Accessible Length Scales Research Articles

Three interacting strings in two dimensions: non-universal and multiple unbinding transitions

Three non-intersecting strings in two dimensions which interact via short-ranged attractive potentials are studied using bath transfer matrix methods and Monte Carlo tech- niques. The critical behavior at the unbinding transition and the critical values of the potential strength are determined for symmetric and asymmetric bundles of strings. In the asymmetric case, for which the two outer strings have diiferent hne tensions (or interact via dilferent po- tentials), the strings unbind in two subsequent transitions, which then exhibit universal critical behavior. In the symmetric case, where the two outer strings have the same line tension, trie three strings unbind simultaneously. The critical behavior at this unbinding transition is found to be non-universal for the whole range of accessible length scales, but its parameter dependence is found to be in strong disagreement with trie predictions of trie so-called necklace model. Trie more flexible the inner string, the deeper the critical potential. However, within the numerical error, three identical strings are found to unbind at the same critical potential strength as two strings with the same line tensions.

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

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.