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

Abstract

A perturbation theory and a diagram technique for a disordered metal are proposed when scattering of quasiparticles by nonmagnetic impurities is caused with a retarded interaction. The perturbation theory generalizes a case of the elastic scattering in a disordered metal. Eliashberg equations for s-wave superconductivity are generalized for such a disordered superconductor. Anderson's theorem is found to be violated in the sense that embedding of the impurities into a s-wave superconductor increases its critical temperature. We showed the amplification of superconducting properties is a result of nonelastic effects in a scattering by the impurities.

Model of a hypothetical high-temperature superconductor

“…Thus the impurities are "smeared"over the system with concentration ρ and they act on quasiparticles as a mean field. Diagram technique for disordered system if interaction of quasiparticles with impurities is retarded has been developed in a work [5].…”

“…Critical temperature of a pure system K 3 C 60 is T C = 19.3K. In a work [5] Eliashberg equations has been generalized for a system metal+impurities. The impurity is a harmonic oscillator with transition frequencies between any of its states φ B and φ A : ω AB = E(B) − E(A), interaction of a conduction electron with the impurity is U (r), the impurities are distributed over the system with concentration ρ.…”

“…Collapse of superconducting state takes place near Anderson's transition metal-insulator, that is when 1 k F l 1. In a work [5] a perturbation theory and a diagram technique have been developed for a disordered metal if interaction of quasiparticles with impurities is retarded and impurity's oscillations are local. Transition amplitudes of the impurities between their states under the action of metal's quasiparticles (an electron-impurity coupling) have been obtained in the adiabatic approximation.…”

“…It found a critical temperature of a system metal+impuryty is more than a critical temperature of the pure metal T * C > T C . In the works [4,5] it has been shown that the equations for the transition temperature T * C of the system metal+impurity can be simplified if we calculate so-called singularity temperature T * only. The singularity temperature is a superconducting transition temperature if we turn off the pairing interaction caused by metal's phonon, therefore we have always T * < T * C .…”

“…The singularity temperature can be used as a lower estimate of the critical temperature of the dirty metal if T * T C . In the articles [4,5] principal possibility of increasing of the superconductive transitional temperature has been shown and method of calculation of the transition temperature was given. However in these articles a model of an impurity was not proposed.…”