Intrinsic spin Hall conductivity of the semimetals MoTe2 and WTe2

We report a comprehensive study on the intrinsic spin Hall conductivity (SHC) of the semimetals MoTe2 and WTe2 by ab initio calculations. Large SHC at the Fermi energy and desirable spin Hall angles have been discovered, due to the strong spin-orbit coupling effect and the low charge conductivities of the semimetals. The unusual reduced crystalline symmetry of MoTe2 and WTe2 results in diverse anisotropic SHC values, consistent with the symmetry restrictions of the response tensor according to the magnetic Laue group. We report an effective method on SHC optimization by Fermi energy tuning, and demonstrate the mechanism of SHC variation with respect to the Fermi energy shifting by the spin Berry curvature. Our work provides insights into the realization of strong and anisotropic spin Hall effects in low-symmetry semimetals.