Phonon-induced electron-electron interaction in disordered superconductors.

Abstract

We have measured the resistivities as a function of temperature of crystalline disordered bulk ${\mathrm{Ti}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}\mathrm{\ensuremath{-}}\mathit{y}}$(Co,Cr,Au${)}_{\mathit{y}}$ (x \ensuremath{\approxeq} 0.072) alloys below 25 K. With a total doping level of 7.2 at. % for Ti, our samples are disordered enough to manifest electron-electron interaction effects. As the temperature T is reduced, a resistivity increase \ensuremath{\Delta}\ensuremath{\rho}(T)/\ensuremath{\rho}(10 K) = [\ensuremath{\rho}(T)-\ensuremath{\rho}(10 K)]/\ensuremath{\rho}(10 K) on the order of a tenth of a percent is observed in all alloys before they eventually undergo superconducting transitions at sufficiently low T (depending on y). Both the functional forms and magnitudes of the observed \ensuremath{\Delta}\ensuremath{\rho}(T)/\ensuremath{\rho}(10 K) are interpreted in terms of electron-electron interaction effects in the presence of disorder. Particularly, the values of the screened Coulomb interaction parameter F\ifmmode \tilde{}\else \~{}\fi{} defined in electron-electron interaction theory are extracted. In the Coa from that of ${\mathrm{Ti}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$, we find that the electron-phonon coupling, including exchange of virtual phonons, is of crucial importance in determining the value of F\ifmmode \tilde{}\else \~{}\fi{}. However, the theory for F\ifmmode \tilde{}\else \~{}\fi{} in its current form fails to account for our experimental results. In the Au-doped alloys, the spin-orbit scattering introduced by the heavy Au atoms causes a small decrease in the value of F\ifmmode \tilde{}\else \~{}\fi{}, i.e., F\ifmmode \tilde{}\else \~{}\fi{} becomes slightly more negative for higher spin-orbit scattering.