# IX Conference of Young Scientists "Problems of Theoretical Physics"

4-5 December 2018
Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine
Europe/Kiev timezone

## Boundary conditions for the superconducting junctions at temperatures close to critical

5 Dec 2018, 12:05
20m
Oral Condensed Matter Physics

### Speaker

Oleksandr Pastukh (Lesya Ukrainka Eastern European National University)

### Description

To calculate the current-phase relation in superconducting junctions, it is necessary to investigate the spatial behavior of the order parameter in the superconducting regions of the junction. In the case of temperatures close to the critical one, the Ginzburg-Landau theory [1] is used for this purpose. However, to apply this theory there is necessary to find the corresponding boundary conditions for the Ginzburg-Landau equation. Boundary condition can be found using the Wiener–Hopf method [2-3], however, use of this method for complicated superconducting junctions is problematic.
In our investigation, the problem of finding boundary conditions for the $\\$Ginzburg-Landau equation, was considered in the case of different superconducting junctions. In particular, superconducting junctions, combining tunnel effects and the proximity effect, with nonmagnetic impurities in superconducting regions were investigated. For finding the boundary condition for the Ginzburg-Landau equation the method of quasiorthogonality to asymptotics was used [4]. In addition, there were no restrictions on the values of the electron transmission coefficient and the thickness of the normal layer.
It has been shown that the boundary condition for the Ginzburg-Landau equation contains unknown constants for the calculation of which the quasiorthogonality to the asymptotics method was used. This method proved to be quite effective for complicated superconducting systems which contain the combination of dielectric layer and normal layer. In addition, boundary conditions obtained using this method, are valid for the arbitrary concentration of nonmagnetic impurities.

[1] A. V. Svidzinskii, Spatially Innhomogeneous Problems in the Theory of Superconductivity, Nauka, Moscow (1982).
[2] R.O. Zaitsev Boundary conditions for the superconductivity equations at temperatures close to critical // Sov. Phys. JETP 21, 1178 (1965).
[3] A. Barone, Yu. N. Ovchinnikov Boundary conditions and critical current of SNS junctions // Zh. Eksp. Teor. Fiz. 77, 1463 (1979).
[4] A. V. Svidzinsky, and V. E. Sakhnyuk, Condens. Matter Phys. 3, 683 (2000).

### Primary author

Oleksandr Pastukh (Lesya Ukrainka Eastern European National University)

### Co-authors

Vasul Sakhnyuk (Lesya Ukrainka Eastern European National University) Arsen Shutovskyi (Lesya Ukrainka Eastern European National University)

### Presentation Materials

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