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

We study the spin Hall effect in the kagomé lattice with Rashba spin-orbit coupling. The conserved spin Hall conductance $σ_{xy}^{s}$ (see text) and its two components, i.e., the conventional term $σ_{xy}^{s0}$ and the spin-torque-dipole term $σ_{xy}^{sτ}$, are numerically calculated, which show a series of plateaus as a function of the electron Fermi energy $ε_{F}$. A consistent two-band analysis, as well as a Berry-phase interpretation, is also given. We show that these plateaus are a consequence of the various Fermi-surface topologies when tuning $ε_{F}$. In particular, we predict that compared to the case with the Fermi surface encircling the $\mathbfΓ$ point in the Brillouin zone, the amplitude of the spin Hall conductance with the Fermi surface encircling the $\mathbf{K}$ points is twice enhanced, which makes it highly meaningful in the future to systematically carry out studies of the $\mathbf{K}$-valley spintronics.