Fermi liquid behaviour in weakly disordered metals close to a quantum critical point

TL;DR

This paper analytically investigates Fermi liquid behavior in weakly disordered metals near a quantum critical point, revealing divergence in certain properties and consistency with experimental observations.

Contribution

It provides an analytical calculation of low-temperature properties near a quantum critical point, highlighting divergence patterns and the conditions for the Kadowaki-Woods ratio's independence from the control parameter.

Findings

Fermi liquid results with temperature-dependent scattering rate and conductivity.

Prefactors diverge as power laws near the critical point.

Kadowaki-Woods ratio is independent of the control parameter for 3D ferromagnetic fluctuations.

Abstract

We calculate analytically the low temperature quasi-particle scattering rate, the conductivity, and the specific heat in weakly disordered metals close to a quantum critical point, via the use of a proper fluctuation potential $V(q,\omega)$ between the quasi-particles. We obtain typical Fermi liquid results proportional to $T^2$ and $T$ respectively, with prefactors which diverge as power laws of the control parameter $a$ upon approaching the critical point. The Kadowaki-Woods ratio is shown to be independent of $a$ (possibly times a logarithmic dependence on $a$) only for the case of three-dimensional ferromagnetic fluctuations. Our results are consistent with experiments on the eight materials CeCoIn$_5$, Sr$_3$Ru$_2$O$_7$, YbRh$_2$Si$_2$, La$_{2-x}$Ce$_x$CuO$_4$, Tl$_2$Ba$_2$CuO$_{6+x}$, CeAuSb$_2$, YbAlB$_4$, and CeRuSi$_2$.