Probing superconducting granularity using nonlocal four-probe measurements

The four-point probe is a relatively simple method of measuring thin-layer surface resistance using separate pairs of current-carrying and voltage-sensing contacts. This approach makes it possible to measure resistivity regardless of the resistance of the contacts that is especially important when the latter are large and non-ohmic, which makes simpler two contact measurements inapplicable. Nevertheless, its results turn out to be significantly dependent on the sample geometry as well as the position of the probes, leading in some cases, as shown below, to qualitatively incorrect conclusions. We demonstrate this with the example of an anomalous resistance peak at temperatures near the critical one T c , which is often observed in experiments on mesoscopic superconducting samples. Below, with an oversimplified model for nonlocal four-probe measurements, we argue that the anomalous resistance behavior near T c observed in traditional four-probe measurements can arise due to noticeable variations in local T c values (superconducting granularity) and attributed the near- T c anomaly to the current redistribution effect. The model results well explain temperature-dependent resistance data for 50 nm thick NbN films, which exhibited not only the resistance peak but also fundamentally different resistance-vs-temperature behavior depending on the arrangement of the contacts. Nonlocal probing performed for in-plane and out-of-plane magnetic fields clearly demonstrates the interplay of orbital and Zeeman couplings different for the two field orientations. We believe that the anomalous temperature behavior of the four-point resistance near the transition from the normal to superconducting state is sometimes an artifact that, if misinterpreted, can lead to incorrect conclusions. On the other hand, we show that such a nonlocal contact arrangement strongly enhances sensitivity to inhomogeneity factors. This gives grounds for using the corresponding experiments as a method of choice for revealing the spatial distribution of the order parameter in superconducting films.