# 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.[1] 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/${\displaystyle r}$ at short distances from the center, and decays slowly, like 1/${\displaystyle r^{2}}$ at long distances. Abrikosov's vortices, in comparison, have very short range interaction and diverge as ${\displaystyle \log(1/r)}$ near the center.

A transport current flowing through a superconducting film may cause these vortices to move with a constant velocity ${\displaystyle v}$ proportional to, and perpendicular to the transport current.[2] 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.[3][4][5] The characteristic length governing the distribution of the magnetic field around the vortex center is given by the ratio ${\displaystyle \Lambda =2\lambda ^{2}}$/${\displaystyle d}$, also known as "Pearl length," where ${\displaystyle d}$ is the film thickness and ${\displaystyle \lambda }$ is London penetration depth.[6] 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.[5]

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

## References

1. ^ Pearl, Judea (1964). "Current distribution in superconducting films carrying quantized fluxoids". Applied Physics Letters. 5 (4): 65–66. Bibcode:1964ApPhL...5...65P. doi:10.1063/1.1754056.
2. ^ Kogan, V.G.; Nakagawa, N. (2021). "Moving Pearl vortices in thin-film superconductors". arXiv:2102.00073 [cond-mat.supr-con].
3. ^ Tafuri, F.; J.R. Kirtley; P.G. Medaglia; P. Orgiani; G. Balestrino (2004). "Magnetic Imaging of Pearl vortices in Artificially layered ${\displaystyle (Ba_{0.9}Nd_{0.1}CuO_{2+x})_{m}/(CaCuO_{2})_{n}}$ Systems" (PDF). Physical Review Letters. 92 (15): 157006. Bibcode:2004PhRvL..92o7006T. doi:10.1103/PhysRevLett.92.157006. hdl:2108/33451. PMID 15169312.
4. ^ Pozzi, G. (2007). "Electron optical effects of a Pearl vortex near the film edge". Physical Review B. 76 (54510): 054510. Bibcode:2007PhRvB..76e4510P. doi:10.1103/PhysRevB.76.054510.
5. ^ a b Bert, Julie A.; Beena Kalisky; Christopher Bell; Minu Kim; Yasuyuki Hikita; Harold Y. Hwang; Kathryn A. Moler (2011). "Direct imaging of the coexistence of ferromagnetism and superconductivity at the ${\displaystyle LaAIO_{3}/SrTiO_{3}}$ interface". Nature Physics. 7 (10): 767––771. arXiv:1108.3150. Bibcode:2011NatPh...7..767B. doi:10.1038/nphys2079. S2CID 10809252.
6. ^ Clem, John R. (2010). "Josephson junctions in thin and narrow rectangular superconducting strips". Physical Review B. 81 (14): 144515. arXiv:1003.0839. Bibcode:2010PhRvB..81n4515C. doi:10.1103/PhysRevB.81.144515. S2CID 119170326.