Pearl vortex

In superconductivity, a Pearl vortex is a vortex of supercurrent in a thin film of type-II superconductor, first described in 1964 by Judea Pearl. A Pearl vortex is similar to Abrikosov vortex except for its magnetic field profile which, due to the dominant air-metal interface, diverges sharply as 1/$$r$$ at short distances from the center, and decays slowly, like 1/$$r^2$$ at long distances. Abrikosov's vortices, in comparison, have very short range interaction and diverge as $$\log(1/r)$$ near the center.

A transport current flowing through a superconducting film may cause these vortices to move with a constant velocity $$v$$ proportional to, and perpendicular to the transport current. Because of their proximity to the surface, and their sharp field divergence at their centers, Pearl's vortices can actually be seen by a scanning SQUID microscope. The characteristic length governing the distribution of the magnetic field around the vortex center is given by the ratio $$\Lambda = 2 \lambda^2$$/$$d$$, also known as "Pearl length," where $$d$$ is the film thickness and $$\lambda$$ is London penetration depth. Because this ratio can reach macroscopic dimensions (~1 mm) by making the film sufficiently thin, it can be measured relatively easy and used to estimate the density of superconducting electrons.

At distances shorter than the Pearl's length, vortices behave like a Coulomb gas (1/$$r$$ repulsive force).