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The investigation of superconductivity in the presence of disorder began 60 years ago with the work of Alexander Shal'nikov at the Institute for Physical Problems in Moscow. The subject has played an ongoing role in condensed matter physics over the years. Interest has recently been heightened by the possibility that the disorder-driven or magnetic-field-driven quenching of superconductivity in systems at the limit of zero temperature and two dimensions might be quantum phase transitions. That would link the physics of the superconductor-insulator transition in thin films to other systems believed to exhibit quantum phase transitions—for example, helium-4 in porous media, high temperature superconductors, Josephson-junction arrays, two-dimensional electron gases and various spin systems.

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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 Tϭ0 critical point, a finite-size scaling analysis was carried out to determine the correlation length exponent 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 Tϭ0.

Electric double layer transistor configurations have been employed to electrostatically dope single crystals of insulating SrTiO3. Here we report on the results of such doping over broad ranges of temperature and carrier concentration employing an ionic liquid as the gate dielectric. The surprising results are, with increasing carrier concentration, an apparent carrier-density dependent conductor-insulator transition, a regime of anomalous Hall effect, suggesting magnetic ordering, and finally the appearance of superconductivity. The possible appearance of magnetic order near the boundary between the insulating and superconducting regimes is reminiscent of effects associated with quantum critical behavior in some complex compounds.

The nonlinear I-V characteristics of thin high-sheet-resistance Hg-Xe alloy films are examined within the context of the Kosterlitz-Thouless theory of the superconducting transition. In the regime below the vortex-unbinding temperature T"where logarithmically bound vortices can be broken apart by a transport current, we find that V-I" '. Comparison with theory allows us to infer the value of T, and the mean-field temperature T,o from a (T), and the dependence of these temperatures on R~appears in approximate agreement with the microscopic theory of dirty superconductors. A systematic deviation appears to be consistent with renormalization of the vortex interaction close to T, due to the presence of small polarizable vortex pairs, and can be described by an effective vortex dielectric constant e, =1.2. Further evidence for this renormalization, which is a key feature of the Kosterlitz-Thouless transition, is obtained by examining the curvature of the log V vs logI plot very close to T,. The current dependence of a (I, T) =d (log V)/d (logI) is a direct measure of the spatial dependence of the vortex interaction, allowing a direct comparison with the analytic predictions of the renormalization equations. Satisfactory agreement is obtained using physically reasonable parameters.

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