Quantum Phase Correlations and Fluctuations in Narrow Thin-Film Superconductors

We have made measurements of the superconducting transition temperatures of very narrow thin films of tin. The transition temperatures of such narrow samples are depressed below those of wider sections of the same films by an amount which depends strongly on the characteristic dimensions of the samples. It is shown that our previously published results as well as those of Parks and Groff et al. can be accounted for satisfactorily by our simple analysis, which considers the thermally induced fluctuations in the quantum-mechanical phase differences between two superconductors. In the previous work, the direct connection of room-temperature measuring circuitry to the small samples led to effective noise temperatures of the order of 25°K, well above the sample temperature. In the present work, low-resistance shunts in parallel with the sample and immersed in the helium bath were used to isolate the sample from external fluctuations. When this precaution is taken, the observed values of $\Delta T_c$ show excellent agreement with the simple analysis proposed earlier. The determination of the undisturbed transition temperature $T_{c0\mathrm{}}$ by fitting the critical current data to the predicted ${(T_{c0\mathrm{}}-T)}^{\frac{3}{2}}$ dependence yields values which are consistent with those obtained by simple measurement of $T_c$ in a very wide section of the same film. Values of $\Delta T_c$ measured on a series of samples produced in a single evaporation and having the same width, but different lengths, show that the apparent dependence of $\Delta T_c$ on sample resistance reported by Groff et al. for samples in which all the dimensions were varied is not generally obeyed. Variation of $R$ by two orders of magnitude in such a series produced no significant change in $\Delta T_c$, in agreement with the earlier Hunt-Mercereau analysis.