  Quantum localization via atomic point defects in semiconductors is of
significant fundamental and technological importance. Quantum defects in
monolayer transition-metal dichalcogenide semiconductors have been proposed as
stable and scalable optically-addressable spin qubits. Yet, the impact of
strong spin-orbit coupling on their dynamical response, for example under
optical excitation, has remained elusive. In this context, we study the effect
of spin-orbit coupling on the electron-phonon interaction in a single chalcogen
vacancy defect in monolayer transition metal dichalcogenides, molybdenum
disulfide (MoS$_2$) and tungsten disulfide (WS$_2$). From ab initio electronic
structure theory calculations, we find that spin-orbit interactions tune the
magnitude of the electron-phonon coupling in both optical and charge-state
transitions of the defect, modulating their respective efficiencies. This
observation opens up a promising scheme of dynamically modulating material
properties to tune the local behavior of a quantum defect.
