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 $R(T)$ of the bridges within a range of eleven orders of magnitude. Over such broad range the resistance follows a simple relation R(T)=RN0.2em0exexp[-(c∕t)(1-t)3∕2], where c=ΔF(0)∕kTc is the normalized free energy of a phase slip at zero temperature, t=T∕Tc is normalized temperature, and RN is the normal resistance of the bridge.