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

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, ω) , 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 behaviour, but with a diverging prefactor of the T2 term for small a.