Current-induced spin polarization and spin Hall effect in III-V compounds two-dimensional materials

We construct a multiband $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonian in monolayer and bilayer double-layer honeycomb III-V compounds including spin-orbit coupling (SOC) based on the invariant theory. The Hamiltonian can describe electronic structures near the $\mathrm{\ensuremath{\Gamma}}$ point of the Brillouin zone and anisotropic spin splitting, which is in good agreement with first-principles calculations. These SOC effects contribute to the existence of current-induced spin polarization (CISP) and spin Hall effect (SHE). The interplay between Zeeman and Rashba SOC leads to Lifshitz transitions for CISP and SHE at the maximum of lower-valence bands. Our work offers a possible approach for constructing 2D III-V compounds spintronic devices.