Josephson currents in point contacts between dirty two-band superconductors

We develop a microscopic theory of the Josephson effect in point contacts between dirty two-band superconductors. A general expression for the Josephson current, which is valid for arbitrary temperatures, is obtained. This formula is used to calculate the current-phase relations and temperature dependence of the critical current in MgB2 superconductors. We also examine the effect of interband scattering on the contact characteristics of dirty superconductors. The correction to the Josephson current owing to interband scattering is found to depend on the phase shift in the bulk superconductors (i.e., the s- or s +/--wave symmetry of the order parameters). (C) 2010 American Institute of Physics. [doi:10.1063/1.3518605]