Explaining the observed conduction-band spin-orbit splitting in MoS₂ monolayer

We develop a microscopic theory that explains the experimentally observed magnitude of the conduction-band spin-orbit splitting (SOS) in monolayer MoS2. In this framework the splitting is not a fixed band parameter but an interaction-renormalized quantity. Using a Hartree–Fock treatment with realistic dielectric screening (Keldysh interaction dressed within the RPA) and a correction to the polarization operator at non-negligicle Wigner-Zeits radius, we quantify the exchange contribution that enhances the bare splitting and reconcile the long-standing discrepancy between standard DFT calculations and transport data. We trace the bare SOS to two competing orbital channels: direct SOS of the sulfur p admixture in the conduction band and second-order coupling of molybdenum d-orbitals to higher-lying states. We show that conventional DFT underestimates the splitting due to accidental cancellation between the two channels. Incorporating on-site and inter-site Coulomb terms within a compact DFT plus U plus V scheme restores agreement with experiment while simultaneously yielding realistic band gaps and valence-band splittings. The same physical ingredients and computational recipe provide transferable, quantitatively accurate spin-orbit and band-edge parameters across semiconducting TMDs . These results supply theory-level inputs for modeling spin and valley transport in TMD devices and for improving large-scale materials databases.