Pearl vortex - Wikiwand

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/ $r$ 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.

In Pearl's thesis,^[2] he uses the London equations to derive the magnetic response of a thin superconducting film in the Meissner state. For a film where the thickness is on the order of the superconducting penetration depth or smaller, the ability to screen magnetic field is geometrically suppressed. Whereas in a bulk superconductor the characteristic length scale over which magnetic field can penetrate is the London penetration depth $\lambda$ , in a thin film this is increased to the Pearl length $\Lambda _{P}=2\lambda ^{2}/d$ . This occurs because in a thin film, inductive coupling through free space plays a stronger role in magnetic field penetration.

This suppressed screening plays a role in film dynamics far beyond vortex dynamics. In most models, including Ginzburg-Landau theory, this can be accounted for by substituting $\Lambda _{P}$ instead of $\lambda$ Because the London equations assume a film in the Meissner state, Ginzburg-Landau theory is a more natural choice for studying vortex dynamics. Studying vortices in Ginzburg-Landau theory with a magnetic penetration depth of $\lambda$ yields Abrikosov vortices, while using a magnetic penetration depth of $\Lambda _{P}$ gives the dynamics of Pearl vortices.

Consequences

Because the magnetic penetration depth of Pearl vortices is a function of both geometry and material properties, their existence implies that in sufficiently thin films the modified Ginzburg-Landau parameter $\kappa =\Lambda _{P}/\xi$ may become greater than $1/{\sqrt {2}}$ even in films with Type-I superconductor behavior in the bulk. In other words, type-I superconducting thin films can host Pearl vortices, when normally in the bulk they transition directly from the Meissner state to the normal state with applied magnetic field.^[3]

Additionally, the long interaction length of Pearl vortices enable the Berezinskii-Kosterlitz-Thouless transition (BKT) to occur in superconducting thin films. The short interaction length of Abrikosov vortices was identified as insufficient to support a BKT transition. However, Beasley, Mooij, and Orlando ^[4] showed that Pearl vortices could theoretically enable a BKT transition in thin film superconductors.

Measuring Pearl vortices

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.^[5] 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.^[6]^[7]^[8] 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.^[9] 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.^[8]

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

References

↑ 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.
↑ Pearl, Judea (1965). Vortex Theory of Superconductive Memories (Thesis).
↑ Dolan, G.J. (1974). "Direct observations of the magnetic structure in thin films of Pb, Sn, and In". Journal of Low Temperature Physics. 15 (1–2): 111–132. Bibcode:1974JLTP...15..111D. doi:10.1007/BF00655630.
↑ Beasley, M.R. (1979). "Possibility of Vortex-Antivortex Pair Dissociation in Two-Dimensional Superconductors". Physical Review Letters. 42 (17): 1165–1168. Bibcode:1979PhRvL..42.1165B. doi:10.1103/PhysRevLett.42.1165.
↑ Kogan, V.G.; Nakagawa, N. (2021). "Moving Pearl vortices in thin-film superconductors". Condensed Matter. 6 (1): 4. arXiv:2102.00073. Bibcode:2021CondM...6....4K. doi:10.3390/condmat6010004.
↑ Tafuri, F.; J.R. Kirtley; P.G. Medaglia; P. Orgiani; G. Balestrino (2004). "Magnetic Imaging of Pearl vortices in Artificially layered $(Ba_{0.9}Nd_{0.1}CuO_{2+x})_{m}/(CaCuO_{2})_{n}$ Systems" (PDF). Physical Review Letters. 92 (15) 157006. Bibcode:2004PhRvL..92o7006T. doi:10.1103/PhysRevLett.92.157006. hdl:2108/33451. PMID 15169312.
↑ 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.
1 2 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 $LaAIO_{3}/SrTiO_{3}$ interface". Nature Physics. 7 (10): 767––771. arXiv:1108.3150. Bibcode:2011NatPh...7..767B. doi:10.1038/nphys2079. S2CID 10809252.
↑ 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.

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