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    Significant band renormalization and optical-phonon waterfall feature enhancing thermoelectric performance of SnTe

    Junchao Xia1,2,*, Jianmin Yang1,*, Yan Wang1,*, Muqing Su3, Hai-Feng Li3,†, and Jiaqing He1,4,‡

    • 1Department of Physics, State Key Laboratory of Quantum Functional Materials, and Guangdong Basic Research Center of Excellence for Quantum Science, Southern University of Science and Technology, Shenzhen 518055, China
    • 2School of Materials Science and Engineering, Chang'an University, Xi'an 710064, China
    • 3Institute of Applied Physics and Materials Engineering, University of Macau, Avenida da Universidade, Taipa, Macao SAR 999078, China
    • 4Guangdong Provincial Key Laboratory of Advanced Thermoelectric Materials and Device Physics, and Shenzhen Key Laboratory of Thermoelectric Materials, Southern University of Science and Technology, Shenzhen 518055, China

    • *These authors contributed equally to this work.
    • †Contact author: haifengli@um.edu.mo
    • ‡Contact author: hejq@sustech.edu.cn

    Phys. Rev. B 113, 155204 – Published 20 April, 2026

    DOI: https://doi.org/10.1103/x3lv-7bb5

    Abstract

    Band convergence is a traditional strategy to optimize the electrical transport properties of SnTe, but conventionally optimized band structures often retain the valence band maximum (VBM) at the low-degeneracy L point (Nv=4). Moreover, the mechanisms of phonon softening remain poorly understood in terms of phonon dispersion, especially regarding the coupling between vacancies and other dopants. Here, the strategic incorporation of ternary MnSb2Te4 into SnTe via nonstoichiometric alloying introduces a synergistic effect of Sn vacancies and Mn dopants. This synergy weakens the Sn-s/Te-p antibonding state, leading to significant band renormalization. Specifically, the VBM shifts from the L point to the high-degeneracy Σ and Λ points (Nv=12 and 8, respectively), where the VBM at these two sites form perfect alignment, substantially enhancing the density-of-states effective mass. In terms of phonon dispersion, both Mn atoms and Sn vacancies soften optical phonon modes at the Γ point, reducing their frequencies from 0.9 THz to 0.3 and 0.6 THz, respectively, forming a pronounced optical-phonon “waterfall” effect. This results in a significant reduction in phonon group velocities and introduces additional optical-acoustic phonon interactions. These combined effects yield a highly optimized thermoelectric quality factor in SnTe-MnSb2Te4 alloys. By further tuning the reduced Fermi level through Ge doping, we achieve a maximum ZT of 1.3 at 723 K and an average ZT of 0.83 (300–823 K), offering a promising pathway for mid-temperature waste heat recovery and shedding light on vacancy engineering in thermoelectrics.

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