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

## TL;DR

This paper uncovers a universal kinematic scaling relation linking the critical temperature and Fermi liquid coefficient in various superconductors, explained through amorphized regions affecting electron scattering.

## Contribution

It introduces a novel universal kinematic relation between $T_c$ and $A$ in superconductors, supported by theoretical modeling and experimental validation.

## Key findings

- Identified a universal scaling relation between $T_c$ and $A$ in superconductors.
- Linked the relation to amorphized regions influencing electron-electron scattering.
- Provided a theoretical framework aligning with experimental data.

## Abstract

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.