Localized states within the gap in a two-band superconductor

Abstract

We present results for strong-coupling calculations for the density of states in the presence of magnetic impurities in a two-band superconductor. Our calculations were done for the particular case of a ${\mathrm{MgB}}_{2}$ compound where two bands $(\ensuremath{\sigma}$ and $\ensuremath{\pi}$ B-like) intersect the Fermi level. If only the $\ensuremath{\pi}$ band is responsible for superconductivity, then an impurity band will form in the energy gap of the $\ensuremath{\pi}$ band. If the $\ensuremath{\sigma}$ band is involved, then new features may be found in the density of states at frequencies between the superconducting gaps corresponding to $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ bands. The validity of our results can be directly verified by measuring the density of states in the presence of magnetic impurities using tunneling experiments in ${\mathrm{MgB}}_{2}.$ We also present analytical results for the doping dependence of the critical temperature.