Impurity and hybridization effects on the symmetry classification and magnetic response function of a two-band superconductor with interband pairing order

The effects of hybridization and impurity (magnetic and nonmagnetic) potentials on the pairing symmetries and magnetic response of a two-band superconductor with an equal-time s-wave interband pairing order parameter in the framework of Green's function technique are investigated theoretically. First, the effects of spin-independent and spin-dependent hybridization on the generation of even- or odd-frequency Cooper pairs which determines the symmetry classification and the response of the superconductor are studied. Next, the impurity effect on creating different symmetry classes and the kernel response function of a two-band superconductor are discussed. By separating the contributions of even- and odd-frequency pairing to the Meissner kernel, it is shown that the competition between these two terms determines the total Meissner effect of the superconductor. For a two-band spin-singlet superconductor, nonmagnetic impurity scatterings do not change transition temperature according to Anderson's theorem, while both intra- and interband magnetic impurity scattering cause superconducting transition temperature suppression with the rate following the Abrikosov-Gor'kov theory. For spin-triplet pairing, interband magnetic scattering has no impact on pair breaking, whereas intraband magnetic scattering acts as a pair breaker and suppresses the transition temperature in the Born limit. In this case, the odd-frequency superconducting pairs can be induced in the simultaneous presence of both intra- and interband magnetic impurities. Thus, by controlling the concentration of magnetic impurities, it is possible to engineer triplet-pairing odd-frequency superconductors with a total diamagnetic Meissner response which stabilizes the superconducting state. This technique opens up an avenue for designing stable odd-frequency superconductors.