The two-dimensional superconductor-insulator transition

Superconductor-to-insulator transitions in ultrathin films can be brought about either by the variation of film properties such as sheet resistance, thickness, and carrier concentration in zero magnetic field, or by the application of a magnetic field. Interest in this problem has been heightened by the prospect that the transitions are zero-temperature quantum phase transitions, which can be described by a Boson-Hubbard model. Variants of this model are relevant to aspects of systems as diverse as helium films, quantum Hall systems, and high temperature superconductors with columnar defects. Ultrathin superconducting films, depending on their properties or the value of the applied magnetic field, exhibit either insulating or superconducting behavior in the limit of zero temperature. However, for films described by certain parameters, or at critical values of the magnetic field, there appears to be a finite, nonzero resistance in the zero temperature limit which has been identified as the resistance at the quantum critical point. The Boson-Hubbard model predicts this resistance to be universal. In the case of the zero-field transition the value of the limiting resistance may indeed be universal and close to the value h 4e², or 6450 Ω.