Using response theory, we calculate the charge current vortex generated by spin pumping at a point-like contact in a system with Rashba spin–orbit coupling (SOC). We discuss the spatial profile of the current density for finite temperature and for the zero-temperature limit. The main observation is that the Rashba spin precession leads to a charge current that oscillates as a function of distance from the spin pumping source, which is confirmed by numerical simulations. In our calculations, we consider a Rashba model on a square lattice, for which we first review the basic properties related to charge and spin transport. In particular, we define the charge current and spin current operators for the tight-binding Hamiltonian as the currents coupled linearly with the U(1) and SU(2) gauge potentials, respectively. By analogy to the continuum model, the SOC Hamiltonian on the lattice is then introduced as the generator of the spin current.

中文翻译：

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自旋轨道耦合系统中的自旋电荷转换和电流涡旋

使用响应理论，我们计算了在具有 Rashba 自旋轨道耦合 (SOC) 的系统中的点状接触处自旋泵浦产生的充电电流涡流。我们讨论了有限温度和零温度限制的电流密度的空间分布。主要观察结果是，Rashba 自旋进动导致电荷电流随着距自旋泵源的距离而振荡，这已通过数值模拟得到证实。在我们的计算中，我们考虑了方形晶格上的 Rashba 模型，为此我们首先回顾了与电荷和自旋输运相关的基本属性。特别是，我们将紧束缚哈密顿量的充电电流和自旋电流算子定义为分别与 U(1) 和 SU(2) 规范电位线性耦合的电流。通过类比连续模型，