Interaction Correction of Conductivity Near a Ferromagnetic Quantum Critical Point

TL;DR

This paper investigates how electron interaction corrections influence conductivity near a ferromagnetic quantum critical point, revealing distinct temperature dependencies in diffusive and ballistic regimes across different dimensions.

Contribution

It provides a detailed calculation of the temperature-dependent conductivity correction near a ferromagnetic quantum critical point, highlighting a new crossover scale and specific power-law behaviors.

Findings

In the quantum critical regime, crossover temperature T* is much lower than 1/τ.

Ballistic regime shows T^{(d-1)/3} dependence of conductivity.

Diffusive regime exhibits T^{1/4} in 3D and ln^2 T in 2D.

Abstract

We calculate the temperature dependence of conductivity due to interaction correction for a disordered itinerant electron system close to a ferromagnetic quantum critical point which occurs due to a spin density wave instability. In the quantum critical regime, the crossover between diffusive and ballistic transport occurs at a temperature $T^{\ast}=1/[\tau \gamma (E_{F}\tau)^{2}]$, where $\gamma$ is the parameter associated with the Landau damping of the spin fluctuations, $\tau$ is the impurity scattering time, and $E_{F}$ is the Fermi energy. For a generic choice of parameters, $T^{\ast}$ is few orders of magnitude smaller than the usual crossover scale $1/\tau$. In the ballistic quantum critical regime, the conductivity has a $T^{(d-1)/3}$ temperature dependence, where $d$ is the dimensionality of the system. In the diffusive quantum critical regime we get $T^{1/4}$ dependence in three dimensions, and $\ln^2 T$ dependence in two dimensions. Away from the quantum critical regime we recover the standard results for a good metal.