Superconductivity, Fermi-liquid transport, and universal kinematic scaling relation for metallic thin films with stabilized defect complexes

Detailed analysis reveals that an incorporation of stabilized defect complexes within metallic thin films, though a highly disordering and nonequilibrium process, gives rise to superconductivity, Fermi-liquid (FL) transport, and a universal correlation among them. This remarkable manifestation of correlated macroscopic quantum effects is attributed to a phonon-mediated electron-electron, e-e, scattering channel which encompasses both Koshino-Taylor and Bergmann's pseudo-Umklapp processes. This channel---denoted below as pseudo-Umklapp e-e scattering channel---is distinctly different from traditional ones in that disorder leads to a breakdown of lattice momentum conservation (significantly enlarging available phase space), to a spectral weight transfer towards lower frequencies (modifying electron-phonon coupling constant $\ensuremath{\lambda}$), and to a relaxation of kinematic constraints (all phonic polarization modes become available for mediation). On modeling the distorted structure in terms of Hosemann's paracrystal and using standard quantum many-body techniques, we demonstrate the role of distortion and softening in establishing this pseudo-Umklapp channel and, consequently, the surge of superconductivity, the FL transport, and the correlation of their parameters. This unifying approach allows us to derive analytical expressions for ${T}_{c}({\ensuremath{\rho}}_{\ensuremath{\circ}})$ (hallmark of superconductivity), the coefficient $A({\ensuremath{\rho}}_{\ensuremath{\circ}})$ (hallmark of FL transport), and the universal kinematic scaling relation $\mathrm{ln}(\frac{{T}_{c}}{\ensuremath{\theta}})\ensuremath{\propto}{A}^{\frac{\ensuremath{-}1}{2}}$: All are in satisfactory agreement with experiments ($\ensuremath{\theta}$ is an energy scale; residual resistivity ${\ensuremath{\rho}}_{\ensuremath{\circ}}$ measures the extent of disorder).