Hydrodynamics of degenerate electrons and their T-square thermal resistivity

Detecting hydrodynamic fingerprints in the flow of electrons in solids has become a dynamic field of investigation. Most attention is focused on the regime near the degeneracy temperature when the thermal velocity can present a spatially modulated profile. We present a study of thermal conductivity in bulk crystals of semi-metallic antimony revealing a hydrodynamic feature in the flow of degenerate and quasi-ballistic electrons. We detect a size-dependent departure from the Wiedemann-Franz law driven by a mismatch between the prefactors of T-square thermal and electrical resistivities. This observation is unexpected in the momentum-relaxing picture of transport, but finds a natural explanation in the hydrodynamic picture where collisions among electrons conserve momentum. In normal-state liquid 3He, both viscosity and thermal diffusivity decrease upon warming and momentum-conserving collisions among fermions produces a T-square thermal resistivity. Our results imply that the presence of this effect in ultraclean metals. Since the Wiedemann-Franz law is recovered when collisions by defects outweigh momentum-conserving collisions, T-square electrical resistivity can arise in absence of Umklapp events in a ‘dirty’ metal. This would provide a solution to the puzzling persistence of T-square resistivity in dilute metals such as doped strontium titanate.