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

• Published in: Annalen der Physik 2022-05, Vol.534 (5), p.n/a
• Main Author: Behnia, Kamran
• Format: Article
• Language: English
• Subjects: Amplitudes; Collisions; Condensed Matter; Diffusivity; Dilution; Electrical resistivity; Electrons; Fermi liquids; Momentum; Physics; Temperature; Temperature dependence; Thermal conductivity; transport properties; Wiedemann–Franz law
• ISSN: 0003-3804; 1521-3889
• DOI: 10.1002/andp.202100588

In 1937, Baber, Landau, and Pomeranchuk postulated that collisions between electrons generates a contribution to the electric resistivity of metals with a distinct T2 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 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/κ$T/\kappa$) and its WiedemannFranz correlation with T‐square electrical resistivity. This paper argues that much insight is provided by the case of normal liquid 3He where the T‐square temperature dependence of energy and momentum diffusivity is driven by fermionfermion collisions. The amplitude of T‐square resistivity in 3He 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. In a metal, the rate of collisions between electrons grows quadratically with temperature. This generates a T‐square electric and thermal resistivity, even when these collisions conserve momentum. By comparing metals with the better understood case of 3He, the origin of T‐square resistivity is tracked to the temperature dependence of diffusivity.