On the Origin and the Amplitude of T-Square Resistivity in Fermi Liquids

In 1937, Baber, Landau, and Pomeranchuk postulated that collisions between electrons generates a contribution to the electric resistivity of metals with a distinct T-2 temperature dependence. The amplitude of this term in metals hosting either heavy carriers or a low concentration of them. The temperature dependence is set by the size of the scattering phase, but the microscopic source of dissipation is not straightforward. To explain how electron-electron collisions lead to momentum leak, Umklapp events or multiple electron reservoirs have been invoked. This interpretation is challenged by several experimental observations: the persistence of T-square resistivity in dilute metals (in which the two mechanisms are irrelevant), the successful extension of Kadowaki-Woods scaling to dilute metals, and the observation of a size-dependent T-square thermal resistivity (T/kappa$T/\kappa$) and its WiedemannFranz correlation with T-square electrical resistivity. This paper argues that much insight is provided by the case of normal liquid He-3 where the T-square temperature dependence of energy and momentum diffusivity is driven by fermionfermion collisions. The amplitude of T-square resistivity in He-3 and in metals share a common scaling. Thus, the ubiquitous T-square electrical resistivity ultimately stems from the Fermi-liquid temperature dependence of momentum diffusivity.

Automated summary

This paper discusses the relationship between electron-electron collisions and the electric resistivity of metals with respect to temperature, as well as the microscopic source of this phenomenon. By comparing it with the case of normal liquid He-3, the paper points out that the temperature dependence of Fermi liquid is the ultimate origin of the ubiquitous T-square electrical resistivity.