Dirty two-band superconductivity with interband pairing order

We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature T_c in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. Because of the two-band degree of freedom, it is possible to define a spin-triplet s-wave pairing order parameter as well as a spin-singlet s-wave order parameter. The former belongs to odd-band-parity symmetry class, whereas the latter belongs to even-band-parity symmetry class. In a spin-singlet superconductor, T_c is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in a spin-triplet superconductor, T_c decreases with the increase of the impurity concentration. We conclude that Cooper pairs belonging to odd-band-parity symmetry class are fragile under the random impurity potential even though they have s-wave pairing symmetry.