Conductivity of weakly disordered metals close to a "ferromagnetic" quantum critical point

TL;DR

This paper analytically investigates the electrical conductivity of weakly disordered metals near a ferromagnetic quantum critical point, highlighting the role of impurity scattering and vertex corrections in the low-temperature regime.

Contribution

It provides a detailed analytical calculation of conductivity considering vertex corrections, revealing their impact near a ferromagnetic quantum critical point.

Findings

Vertex corrections due to impurity scattering significantly affect conductivity.

Resistivity exhibits a T^2 dependence with a diverging prefactor near the critical point.

Results align with experimental observations of Fermi liquid behavior in related materials.

Abstract

We calculate analytically the conductivity of weakly disordered metals close to a "ferromagnetic" quantum critical point in the low temperature regime. Ferromagnetic in the sense that the effective carrier potential $V(q,\omega)$, due to critical fluctuations, is peaked at zero momentum $q=0$. Vertex corrections, due to both critical fluctuations and impurity scattering, are explicitly considered. We find that only the vertex corrections due to impurity scattering, combined with the self-energy, generate appreciable effects as a function of the temperature $T$ and the control parameter $a$, which measures the proximity to the critical point. Our results are consistent with resistivity experiments in several materials displaying typical Fermi liquid behavior, but with a diverging prefactor of the $T^2$ term for small $a$.