三维节线半金属中的量子化自旋霍尔效应：几何标度与对称调控的自旋响应
Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response
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中文总结 AI 辅助
本研究发现三维节线半金属中量子化自旋霍尔电导率与节线半径线性标度，揭示自旋轨道耦合对称性可独立调控响应幅度与张量对称性，并在氮化钇中验证，为三维量子化几何响应工程提供新范式。
中文摘要 AI 辅助
磁性外尔半金属中的反常霍尔电导率与外尔节点间的动量间隔呈线性标度关系，为三维霍尔响应建立了几何范式。本研究在自旋霍尔效应中发现了类似现象：节线半金属中存在量子化自旋霍尔电导率（SHC），其与节线半径$R$呈线性标度关系。从含单个节线的理想模型出发，我们解析推导得出，自旋轨道耦合能隙内的SHC满足$σ_{αβ}^{S, 3D}=σ_0^{S,2D} \cdot (πR/2 π)$，其中$σ_0^{S,2D}=(e^2/h) \cdot (\nbar/2 e)$为二维量子自旋霍尔电导。关键在于，自旋轨道耦合的对称性可作为独立开关：Rashba耦合仅产生常规SHC分量，而Weyl耦合还能激活非常规分量，实现响应幅度与张量对称性的独立调控。我们在氮化钇中验证了这一原理，其中应变可调控$R$，对称性破缺可切换响应类型。本研究为三维量子化几何响应的工程化建立了新范式，为定制化自旋轨道功能开辟了路径。
英文摘要
The anomalous Hall conductivity in magnetic Weyl semimetals scales linearly with the momentum separation between Weyl nodes, establishing a geometric paradigm for three-dimensional Hall responses. Here we discover an analogous phenomenon in the spin Hall effect: a quantized spin Hall conductivity (SHC) in nodal-ring semimetals that scales linearly with the nodal-ring radius $R$. From an ideal model with a single nodal ring, we derive analytically that the SHC inside the spin-orbit-coupled gap obeys $σ_{αβ}^{S, 3D}=σ_0^{S,2D} \cdot (πR/2 π)$, where $σ_0^{S,2D}=(e^2/h) \cdot (\hbar/2 e)$ is the two-dimensional quantum spin Hall conductance. Crucially, the symmetry of the spin-orbit coupling acts as an independent switch: Rashba coupling generates purely conventional SHC components, while Weyl coupling additionally activates unconventional ones, providing separate control over response magnitude and tensor symmetry. We validate this principle in yttrium nitride, where strain tunes $R$ and symmetry breaking toggles between response types. Our work establishes a new paradigm for engineering quantized geometric responses in three dimensions, opening pathways to tailored spin-orbit functionalities.
