Supercurrent flow in inhomogeneous superconductors

We study how the supercurrent flow pattern is altered by inhomogeneities in superconducting films. Working in the vicinity of the critical temperature and assuming a model of short-range disorder in the quadratic term of the Ginzburg-Landau functional, we develop a perturbation theory in the inhomogeneity strength. Absorbing the ultraviolet divergences into the renormalization of the critical temperature, we arrive at a well-defined theory governed by large-scale physics. In the presence of inhomogeneities, the correlation functions of the order parameter and supercurrent exhibit a long-range power-law behavior, which can be attributed to the mixing of the amplitude and phase modes. The fluctuation magnitude grows with increasing the average current, and the system becomes strongly inhomogeneous near the critical current. An inhomogeneous superflow will generate a random magnetic field, whose magnitude in thin NbN films can be comparable to Earth's magnetic field. We discuss the feasibility of detecting it using the SQUID-on-tip technique.