Long-range proximity effect in aluminum thin films with regions of nearly identical transition temperatures.

Abstract

We have investigated the resistive transition of dirty aluminum thin films whose transition temperature is spatially modulated by \ensuremath{\sim}2--4 % along the current path. At current densities as high as 600 A/${\mathrm{cm}}^{2}$, the system exhibits a single homogeneous transition for modulation lengths up to 50 \ensuremath{\mu}m, an order of magnitude longer than predicted by current theories. In the limit that the modulation length is 50 \ensuremath{\mu}m, the ${\mathit{T}}_{\mathit{c}}$ depends sensitively and monotonically on the ratio of the lengths of the etched and the unetched regions (${\mathit{d}}_{1}$/${\mathit{d}}_{2}$), but only weakly on their absolute magnitudes. This behavior is reproduced for ${\mathit{T}}_{\mathit{c}}$ modulation parallel or perpendicular to the current flow. For samples with a controlled aperiodic (Fibonacci) modulation, the ${\mathit{T}}_{\mathit{c}}$ is compatible with that of periodically modulated films. The dependence of the ${\mathit{T}}_{\mathit{c}}$ on ${\mathit{d}}_{1}$/${\mathit{d}}_{2}$ can be fitted to a simple Ginzburg-Landau theory which assumes that the effective pair coherence length is long in comparison with the modulation period. Despite the good fit, data for the full range of experimentally accessible modulation length scales are not consistent with a more detailed microscopic theory. We believe this long-range proximity effect is not the consequence of pair tunneling, but is a manifestation of the long distance over which quasiparticle phase coherence is maintained in a two-dimensional metal film.