AI 中文总结
该研究基于电子能带和费米面的局域几何结构，建立自旋依赖输运的几何描述，揭示费米面几何与本征自旋输运的直接联系，为自旋输运提供了新的几何视角。
AI 中文摘要
我们基于电子能带和费米面的局域几何结构，建立了自旋依赖输运的几何描述。对于准二维系统，我们证明了等能面的双曲区域会产生费米速度的几何贡献，该贡献可自然耦合到电子自旋并产生自旋电流响应。我们进一步表明，在时间反演对称性存在时，自旋算符的代数可与能带切空间的外代数关联，为动量空间中的自旋提供额外的几何解释。该框架推动了费米面上自旋分离输运的辛描述及其通过接触几何向三维能带流形的扩展。我们的结果建立了费米面几何与本征自旋输运之间的直接联系。
英文摘要
We develop a geometric description of spin-dependent transport based on the local geometric structure of electronic bands and the Fermi surfaces. For quasi-two-dimensional systems, we show that hyperbolic regions of constant-energy surfaces generate a geometrical contribution to the Fermi velocity that couples naturally to electron spin and produces a spin-current response. We further show that, in the presence of time-reversal symmetry, the algebra of spin operators can be related to the exterior algebra of the band's tangent space, providing an additional geometric interpretation of spin in momentum space. This framework motivates a symplectic description of spin-separated transport on Fermi surfaces and its extension to three-dimensional band manifolds through contact geometry. Our results establish a direct connection between Fermi-surface geometry and intrinsic spin transport.
