  Atomic disorder is a common limiting factor for the low-temperature mobility
in monolayer transition-metal dichalcogenides (TMDs; MX2). Here, we study the
effect of often occurring atomic vacancies on carrier scattering and transport
in p- and n-type monolayer MoS2. Due to charge trapping in vacancy-induced
in-gap states, both neutral and charged vacancies resembling, respectively,
short-range and combined short-range and long-range Coulomb scatterers, must be
considered. Using the T-matrix formalism, we demonstrate a strong
renormalization of the Born description of short-range scattering, manifested
in a pronounced reduction and a characteristic energy dependence of the
scattering rate. As a consequence, carrier scattering in TMDs with charged
vacancies is dominated by the long-range Coulomb-disorder scattering, giving
rise to a strong screening-induced temperature and density dependence of the
low-temperature carrier mobility. For TMDs with neutral vacancies, the absence
of intrinsic Coulomb disorder results in significantly higher mobilities as
well as an unusual density dependence of the mobility which decreases with the
carrier density. Our work illuminates the transport-limiting effects of
atomic-vacancy scattering relevant for high-mobility TMD devices.
