Onset of high-temperature superconductivity in the two-dimensional limit

The transition between insulating and superconducting behavior in the low-temperature limit has been explored with use of ultrathin Dy-Ba-Cu-O c-axis-oriented films prepared by molecular-beam epitaxy. The transition appears as a separatrix between sets of R(T) curves that exhibit either insulating or superconducting behavior in the T→0 limit. Superconductivity is found only when the normal-state sheet resistance is below a value close to h/4${\mathit{e}}^2$, or 6450 Ω. Hall-effect data relate the depression of ${\mathit{T}}_{\mathit{c}}$ with increasing sheet resistance to a reduction in hole concentration.