Effect of impurities with retarded interaction with quasiparticles upon critical temperature of s-wave superconductor

Abstract

Generalization of a disordered metal's theory has been proposed when scattering of quasiparticles by impurities is caused with a retarded interaction. It was shown that in this case Anderson's theorem was violated in the sense that embedding of the impurities in s-wave superconductor increases its critical temperature. The increasing depends on parameters of the metal, impurities and their concentration. At a specific relation between the parameters the critical temperature of the dirty superconductor can essentially exceed critical temperature of pure one up to room temperature. Thus the impurities catalyze superconductivity in an originally low-temperature superconductor.

Impurities with retarded interaction with quasiparticles in a s-wave superconductor

“…This process means a retarded interaction with impurities. The interaction was considered in the simplest form in an article [14]. In an analytical form a mass operator is…”

“…A function D AB (ω) has a form of a collective excitation's propagator. Therefore we name this function as "pseudopropagator" [14]. A prefix "pseudo" means this propagator is a result of the averaging (4) and the corresponding correlations (A4).…”

“…We can see this expression for a mass operator is analogous to electron-phonon interaction (phonons with Einstein specter), where a value ρ U (q) B|A q 2 plays a role of a coupling constant. Eq.14 corresponds to result of an article [14] (if we suppose U (q) B|A q 2 = const and an impurity is two-level system) when the integration over q be done within the boundaries 2k F 0 q 2 dq. We have to consider a case when ω AB = 0, φ B = φ A , that is the scattering is elastic.…”

“…However Eq. (45) has a solution at another temperature T * -the singularity temperature introduced in [14]. The singularity temperature is T * < T * C and it can be used as a lower estimation of the critical temperature of the dirty metal.…”

“…In a work [14] a case was considered when when scattering of quasiparticles by nonmagnetic impurities is caused with a retarded interaction. The retarded interaction occurs because the impurities have an internal structure and make transitions between their states under the action of metal's quasiparticles.…”