Multiband model for tunneling inMgB2junctions

A theoretical model for quasiparticle and Josephson tunneling in multiband superconductors is developed and applied to ${\mathrm{MgB}}_2$-based junctions. The gap functions in different bands in ${\mathrm{MgB}}_2$ are obtained from an extended Eliashberg formalism, using the results of band structure calculations. The temperature and angle dependencies of ${\mathrm{MgB}}_2$ tunneling spectra and the Josephson critical current are calculated. The conditions for observing one or two gaps are given. We argue that the model may help to settle the current debate concerning two-band superconductivity in ${\mathrm{MgB}}_2.$