Fig. 10-1 Superconductors under a magnetic field (current and charge distributions in a quantized magnetic vortex) In superconductors, when a magnetic field that is lower than the critical field is applied, the magnetic field is excluded. However, when the magnetic field is stronger than the critical field, the magnetic field penetrates as a vortex, as shown schematically above. Around the vortex, indicated by the circle, the current flows circularly, as shown in the upper right panel. In this research, we calculated the charge distribution along the green arrow path in a first-principle manner, and found that the charge was unevenly distributed depending on the distance from the center of the vortex (the distance unit is 0.053 nm as shown in the lower right panel. The two calculation examples (the lower right panel) reveal that the charge is largely depressed at the vortex center.

A weak magnetic field cannot enter a superconductor, but a strong magnetic field can penetrate a superconductor as a quantized magnetic vortex, which forms a circular current around the vortex core as shown in Fig. 10-1. This striking fact proves that superconductivity is a macroscopic quantum phenomenon, which has attracted tremendous attention from renowned scientists. In addition, the quantized vortex has a very important role in superconductor applications. This is because the vortex motion, driven by Lorenz force under the applied current, moves non-superconducting electrons that lie inside the vortex core as the vortex pinning effects do not exist. As a result, electrical resistance breaks out, and this may incidentally lead to superconductivity collapse. Thus, the prevention of vortex movement is an important issue in superconductor applications involving magnetic field generation by superconducting coils. Since the discovery of the High-Tc superconductor in 1986, its high transition temperature has inspired many research fields of superconducting applications, and therefore, the structure of the vortex has been intensively examined. However, few studies have addressed the vortex structure by the use of the first-principal calculation method, (which computes material properties only by constituent elements, like nuclear and electron components), with consideration for electron-electron interactions. This is because such a calculation requires a complex numerical technique and a significant computational resource. However, since the size of the vortex in High-Tc superconductors is so small (2~3 nm), an understanding of its electronic structure is regarded to be crucial. Therefore, we have performed a first-principle calculation to reveal the electronic structure microscopically. As a result, a charge modulation around the vortex was obtained as shown in the lower right panel of Fig. 10-1. This is in marked contrast to the conventional concept, that is, any charge modulations are unstable by Coulomb interaction in uniform solid matter. Moreover, this result means that the vortex can confine charge as well as magnetic field. Although this finding does not immediately affect superconductor application fields, we believe that it leads to a comprehensive understanding of the vortex dynamics.

Reference M. Machida et al., Friedel Oscillation in Charge Profile and Position Dependent Screening around a Superconducting Vortex Core, Phys. Rev. Lett., 90, 077003 (2003).

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