The normalized conductance for a N-I-MgB2 tunnel junction: Thick barrier limit

The conductance in a N-I-MgB2 tunnel junction is studied for the case where the c-axis of the MgB2 is orientated perpendicular to the interface. The thick barrier limit is taken. It is assumed that the electric current is composed of two currents, one which describes the tunneling in the π-band in the MgB2 and the other, the tunneling into the σ-band. The Bogoliubov-de Gennes equations are used to determine the nature of the quasi-particles in the different regions of the junctions. An exact expression for the normalized conductance in the c-axis direction is obtained by applying the usual boundary conditions at the two interfaces of the junction. The numerical evaluations lead to results which are in excellent agreement with the published result of Cucolo et al. [A.M. Cucolo, F. Giubileo, D. Roditchev, Physica A 339 (2004) 112].