Journal of Physical Studies 5(3/4), 316–322 (2001)
DOI: https://doi.org/10.30970/jps.05.316

A STUDY OF THE MODIFIED GINZBURG–LANDAU TYPE EQUATION FOR A JOSEPHSON JUNCTION

T. L. Boyadjiev^{1}, Z. D. Genchev²
¹Faculty of Mathematics and Computer Science,%
University of Sofia ‟St. Kl. Ohridski", BG–1164, Sofia, Bulgaria
E-mail: todorlb@fmi.uni-sofia.bg
²Institute of Electronics, Bulgarian Academy of Sciences, BG–1784, Sofia, Bulgaria
E-mail: zgenchev@ie.bas.bg

The formalism of Ginzburg-Landau (GL) provides a simple method to study the global properties of non-homogeneous superconducting structures. In this paper we investigate a class of supercondicting/normal/superconducting (SNS) structures (sandwiches) with plane boundaries on the basis of the modified Ginzburg-Landau (GL) type equations. The corresponding non-linear boundary value problem for the amplitude of the order parameter is solved numerically. We show, that for fixed values of the phenomenological coefficients of the SNS structure there exist various solutions with different energies and their own phase differences. The two basic solutions with minimal energy in the case of an infinite sandwich are also obtained analytically. The resulted current density-phase offset dependence is constructed. Due to the existence of different nonlinear terms in the normal and superconducting regions, this dependence is not sinusoidal. In order to estimate the influence of the phenomenological coefficients on the form of current density – phase offset curve – a Fourier decomposition of this curve is also made.

PACS number(s): 74.20.De, 02.60.Lj, 02.70.Dh.