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

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\(_2\).