Strong Rashba effect in the localized impurity states of halogen-doped monolayer PtSe2

The recent epitaxial growth of the $1T$ phase of the ${\mathrm{PtSe}}₂$ monolayer (ML) has opened the possibility for novel applications, in particular for a spintronics device. However, in contrast to the $2H$ phase of transition-metal dichalcogenides (TMDs), the absence of spin splitting in the ${\mathrm{PtSe}}₂$ ML may limit the functionality for spintronics application. Through fully relativistic density-functional theory calculations, we show that large spin splitting can be induced in the ${\mathrm{PtSe}}₂$ ML by introducing a substitutional halogen impurity. Depending on the atomic number $Z$ of the halogen dopants, we observe an enhancement of the spin splitting in the localized impurity states (LIS), which is due to the increased contribution of the $p\text{\ensuremath{-}}d$ orbital coupling. More importantly, we identify very large Rashba splitting in the LIS near the Fermi level around the $\mathrm{\ensuremath{\Gamma}}$ point characterized by hexagonal warping of the Fermi surface. We show that the Rashba splitting can be controlled by adjusting the doping concentration. Therefore, this work provides a possible way to induce significant Rashba splitting in the two-dimensional TMDs, which is useful for spintronic devices operating at room temperature.