Purity-dependent Lorenz number,electron hydrodynamics and electron-phonon coupling in WTe_(2)

We present a study of electrical and thermal transport in Weyl semimetal WTe_(2)down to 0.3 K.The Wiedemann-Franz law holds below 2 K and a downward deviation starts above.The deviation is more pronounced in cleaner samples,as expected in the hydrodynamic picture of electronic transport,where a fraction of electron-electron collisions conserve momentum.Phonons are the dominant heat carriers and their mean-free-path does not display a Knudsen minimum.This is presumably a consequence of weak anharmonicity,as indicated by the temperature dependence of the specific heat.Frequent momentum exchange between phonons and electrons leads to quantum oscillations of the phononic thermal conductivity.Bloch-Grüneisen picture of electron-phonon scattering breaks down at low temperature when Umklapp ph-ph collisions cease to be a sink for electronic flow of momentum.Comparison with semi-metallic Sb shows that normal ph-ph collisions are amplified by anharmonicity.In both semimetals,at cryogenic temperature,e-ph collisions degrade the phononic flow of energy but not the electronic flow of momentum.