Josephson Effect in Two-Gap Iron-Based Superconductors

The Josephson effect is studied in SIS junctions made of two band reversed sign s-wave superconductors. The insulator region I is considered to have finite thickness. The solutions of the Bogoliubov de genes equation are considered in two superconducting regions and also in intermediate insulator region. Then, the appropriate boundary value conditions are applied on the wave functions. An eigenvalue equation is obtained for the energy spectrum which depends on a few parameters of the problem, like the thickness of the insulator region. For some special values for parameters of the problem, changing the thickness of the insulator region, a zero-pi phase transition is observed.