Defect-induced spin-split localized states with strong out-of-plane spin polarization in monolayer 1H-WSe 2 : DFT and k ⋅ p analysis

This study presents a comprehensive density functional theory analysis of the structural and electronic modifications induced by point defects and spin–orbit coupling in monolayer 1H-WSe 2 . Among intrinsic point defects, the selenium vacancy is identified as the most energetically favorable and is shown to generate well-localized in-gap states predominantly originating from the d orbitals of neighboring W atoms. Spin–orbit coupling lifts the spin degeneracy of these defect states, giving rise to pronounced spin splitting with a dominant out-of-plane spin component as a consequence of broken local in-plane mirror symmetry and the strong atomic spin–orbit interaction of tungsten. Spin-resolved band structure calculations further reveal valley-dependent spin polarization with a dominant out-of-plane spin component at the K and K ′ points, indicating a nontrivial coupling between defect states and the spin and valley degrees of freedom. The essential features of the defect-induced spin splitting and spin texture are captured by a minimal k ⋅ p Hamiltonian, providing analytical insight into the underlying symmetry and spin–orbit mechanisms. Our results establish defect engineering as an effective route to realize localized spin-polarized states in two-dimensional transition metal dichalcogenides, offering promising prospects for spintronic and valleytronic quantum device applications.