Spatially resolving superconductivity in type-II superconductors
Superconductivity is identified by the emergence of a macroscopic zero-resistance state, typically inferred from a vanishing four-probe voltage at finite current. That inference assumes spatially uniform conduction-e.g., at least one continuous superconducting path between the current leads and voltage electrodes that sample a finite potential gradient-and can fail if the drive current bypasses the electrodes or if narrow filaments short the current contacts. Here we introduce a methodology to test these assumptions in superconductors, by using spatially resolved measurements of local variations in dc using cryogenic conductive atomic-force microscopy (cAFM). Using Fe(Se,Te) as a model system, we find that despite bulk measurements consistent with a homogeneous superconducting state, the material exhibits a heterogeneous conducting landscape: micrometre-scale superconducting regions coexist with relatively insulating areas. We further show that cAFM resolves conductance fluctuations at 20 K (> TC) that vary between repeated scans, consistent with expectations for short-lived, pre-formed Cooper pairs in the BCS-BEC crossover regime. These results establish cAFM as a practical tool to validate assumptions underlying four-probe transport and underscore the need for direct spatial probes in materials whose macroscopic response can conceal nanoscale inhomogeneity. Accurate identification of macroscopic properties is critical for materials classes like superconductors that are defined by their macroscopic properties.