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

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${}_2$.