Thermal resistivity and hydrodynamics of the degenerate electron fluid in antimony

TL;DR

This paper reports the observation of hydrodynamic behavior in the flow of degenerate electrons in bulk antimony, revealing size-dependent deviations from classical laws and providing insights into fermion-fermion interactions.

Contribution

It provides experimental evidence of hydrodynamic electron flow in antimony and links it to theoretical models of momentum-conserving collisions in Fermi liquids.

Findings

Size-dependent departure from Wiedemann-Franz law

Quadratic reduction of viscosity and thermal diffusivity with temperature

Comparison with $^3$He highlights fermion-fermion collision rates

Abstract

Detecting hydrodynamic fingerprints in the flow of electrons in solids constitutes a dynamic field of investigation in contemporary condensed matter physics. Most attention has been focused on the regime near the degeneracy temperature when the thermal velocity can present a spatially modulated profile. Here, we report on the observation of a hydrodynamic feature in the flow of quasi-ballistic degenerate electrons in bulk antimony. By scrutinizing the temperature dependence of thermal and electric resistivities, we detect a size-dependent departure from the Wiedemann-Franz law, unexpected in the momentum-relaxing picture of transport. This observation finds a natural explanation in the hydrodynamic picture, where upon warming, momentum-conserving collisions reduce quadratically in temperature both viscosity and thermal diffusivity. This effect has been established theoretically and experimentally in normal-state liquid $^3$He. The comparison of electrons in antimony and fermions in $^3$He paves the way to a quantification of momentum-conserving fermion-fermion collision rate in different Fermi liquids.