Supercurrent flow in inhomogeneous superconductors

TL;DR

This paper develops a perturbation theory to analyze how inhomogeneities affect supercurrent flow in superconducting films near the critical temperature, revealing long-range correlations and potential magnetic field detection.

Contribution

It introduces a perturbative approach to study inhomogeneous superconductors near criticality, linking disorder to supercurrent behavior and magnetic field generation.

Findings

Inhomogeneities induce long-range power-law correlations in the order parameter and supercurrent.

Supercurrent fluctuations increase with current, leading to strong inhomogeneity near the critical current.

Inhomogeneous superflow can produce detectable magnetic fields in thin NbN films.

Abstract

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.