Spin Hall effect and spin swapping in diffusive superconductors
Spin Hall effect and spin swapping in diffusive superconductors
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DOI：
10.1103/physrevb.95.054509
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发表时间：
2017-02-17
影响因子：
3.7
通讯作者：
Brataas, Arne
中科院分区：
文献类型：
--
作者：
Espedal, Camilla;Lange, Peter;Brataas, Arne
本文研究了扩散超导体中自旋-轨道诱导的自旋霍尔效应和自旋交换。采用准经典近似下的非平衡Keldysh绿色函数方法，导出了弹性散射区自旋和粒子谱分布以及能量密度的耦合输运方程.我们计算四个贡献的自旋霍尔电导率，即，斜散射，侧跳，异常速度，和Yafet的贡献。超导体中态密度的降低导致自旋霍尔角的重整化。我们证明，所有这四个贡献的自旋霍尔电导率重整化以同样的方式在超导状态。在其最简单的表现形式中，自旋交换将主自旋流转换为具有交换的电流和极化方向的次级自旋流。我们发现，自旋交换系数不是显式的，但只有隐含的超导间隙通过重整化扩散系数的影响。我们讨论的（逆）自旋霍尔效应和自旋交换在四端几何测量的实验后果。在我们的几何结构中，低于超导转变温度，自旋交换信号增加一个数量级，而（逆）自旋霍尔信号的变化是温和的。
We consider the spin-orbit-induced spin Hall effect and spin swapping in diffusive superconductors. By employing the nonequilibrium Keldysh Green's function technique in the quasiclassical approximation, we derive coupled transport equations for the spectral spin and particle distributions and for the energy density in the elastic scattering regime. We compute four contributions to the spin Hall conductivity, namely, skew scattering, side jump, anomalous velocity, and the Yafet contribution. The reduced density of states in the superconductor causes a renormalization of the spin Hall angle. We demonstrate that all four of these contributions to the spin Hall conductivity are renormalized in the same way in the superconducting state. In its simplest manifestation, spin swapping transforms a primary spin current into a secondary spin current with swapped current and polarization directions. We find that the spin-swapping coefficient is not explicitly but only implicitly affected by the superconducting gap through the renormalized diffusion coefficients. We discuss experimental consequences for measurements of the (inverse) spin Hall effect and spin swapping in four-terminal geometries. In our geometry, below the superconducting transition temperature, the spin-swapping signal is increased an order of magnitude while changes in the (inverse) spin Hall signal are moderate.