Quantum phase transitions in disordered two-dimensional superconductors

It is argued that with increasing applied magnetic field, a disordered, superconducting thin film will undergo a zero-temperature transition into an insulating state. At this superconductor-insulator transition the field-induced vortices Bose condense. A scaling theory for this field-tuned transition is described. Right at the transition, both the longitudinal and Hall resistivities are predicted to be finite, nonzero, and have universal values.