a, Temperature-dependent resistivity \({R}_{\square }(p,T)\) of sample A. The doping level, fixed for each curve, is tuned by repeated annealing cycles under vacuum (pressure below 10−4 mbar). The initially superconducting sample becomes insulating via a QPT. Broken line marks the separatrix where the transition occurs. Blue shaded region indicates the temperature range in which we perform the finite-size scaling analysis; the slight up-turn in resistivity at lower temperatures suggests intermediate phase or additional QCP between the superconducting and insulating phases49. b, Same dataset in a plotted inversely, that is, \({R}_{\square }(p,T)\) plotted as a function of doping level at fixed temperatures between 6 K and 24 K. Each colour refers to a fixed temperature. Continuous curves are interpolations of data points at different temperatures. The point where all curves cross defines the critical point the QPT, \(({R}_{{\rm{c}}}=10.2\pm 0.6\,{\rm{k}}\Omega ,{p}_{{\rm{c}}}=0.022\pm 0.002)\). c, Scaling of the same data with respect to variable \(u=|p-{p}_{{\rm{c}}}|t(T)\). A single set of temperature-dependent parameters t(T) can force all data to collapse to a universal scaling function on both sides of the SIT. d, Temperature-dependent resistivity of sample B. Data were obtained between annealing cycles performed under \({10}^{-1}\,{\rm{mbar}}\) of air that contains about \(3\times {10}^{-3}\,{\rm{mbar}}\) of water vapour. The annealing cycles progressively increase the normal state resistivity, and induces SIT in the monolayer. Blue shaded region marks the temperature range in which we perform the finite-size scaling analysis.e, Same resistivity data in d plotted as a function of \(x=194\,\Omega /{R}_{\square }(T=200\,{\rm{K}})\). Here x is a phenomenological variable that parametrizes the external factor (doping or disorder level) that drives the SIT; the precise value of x does not affect the finite-size scaling analysis according to formula (1). The critical point of the SIT is identified as \(({R}_{{\rm{c}}}=8.7\pm 0.6\,{\rm{k}}\Omega ,{x}_{{\rm{c}}}=0.022\pm 0.002)\). f, Scaling analysis of the dataset in e. The analysis yields a critical exponent of νz = 2.45. The νz differs from the critical exponent in doping-driven SIT in sample A, but coincides with the value in disorder-driven SIT in sample C. Similar to sample C, sample B also features a two-step superconducting transition (marked by black arrow) that indicates considerable amount of disorder. We therefore conclude that disorder level drives the SIT in sample B. g, Temperature-dependent resistivity of sample C. Curves are obtained between annealing cycles performed under about 10 mbar of air. Such annealing cycles introduce disorders into the monolayer, and the superconductivity transition occurs in two steps. The disorder-driven SIT takes place at the lower-temperature transition (blue shaded region). h, Inverse of the dataset in g. Horizontal axis represents the phenomenological disorder level that is parametrized as \(d=213\,\Omega /{R}_{\square }(T=200\,{\rm{K}})\). Smooth interpolations of the data points cross at the critical point \(({R}_{{\rm{c}}}=2.86\pm 0.17\,{\rm{k}}\Omega ,{x}_{{\rm{c}}}=0.028\pm 0.002)\). i, Scaling of the same data in h with respect to variable \(u=|d-{d}_{{\rm{c}}}|t(T)\). \(t(T)\) is chosen such that all data collapse to a universal scaling function.