# Universal relation between residual resistivity and A coefficient in correlated metals

## TL;DR

This study uncovers a universal linear relationship between residual resistivity and the A coefficient in correlated metals, linking disorder effects to electronic mass enhancement across various material classes.

## Contribution

It reveals a universal scaling law between residual resistivity and the A coefficient, connecting disorder and electronic correlations in a broad range of correlated metals.

## Key findings

- Residual resistivity grows linearly with the A coefficient at fixed disorder.
- The scaling is explained by chemical-potential fluctuations.
- The relation is universal across different correlated materials.

## Abstract

The effects of strong electronic correlations and disorder are crucial for emergent phenomena such as unconventional superconductivity, metal-insulator transitions, and quantum criticality. While both are omnipresent in real materials, their individual impacts on charge transport remain elusive. To disentangle their respective roles, we have independently varied the degree of randomness and the strength of electronic correlations -- by chemical substitution and physical pressure, respectively -- within the metallic phase nearby a Mott-insulating state. We find a distinct correlation dependence of the disorder-dependent residual resistivity $\rho_0$ in the Fermi-liquid regime $\rho(T)=\rho_0 + A T^2$, where $A\propto (m^{\star}/m)^2$ quantifies the electronic mass enhancement. Contrary to conventional expectations, we observe that at fixed disorder level $\rho_0$ grows linearly with $A$. This scaling can be understood in terms of chemical-potential fluctuations with variance $\sigma_\mu^2$, yielding $\rho_0 \propto A\,\sigma_\mu^2$. By comparing our findings to transport data on other organic Mott systems, oxides, heavy-fermion compounds, and moir\'e materials, we demonstrate that this new relation between residual resistivity and mass enhancement is a universal feature of correlated metals.