Origin of the finite-temperature violation of the Wiedemann-Franz law in semi-metals

We present a study of the electrical and thermal conductivities of the semimetals WP₂, WTe₂ and Sb in the 2K-40K temperature range. At low temperature, the Wiedemann-Franz law holds (κ/T = L₀/ρ with κ the thermal conductivity, ρ the electrical resistivity and L₀ the Lorenz number). However, upon warming, a downward deviation from the Wiedemann-Franz law is observed. In the case the Weyl semimetal WP₂ [1], the difference reaches an exceptionally large value compared to what we determined in WTe₂ and Sb and what was previously reported in other metals [2]. We identify electron-electron scattering as the origin of this departure [3]. We were further able to quantify the mismatch in the frequency of inter-electronic collisions which conserve momentum (i.e. electric current) but degrade energy (as in the case of normal-state liquid ³He). This sets a narrow temperature window between the ballistic and diffusive regimes where the hierarchy of scattering times corresponds to the hydrodynamic requirements for charge carriers [4].

[1] J. Gooth et al., Nat. Comm. 9, 4093 (2018)
[2] J. Paglione et al., Phys. Rev. Lett. 94, 216602 (2005)
[3] A. Jaoui et al., arXiv (2018)
[4] R. N. Gurzhi, Soviet Physics Uspekhi 11, 255 (1968).