Hydrodynamic flow of electrons in topological semimetals

Materials with strongly-correlated electrons exhibit interesting phenomena such as metal-insulator transitions and high-temperature superconductivity. In stark contrast to ordinary metals, electron transport in these materials is thought to resemble the flow of viscous fluids. Despite their differences, it is predicted that transport in both, conventional and correlated materials, is fundamentally limited by the uncertainty principle applied to energy dissipation. Here we present recent experiments on the hydrodynamic electron flow in the Weyl-semimetal WP₂ as well as in the Dirac semimetal PtSn₄. Using thermal and magneto-electric transport experiments to explore WP₂, we observe the transition from a conventional metallic state, at higher temperatures, to a hydrodynamic electron fluid below 20 K. The hydrodynamic regime is characterized by a viscosity-induced dependence of the electrical resistivity on the square of the channel width, and by the observation of a strong violation of the Wiedemann-Franz law. From magneto-hydrodynamic experiments and complementary Hall measurements, the relaxation times for momentum and energy dissipating processes are extracted. Following the uncertainty principle, both are limited by the Planckian bound of dissipation, independent of the underlying transport regime. Moreover, exprimental signatures of a hydrodynamic electron-phonon liquid in PtSn₄ will be discussed.