Josephson effects in MgB 2 /Thin Insulator/ MgB 2 tunnel junction

Abstract

The Josephson currents in MgB 2/I/MgB 2 tunnel junction for both c -axis and a b -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 ) -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 π - and σ -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 c -axis and a b -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 MgB 2, the calculated maximum Josephson current in a c -axis orientation junction exhibits a ( T − T C ) 2 dependence. However, the calculated current in the a b -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 ( π and σ ) are taken to be the same. The calculated current for c -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 a b -plane orientation junction.