The critical Josephson currents in MgB2/normal metal/MgB2 tunnel junctions: Bogoliubov-de Gennes approach

The Josephson currents passing through the S1/N/S2 double tunnel junctions where S1 can be either an MgB2 or a conventional superconductor (CS), S2 is MgB2 and N is a normal metal are investigated. The Bogoliubov-de Gennes approach is used to calculate the Andreev reflection coefficients at the S1/N interface barrier. The Fermi wave vectors mismatch among S1, N and S2, and the difference in the TC’s of the two superconductors are taken into account. For the MgB2/N/MgB2 junction, the Josephson currents in both the c-axis and the ab-plane orientation alignments are studied. For the CS/N/MgB2 junctions, only the Josephson current in the c-axis orientation is studied. Our results for critical Josephson currents flowing along c-axis orientation of both types of S1/N/S2 junctions are compared to four sets of the experimental data. We find that the fitting of the experimental data for the temperature dependence of the Josephson junctions to our results are in good agreement in all four cases.