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

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In 1937, Baber, Landau and Pomeranchuk postulated that collisions between electrons generates a contribution to the electric resistivity of metals with a distinct T temperature dependence. The amplitude of this… Click to show full abstract

In 1937, Baber, Landau and Pomeranchuk postulated that collisions between electrons generates a contribution to the electric resistivity of metals with a distinct T temperature dependence. The amplitude of this term is small in common metals, but dominant in metals hosting either heavy carriers or a low concentration of them. The link between the temperature dependence and the size of the scattering phase space is straightforward, but not the microscopic source of dissipation. To explain how electron-electron collisions lead to momentum leak, Umklapp events or multiple electron reservoirs have been invoked. This interpretation is challenged by a number of 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/κ) and its WiedemannFranz (WF) correlation with T-square electrical resitivity. This paper argues that much insight is provided by the established picture of fermion transport in normal liquid He. There, thermal resistivity displays a T-square temperature dependence driven by fermion-fermion collision with no need for Umklapp or multiple reservoirs. The amplitude of this term scales with what has been found for electrons in a variety of metals. Thus, the ubiquitous T-square electrical resistivity ultimately stems from the Fermi-liquid momentum diffusivity.

Keywords: amplitude square; square resistivity; resistivity fermi; origin amplitude; temperature dependence; resistivity

Journal Title: Annalen der Physik
Year Published: 2022

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