Intrinsic Spin Hall Effect with Spin-Tensor-Momentum Coupling

We study the two-dimensional Fermion system with the spin-orbit coupling and spin-tensor-momentum coupling. A new type of spin-tensor Hall current is found. Unlike the conventional spin Hall effect, the spin-tensor Hall effect originates from the coupling of the spin tensor and the momentum. The total spin Hall conductivity with the presence of the spin-tensor Hall current is calculated. The numerical results indicate that the total spin Hall conductivity is enhanced by the contribution of the spin-tensor-momentum coupling.