We investigate transport through ionic liquid gated field effect transistors (FETs) based on exfoliated crystals of semiconducting WS$_2$. Upon electron accumulation, at surface densities close to -or just larger than- 10$^{14}$ cm$^{-2}$, transport exhibits metallic behavior, with the surface resistivity decreasing pronouncedly upon cooling. A detailed characterization as a function of temperature and magnetic field clearly shows the occurrence of a gate-induced superconducting transition below a critical temperature $T_c approx 4$ K, a finding that represents the first demonstration of superconductivity in tungsten-based semiconducting transition metal dichalcogenides. We investigate the nature of superconductivity and find significant inhomogeneity, originating from the local detaching of the frozen ionic liquid from the WS$_2$ surface. Despite the inhomogeneity, we find that in all cases where a fully developed zero resistance state is observed, different properties of the devices exhibit a behavior characteristic of a Berezinskii-Kosterlitz-Thouless transition, as it could be expected in view of the two-dimensional nature of the electrostatically accumulated electron system.
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