Onset of superconductivity in the two-dimensional limit

The onset of superconductivity in homogeneous ultrathin films is found to occur when their normal-state sheet resistance falls below a value close to h/4$e^2$, the quantum resistance for pairs. The data further suggest that in the T→0 limit such films are either superconducting or insulating. The existence of a threshold in systems which are not granular implies that its explanation involves more general arguments than those which follow from the modeling of films by Josephson-coupled arrays.