On the effect of the scattering processes on the singularities of the order parameter of a superconductor

It is shown that, in the presence of impurities, the order parameter Δ(p, ω) of a superconductor has two types of singularities. The first type of singularities is due, as in the case of pure superconductors, to a change in the topology of the lines of intersection of the two surfaces ε(p + q) = εF and ωλ (q) = const (the lq line). The second type of singularities, whose amplitude is proportional to the attenuation factor Γ(p), is due to a change in the topology of the lines of intersection of the surfaces ε(p + q) = εF, ε(p) = εF and the lq line. It is found that at the frequencies corresponding to the singularities of the function dΔ(p, ω)/dω the value of the function is proportional to (s/υΓ/Δ0)−1/2 (s is the velocity of sound, υ is the Fermi velocity, and Δ0 is the energy gap), and the characteristic damping range in which the anisotropy of the gap of the superconductor is significantly reduced is equal to (s/υ) Δ0 at the singularities.

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