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

Identifying universal scaling relations between two or more variables in a complex system plays a pivotal role in understanding various phenomena in different branches of science. Examples include the allometric scaling among food webs in biology, the scaling relationship between fluid flow and fracture stiffness in geophysics, and the gap-to-$T_c$ ratio, between energy gap, $\Delta$, and critical transition temperature, $T_c$, hallmarks of superconductivity. Kinematics, in turn, is the branch of physics that governs the motion of bodies by imposing constraints correlating their masses, momenta, and energy; it is an essential ingredient for the analysis of high-energy quarkonium 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, we report on the identification of a novel, universal kinematic scaling relation between $T_c(\rho_\circ)$ and $A(\rho_\circ)$ found in a plethora of defect-bearing conventional and non-conventional superconductors within their FL regime. We traced back this relation to the triggering and stabilization of an electron-electron scattering channel within a very specific, yet common, type of amorphized regions, ubiquitous in all such superconductors. Our theoretical treatment consisted of, first, analyzing the construct of a distorted lattice as a mimic of the kinematic aftermath of the formation of such amorphized regions. Then we applied standard many body techniques to derive expressions for $T_c(\rho_\circ)$, $A(\rho_\circ)$, and their correlations. Our results are in agreement with experiments and provide a solid theoretical foundation for reconciling superconductivity with FL transport in these systems.