We study the effects of random nonmagnetic impurities on the superconducting
transition temperature Tc in a two-band superconductor, where we assume the
equal-time spin-singlet s-wave pair potential in each conduction band and the
hybridization between the two bands as well as the band asymmetry. In the clean
limit, the phase of hybridization determines the stability of two states:
called s++ and s+−. The interband impurity scatterings decrease Tc
of the two states exactly in the same manner when the Hamiltonian preserves
time-reversal symmetry. We find that a superconductor with larger hybridization
shows more moderate suppression of Tc. This effect can be explained by the
presence of odd-frequency Cooper pairs which are generated by the band
hybridization in the clean limit and are broken by impurities.Comment: 11 pages, 2 figure