Abstract Body

Superconductivity in nano-size shows special properties. Previously, we investigated transition temperature of nano-sized clean and dirty superconductors [1,2]. We found that the transition temperature is increased with oscillation as size of the superconductor is decreased. This is quantum effect. Electrons are confined in small region and the energy levels become discrete. Decreasing the size, energy level distance becomes large and effective electron density within the range of the attractive interaction between electrons becomes large.

In a dirty superconductor, the transition temperature is strongly increased because of the localization of superconducting electrons and increase of local density of states [3]. In figure, we show the Tc-enhancement (a) and localized superconducting state (b). However, in such localized superconductivity, zero-resistivity may disappear because there remain normal regions. In order to obtain superconductivity in whole region, we should decrease the temperature.

Here, we investigate how localized superconductivity extend the whole region with decreasing the temperature. We solve the Bogoliubov-de Gennes equations with impurity potential using the finite element method. We have found that superconductivity extend gradually, but this behavior depends on the impurity potential.

References

[1] M. Umeda, M. Kato, and O. Sato, IEEE Trans. on Appl. Superconductivity 26 8600104 (2016).

[2] M. Umeda, M. KatoPhysica C 560 (2019).

[3] M. Umeda, M. KatoJ. Appl. Phys. 126 143905 (2019).

Acknowledgment

This work supported by the KAKENHI Grant No. 24K08236.

Figure 1. (a) Size dependence of transition temperature of a rectangular superconductor. (b)Distribution of superconducting order parameter of localized state.

Keywords: Tc enhancement, Bogoliubov-de Gennes equation, Finite element method, Localization