Spin currents proportional to the first and second order of the electric field are calculated in a specific tight-binding model with time-reversal symmetry. Specifically, a tight-binding model with time-reversal symmetry is constructed with chiral hopping and spin-orbit coupling. The spin conductivity of the model is calculated using the Boltzmann equation. As a result, it is clarified that the first-order spin current of the electric field vanishes, while the second-order spin current can be finite. Furthermore, the spin current changes its sign by reversing the chirality of the model. The present results reveal the existence of spin currents in systems with time-reversal symmetry depending on the chirality of the system. They may provide useful information for understanding the chirality-dependent spin polarization phenomena in systems with time-reversal symmetry.

中文翻译：

---

具有时间反转对称性的系统中与手性相关的二阶自旋电流

与一阶和二阶电场成比例的自旋电流是在具有时间反演对称性的特定紧束缚模型中计算的。具体来说，通过手性跳跃和自旋轨道耦合构建了具有时间反演对称性的紧束缚模型。使用玻尔兹曼方程计算模型的自旋电导率。结果，阐明了电场的一阶自旋电流消失，而二阶自旋电流可以是有限的。此外，自旋电流通过反转模型的手性来改变其符号。目前的结果揭示了在具有时间反转对称性的系统中存在自旋电流，这取决于系统的手性。