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, ω) 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 threedimensional ferromagnetic fluctuations. Our results are consistent with experiments on the eight materials CeCoIn5,

Conductivity of Weakly Disordered Metals Close to a “Ferromagnetic” Quantum Critical Point

“…For the purpose of our calculations, we will treat ξ and a as independent parameters. This procedure, also followed in 12 , is entirely consistent, as can be seen from the details of the calculations below. Also, after eq.…”

“…It is possible that in this regime T is less or at most of the order of the impurity scattering rate τ −1 o . We have shown in 12 , via analytic diagrammatic calculations, that this critical FL behaviour can be consistently understood as arising from the exchange of relevant ferromagnetic fluctuations with small momentum q among the quasi-particles. Our approach assumes that we deal with weakly disordered metallic systems.…”

“…This possibility only arises if ξ and a are independent parameters -c.f. also 12 . We do not explicitly evaluate the integral in Q k of eq.…”

“…(3) is due to the finite τ −1 o . The dominant electron-electron interaction is assumed to be the "ferromagnetic" fluctuation potential (or fluctuation propagator) 12,15,16 peaked at q = 0…”

“…However, the prefactors of these quantities diverge in the vicinity of the respective QCP's as power laws of the criticality parameter a, which measures the proximity to the QCP. a may be determined by the electron filling factor, the pressure, or the magnetic field H (which is related to filling, through the Zeeman term) 11,12 . The T 2 resistivity appears within various material and H dependent ranges.…”