Electron and Phonon Hydrodynamics in Antimony

We present a study of the electrical and thermal resistivities in millimetric samples of the semimetal Sb down to sub-Kelvin temperatures. By applying a large magnetic field, we can clearly separate the electronic and phononic thermal resistivities. The Wiedemann-Franz (WF) law is recovered at low temperature (T ≈ 4K) in all samples. Yet, a size-dependent departure from the WF law is observed at higher temperatures. We show that this deviation is due to a mismatch between the prefactors of the thermal and electrical T²-resistivities. By analogy with the case of normal-state liquid ³He, where fermion-fermion collisions generate a thermal conductivity inversely proportional to temperature [1], we can associate the larger T²-thermal resistivity to the momentum-conserving electronic collisions [2]. In this scenario, the size-dependence of the ratio of the thermal to the electrical T²-prefactors in Sb points to a hydrodynamic flow of electrons [3]. Furthermore, in the 1K-7K range, we also report on a large increase of the thermal diffusivity of phonons, in the same samples, i.e. a signature that the flow of phonons is partially hydrodynamic.

[1] W. R. Abel et al., Phys. Rev. Lett. 18 (1967)
[2] A. Jaoui et al., npj Quant. Mat. 3 (2018)
[3] R.N. Gurzhi, Sov. Phys. Uspekhi 11 (1968)