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    Semiclassical theory for proximity-induced superconducting systems with spin-orbit coupling

    Zhen-Cheng Liao1, Cong Xiao2,*, Zhi Wang1,3,†, and Qian Niu4

    • *Contact author: congxiao@fudan.edu.cn
    • †Contact author: wangzh356@mail.sysu.edu.cn

    Phys. Rev. B 114, 024510 – Published 20 July, 2026

    DOI: https://doi.org/10.1103/yhp1-ftm5

    Abstract

    We develop a semiclassical theory of superconducting quasiparticles for proximity-induced superconducting systems, where spin-orbit coupling plays a critical role in shaping the quasiparticle dynamics. We reveal the structure of superconducting Berry curvatures in such systems, and derive the Berry curvature induced thermal Edelstein effect and spin Nernst effect. We calculate these two thermospin responses with model systems where Rashba spin-orbit coupling, proximity-induced superconductivity, and ferromagnetic order are coexisting.

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