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.