Strong Intrinsic Spin Hall Effect in the TaAs Family of Weyl Semimetals

Since their discovery, topological insulators are expected to be ideal spintronic materials owing to the spin currents carried by surface states with spin-momentum locking. However, the bulk doping problem remains an obstacle that hinders such an application. In this work, we predict that a newly discovered family of topological materials, the Weyl semimetals, exhibits a large intrinsic spin Hall effect that can be utilized to generate and detect spin currents. Our ab initio calculations reveal a large spin Hall conductivity in the TaAs family of Weyl materials. Considering the low charge conductivity of semimetals, Weyl semimetals are believed to present a larger spin Hall angle (the ratio of the spin Hall conductivity over the charge conductivity) than that of conventional spin Hall systems such as the $4d$ and $5d$ transition metals. The spin Hall effect originates intrinsically from the bulk band structure of Weyl semimetals, which exhibit a large Berry curvature and spin-orbit coupling, so the bulk carrier problem in the topological insulators is naturally avoided. Our work not only paves the way for employing Weyl semimetals in spintronics, but also proposes a new guideline for searching for the spin Hall effect in various topological materials.

Figure 1

Spin Hall effect in a quantum spin Hall insulator and a Weyl semimetal based on simple analytical models. In a QSHE, the valence and conduction bands get inverted (a) and SOC opens an energy gap at the nodal-ring band crossing points (b). (c) The resultant SHC is quantized inside the energy gap, which is mainly contributed by the nodal-ring area of the band structure. (d) Energy dispersion in the $k_y=0$ plane for the WSM and the corresponding spin Berry curvature distribution with the chemical potential crossing at the Weyl points. (e) The upper panel is the energy dependent SHC for the WSM, where the maximum value appears at the the Weyl points. And the lower panel is the $k_z$ dependent SHC (${\sigma }_{yx}^z$, red line) and AHC (${\sigma }_{yx}^{\mathrm{AH}}$, dashed blue line) integrated in the $k_x{k}_y$ plane. The nonzero quantized SHC and AHC only exist between these two Weyl points. The color bars in (b) and (d) are in arbitrary units. The units for the AHC and SHC are $(e^2/h)$ and $(e^2/h)(\hslash /2e)$, respectively.

Figure 2

Energy-dependent spin Hall conductivity tensor elements (${\sigma }_{xy}^z$, ${\sigma }_{zx}^y$, and ${\sigma }_{yz}^x$) for (a) TaAs, (b) TaP, (c) NbAs, and (d) NbP. The Fermi energy is set to zero at the charge neutral point. (e) The temperature-dependent SHC for TaAs. (f) For completeness, the energy dispersion is shown.

Figure 3

Spin Berry curvature in the Brillouin zone. (a) First Brillouin zone of TaAs. The black circles represent nodal line loops, and the green and yellow points represent Weyl points with opposite chirality. The nodal lines lie in the mirror planes, which are shown in gray. (b) Spin Berry curvature projected to the $k_x{k}_y$ plane. The green and yellow points represent the positions of the projected Weyl points with opposite chirality. (c) Spin Berry curvature projected to the $k_y{k}_z$ plane. The black loops indicate nodal lines. One can find that the spin Hall conductivity arises mainly from the energy bands around the nodal lines. The color bar is in arbitrary units.