Defect-induced large spin-orbit splitting in the monolayer of PtSe$_2$

The effect of spin-orbit coupling (SOC) on the electronic properties of monolayer (ML) PtSe$_2$ is dictated by the presence of the crystal inversion symmetry to exhibit spin polarized band without characteristic of spin splitting. Through fully-relativistic density-functional theory calculations, we show that large spin-orbit splitting can be induced by introducing point defects. We calculate stability of native point defects such as a Se vacancy (V$_{\texttt{Se}}$), a Se interstitial (Se$_{i}$), a Pt vacancy (V$_{\texttt{Pt}}$), and a Pt interstitial (Pt$_{i}$), and find that both the V$_{\texttt{Se}}$ and Se$_{i}$ have the lowest formation energy. We also find that in contrast to the Se$_{i}$ case exhibiting spin degeneracy in the defect states, the large spin-orbit splitting up to 152 meV is observed in the defect states of the V$_{\texttt{Se}}$. Our analyses of orbital contributions to the defect states show that the large spin splitting is originated from the strong hybridization between Pt-$d_{x{^2}+y{^2}}+d_{xy}$ and Se-$p_{x}+p_{y}$ orbitals. Our study clarifies that the defects play an important role in the spin splitting properties of the PtSe$_2$ ML, which is important for designing future spintronic devices.