Spin Hall effect on the kagome lattice with Rashba spin-orbit interaction

We study the spin Hall effect in the kagome lattice with Rashba spin-orbit coupling. The conserved spin Hall conductance σxyˢ (see text) and its two components, i.e., the conventional term σxyˢ⁰ and the spin-torque-dipole term σxy^sτ, are numerically calculated, which show a series of plateaus as a function of the electron Fermi energy ϵF. A consistent two-band analysis, as well as a Berry-phase interpretation, is also given. We show that these plateaus are a consequence of various Fermi-surface topologies when tuning ϵF. In particular, we predict that compared to the case with the Fermi surface encircling the Γ point in the Brillouin zone, the amplitude of the spin Hall conductance with the Fermi surface encircling the K points is twice enhanced, which makes it highly meaningful in the future to systematically carry out studies of the K-valley spintronics.