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Identifying universal scaling relations between two or more variables in acomplex system plays a pivotal role in understanding various phenomena indifferent branches of science. Examples include the allometric scaling amongfood webs in biology, the scaling relationship between fluid flow and fracturestiffness in geophysics, and the gap-to-$T_c$ ratio, between energy gap,$\Delta$, and critical transition temperature, $T_c$, hallmarks ofsuperconductivity. Kinematics, in turn, is the branch of physics that governsthe motion of bodies by imposing constraints correlating their masses, momenta,and energy; it is an essential ingredient for the analysis of high-energyquarkonium production, galaxy formation, as well as the $\rho_\circ+AT^2$contribution to the normal state resistivity in a Fermi liquid (FL),$\rho_\circ$ being a measure of disorder and $A$ the hallmark of FL. Here, wereport on the identification of a novel, universal kinematic scaling relationbetween $T_c(\rho_\circ)$ and $A(\rho_\circ)$ found in a plethora ofdefect-bearing conventional and non-conventional superconductors within theirFL regime. We traced back this relation to the triggering and stabilization ofan electron-electron scattering channel within a very specific, yet common,type of amorphized regions, ubiquitous in all such superconductors. Ourtheoretical treatment consisted of, first, analyzing the construct of adistorted lattice as a mimic of the kinematic aftermath of the formation ofsuch amorphized regions. Then we applied standard many body techniques toderive expressions for $T_c(\rho_\circ)$, $A(\rho_\circ)$, and theircorrelations. Our results are in agreement with experiments and provide a solidtheoretical foundation for reconciling superconductivity with FL transport inthese systems.

Defect-engineered, universal kinematic correlations between superconductivity and Fermi liquid transport