Spin-orbit coupling, optical transitions, and spin pumping in mono- and few-layer InSe.

We show that spin-orbit coupling (SOC) in InSe enables the optical transition across the principal band gap to couple with in-plane polarized light. This transition, enabled by $p_{x,y}\leftrightarrow p_z$ hybridization due to intra-atomic SOC in both In and Se, can be viewed as a transition between two dominantly $s$- and $p_z$-orbital based bands, accompanied by an electron spin-flip. Having parametrized $\mathbf{k\cdot p}$ theory using first principles density functional theory we estimate the absorption for $\sigma^{\pm}$ circularly polarized photons in the monolayer as $\sim 1.5\%$, which saturates to $\sim 0.3\%$ in thicker films ($3-5$ layers). Circularly polarized light can be used to selectively excite electrons into spin-polarized states in the conduction band, which permits optical pumping of the spin polarization of In nuclei through the hyperfine interaction.