Phase slips in superconducting films with constrictions

A system of two coplanar superconducting films seamlessly connected by a bridge is studied. We observe two distinct resistive transitions as the temperature is reduced. The first one, occurring in the films, shows some properties of the Berezinskii-Kosterlitz-Thouless (BKT) transition. The second apparent transition (which is in fact a crossover) is related to freezing out of thermally activated phase slips (TAPS) localized on the bridge. We also propose a powerful indirect experimental method allowing an extraction of the sample’s zero-bias resistance from high-current-bias measurements. Using direct and indirect measurements, we have determined the resistance $R\left(T\right)$ of the bridges within a range of eleven orders of magnitude. Over such broad range the resistance follows a simple relation $R\left(T\right)=R_N\exp [-(c∕t){(1-t)}^{3∕2}]$, where $c=\Delta F\left(0\right)∕k{T}_c$ is the normalized free energy of a phase slip at zero temperature, $t=T∕T_c$ is normalized temperature, and $R_N$ is the normal resistance of the bridge.