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)=R_N exp[−(c∕t)(1−t)^3∕2], where c=ΔF(0)∕kT_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.