The intrinsic spin Hall conductivity of typical topological insulators ${\mathrm{Sb}}_2{\mathrm{Se}}_3,$ ${\mathrm{Sb}}_2{\mathrm{Te}}_3,$ ${\mathrm{Bi}}_2{\mathrm{Se}}_3,$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ in the bulk form, is calculated from first principles by using density functional theory and the linear response theory in a maximally localized Wannier basis. The results show that there is a finite spin Hall conductivity of 100–200 $(\hslash /2\mathrm{e})(\mathrm{S}/\mathrm{cm})$ in the vicinity of the Fermi energy. Although the resulting values are an order of magnitude smaller than that of heavy metals, they show a comparable spin Hall angle due to their relatively lower longitudinal conductivity. The spin Hall angle for different compounds are then compared to that of recent experiments on topological-insulator/ferromagnet heterostructures. The comparison suggests that the role of the bulk in generating a spin current and consequently a spin torque in magnetization switching applications is comparable to that of the surface including the spin-momentum locked surface states and the Rashba-Edelstein effect at the interface.

中文翻译：

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拓扑绝缘体的本征自旋霍尔效应：第一性原理研究

典型拓扑绝缘体的本征自旋霍尔电导率 ${锑}_2{硒}_3，$ ${锑}_2{特}_3，$ ${双}_2{硒}_3，$ 和 ${双}_2{特}_3$在最大局部Wannier基础上，通过使用密度泛函理论和线性响应理论，从第一原理计算出本体形式的分子质量。结果表明，自旋霍尔电导率为100–200$（\hslash /2\mathrm{Ë}）（\mathrm{小号}/\mathrm{厘米}）$在费米能量附近。尽管所得到的值比重金属小一个数量级，但由于它们的纵向电导率相对较低，它们显示出可比的自旋霍尔角。然后将不同化合物的自旋霍尔角与拓扑绝缘体/铁磁体异质结构的最新实验进行比较。比较表明，在磁化开关应用中，本体在产生自旋电流以及自旋转矩中的作用与包括自旋动量锁定表面状态和界面处的拉什巴-爱德斯坦效应的表面的作用相当。