Spin Hall effect in spin-valley coupled monolayer transition-metal dichalcogenides

We study both the intrinsic and extrinsic spin Hall effect in spin-valley coupled monolayers of transition metal dichalcogenides. We find that whereas the skew-scattering contribution is suppressed by the large band gap, the side-jump contribution is comparable to the intrinsic one with opposite sign in the presence of scalar and magnetic scattering. Intervalley scattering tends to suppress the side-jump contribution due to the loss of coherence. By tuning the ratio of intra- to intervalley scattering, the spin Hall conductivity shows a sign change in hole-doped samples. Multiband effect in other doping regime is considered, and it is found that the sign change exists in the heavily hole-doped regime, but not in the electron-doped regime

Boundedness for a Class of Generalized Commutators of Fractional Hardy Operators with a Rough Kernel

The authors consider the generalized commutator of fractional Hardy operator with a rough kernel as follows: where , , and with . The authors prove that is bounded on Herz type space and -Central Morrey space with , which is an open problem for