Josephson effects in MgB2 /Thin Insulator/ MgB2 tunnel junction

The Josephson currents in MgB2/I/MgB2 tunnel junction for both cc-axis and abab-plane orientation alignments are calculated by using the B-dG equation to derive the Andreev reflection coefficients at the interface. The differences between the insulating barrier strengths due to the differences in the interactions between the π(σ)π(σ)-bands electron (hole)-like quasi particles with the insulator are taken into account in the calculations of the Josephson currents. Also, the difference in the effective cross sectional area for the two types of quasi-particles (the ππ- and σσ-bands) flow through the junction is taken into account. Both the current-phase relation and the temperature dependence of the maximum (or critical) Josephson current are studied. The results show that the temperature dependence of the maximum Josephson current for cc-axis and abab-plane orientation junctions are quite different from those of an S/I/S Josephson tunnel junction when S is a conventional superconductor. When the insulator is absent and S is MgB2, the calculated maximum Josephson current in a cc-axis orientation junction exhibits a (T−TC)2(T−TC)2 dependence. However, the calculated current in the abab-plane orientation junction exhibits a nearly linear temperature dependence when the effective cross sectional areas and the interface interaction between the insulator and the two types of quasi particles (ππ and σσ) are taken to be the same. The calculated current for cc-axis orientation junction agrees very well with the experimental data. The prediction that the Josephson current will be a combination of two sinusoidal functions is observed in the current-phase relation of an abab-plane orientation junction.