Tunable Giant Rashba-type Spin Splitting in PtSe${}_2$/MoSe${}_2$ Heterostructure

We report a giant Rashba-type spin splitting in two-dimensional heterostructure PtSe${}_2$/MoSe${}_2$ with first-principles calculations. We obtain a large value of spin splitting energy 110 meV at the momentum offset $k_0$=0.23 \AA${}^{-1}$ around $\mathrm{\Gamma }$ point, arising from the emerging strong interfacial spin-orbital coupling induced by the hybridization between PtSe${}_2$ and MoSe${}_2$. Moreover, we find that the band dispersion close to valence band maximum around $\mathrm{\Gamma }$ point can be well approximated by the generalized Rashba Hamiltonian $H(k_{||})=-\frac{\hbar^2 k_{||}^2}{2m}+c k_{||}+\alpha_R \vec{\sigma}\cdot(\vec{k}_{||} \times \vec{z})$. It is found that the generalized Rashba constant ${\eta }_R=c+{\alpha }_R$ in PtSe${}_2$/MoSe${}_2$ is as large as 1.3 eV$\cdot \mathring{\text{A}}$, and importantly ${\eta }_R$ can be effectively tuned by biaxial strain and external out-of-plane electrical field, presenting a potential application for the spin field-effect transistor. In addition, with the spin-valley physics at $\mathrm{K}\mathrm{/}{\mathrm{K}}^{\mathrm{\prime }}$ points in monolayer MoSe${}_2$, we propose a promising model for spin field-effect transistor with opto-valleytronic spin injection based on PtSe${}_2$/MoSe${}_2$ heterostructure.