Switch effect of the nonquantized intrinsic spin Hall conductivity in monolayered monoclinic transition metal...

First-principles calculations have been performed to study the intrinsic spin Hall effect (SHE) and its behavior under vertical electric field in monoclinic transition metal dichalcogenide monolayers (1T'-MX₂ with M  =  Mo, W and X  =  S, Se, Te). We find that the pristine systems exhibit nonquantized intrinsic spin Hall conductivity (SHC) due to the unconserved spin around the direct band gaps though they have nontrivial band topology. The unconserved spin is attributed to the band crossings at Fermi levels for systems without spin-orbit coupling and the distinct composition of the band states around the crossings. Despite the nonquantization of SHC, calculations with the hybrid functional predict SHC approaching the quantized value in W based systems, especially 1T'-WTe₂, which has been realized in experiments. More interesting, a sharp drop of SHC to almost zero in semiconducting systems induced by vertical electric field is observed at the topological phase transition point, suggesting that such systems exhibit a strong switch effect of SHC. In contrast, the switch effect is weak in semi-metallic systems, where the SHC decreases almost continuously with increasing field strength for the chemical potential around the Fermi levels. Our findings suggest potential applications of the pristine 1T'-MX₂ and those under vertical electric field in spintronics devices by utilizing the intrinsic SHE of their bulk states.