The superconductor-insulator transition of ultrathin films of bismuth, grown on liquid helium cooled substrates, has been studied. The transition was tuned by changing both film thickness and perpendicular magnetic field. Assuming that the transition is controlled by a T=0 critical point, a finite size scaling analysis was carried out to determine the correlation length exponent v and the dynamical critical exponent z. The phase diagram and the critical resistance have been studied as a function of film thickness and magnetic field. The results are discussed in terms of bosonic models of the superconductor-insulator transition, as well as the percolation models which predict finite dissipation at T=0.
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