, 1379 (2021). 19. A. Yamashita, K. Hashimoto, S. Suzuki, Y. Nakanishi, Y. Miyata, T. Maeda, Y. Mizuguchi, Jpn. J. Appl. Phys. 61, 050905 (2022). 20. Y. Mizuguchi, J. Phys. Soc. Jpn. 88, 124708 (2019). 21. Md. R. Kasem, K. Hoshi, R. Jha, M. Katsuno, A. Yamashita, Y. Goto, T. D. Matsuda, Y. Aoki, Y. Mizuguchi, Appl. Phys. Express 13, 033001 (2020). 22. A. Yamashita, R. Jha, Y. Goto, T. D. Matsuda, Y. Aoki, Y. Mizuguchi, Dalton Trans. 49, 9118 (2020). 23. Md. R. Kasem, R. Ishii, T. Katase, O. Miura, Y. Mizuguchi, J. Alloys Compd. 920, 166013 (2022). 24. J. Guo, H. Wang, F. von Rohr, Z. Wang, S. Cai, Y. Zhou, K. Yang, A. Li, S. Jiang, Q. Wu, R. J. Cava, L. Sun, PNAS 114, 13144 (2017). 25. Md. R. Kasem, Y. Nakahira, H. Yamaoka, R. Matsumoto, A. Yamashita, H. Ishii, N. Hiraoka, Y. Takano, Y. Goto, Y. Mizuguchi, Sci. Rep. 12, 7789 (2022). 26. Y. Mizuguchi, H. Usui, R. Kurita, K. Takae, Md. R. Kasem, R. Matsumoto, K. Yamane, Y. Takano, Y. Nakahira, A. Yamashita, Y. Goto, A. Miura, C. Moriyoshi, Mater. Today Phys. 32, 101019 (2023). 27. A. Bhattacharyya, D. T. Adroja, M. Smidman, V. K. Anand, Sci. China Phys. Mechanics 8  Astronomy 61, 127402 (2018). 28. K. Motla, P. K. Meena, Arushi, D. Singh, P. K. Biswas, A. D. Hillier, R. P. Singh, Phys. Rev. B 105, 144501 (2022). 29. C. Wang, M. R. Kasem, Y. Mizuguchi, Investigation of the high-entropy alloy superconductor XZr2 (X = Fe, Co, Ni, Rh, Ir) using muon spin spectroscopy (μSR). In J. Kitagawa & Y. Mizuguchi (Eds.), Springer series in solid-state sciences: Vol. 202. High-entropy alloy superconductors. Exotic properties, applications and materials design (pp. 215-234) (2024). https://doi.org/10.1007/978-981-97-4129-8 30. J. Bardeen, L. N. Cooper, J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 31. F. Izumi and K. Momma, Solid State Phenom. 130, 15 (2007). 32. K. Momma and F. Izumi, J. Appl. Cryst. 41, 653 (2008). 33. N. R. Werthamer E. Helfand, P. C. Hohenberg, Phys Rev. 147, 295–302 (1966).   https://doi.org/10.1007/978-981-97-4129-89  Figures   Fig. 1. (a) Schematic image of the crystal structure of AgInSnPbBiTe5. (b) Powder XRD pattern. The numbers are Miller indices. (c) EDX mapping results.  10   Fig. 2. Temperature dependence of (a) Magnetic susceptibility (4πχ) measured at H = 10 Oe and (b) specific heat at μ0H = 0.0–1.0 T for AgInSnPbBiTe5. (c) Magnetic field-temperature phase diagram. (d) Temperature dependence of electronic specific heat Cele in the form of Cele/T.    11   Fig. 3. Obtained asymmetry spectrum at T = 0.32 K and fitting result for AgInSnPbBiTe5.    Fig. 4. Temperature dependence of λ-2 for AgInSnPbBiTe5 and the fitting result with a dirty-limit model.   12  Supporting information  Investigation of superconducting gap of high-entropy telluride AgInSnPbBiTe5  Asato Seshita1, H. Okabe2,3, Riad Kasem1, Y. Watanabe1, Jumpei G. Nakamura2,4, Shoichiro Nishimura2,4, Kensei Terashima5, Ryo Matsumoto5, Yoshihiko Takano5, A. Yamashita1, Masaki Fujita3, Yoshikazu Mizuguchi1*  1 Department of Physics, Tokyo Metropolitan University, Hachioji 192-0397, Japan 2 Muon Science Division, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan 3 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan  4 Materials and Life Science Division, J-PARC Center, Tokai 319-1106, Japan 5 National Institute for Materials Science, Tsukuba 305-0047, Japan  *mizugu@tmu.ac.jp   Table S1. Information of 2Δ(0)/kBTc estimated using μSR of various high-entropy superconducting materials and examples of superconductors having a strong-coupling nature. Two values of 2Δ(0)/kBTc are obtained from fitting using a multi-gap model. Material 2Δ(0)/kBTc Reference AgInSnPbBiTe5 10(2) This study (Fe, Co, Ni, Rh, Ir)Zr2 4.69 [S1] Hf-Nb-Mo-Re-Ru 3.37 [S2] Zr-Nb-Mo-Re-Ru 3.94 [S2] Nb-Re-Zr-Hf-Ti 5.31 [S3] Ba0.6K0.4Fe2As2 7.3, 4.1 [S4] KCa2Fe4As4F2 7.03, 1.28 [S5] Cs2Cr3As2 6 [S6]   mailto:*mizugu@tmu.ac.jp13   Fig. S1 The result of Rietveld refinement for AgInSnPbBiTe5. Green and purple solid lines represent the peak positions of AgInSnPbBiTe5 and BN, respectively.   Fig. S2 Temperature dependence of Magnetic susceptibility (4πM) measured at H = 10 Oe for AgInSnPbBiTe5. Several weeks later from synthesis date, Tc decreased due to the strain release. 14   Reference [S1] C. Wang et al., Investigation of the high-entropy alloy superconductor XZr2 (X = Fe, Co, Ni, Rh, Ir) using muon spin spectroscopy (μSR). In J. Kitagawa & Y. Mizuguchi (Eds.), Springer series in solid-state sciences: Vol. 202. High-entropy alloy superconductors. Exotic properties, applications and materials design (pp. 215-234) (2024). https://doi.org/10.1007/978-981-97-4129-8 [S2] K. Motla, et al., Phys. Rev. B 104, 094515 (2021).  [S3] K. Motla, et al., Phys. Rev. B 105, 144501 (2022). [S4] M. Hiraishi et al., J. Phys. Soc. Jpn. 78, 023710 (2009). [S5] M. Smidman et al., Phys. Rev. B 97, 060509 (2018). [S6] D. T. Adroja et al., J. Phys. Soc. Jpn. 87, 124705 (2018).  https://doi.org/10.1007/978-981-97-4129-8https://doi.org/10.1007/978-981-97-4129-8