Sondheimer oscillations as a probe of non-ohmic flow in type-II Weyl semimetal WP2

As conductors in electronic applications shrink, microscopic conduction processes lead to strong deviations from Ohm’s law. Depending on the length scales of momentum conserving (l_MC) and relaxing (l_MR) electron scattering, and the device size (d), current flows may shift from ohmic to ballistic to hydrodynamic regimes and more exotic mixtures thereof. So far, an in situ, in-operando methodology to obtain these parameters self-consistently within a micro/nanodevice, and thereby identify its conduction regime, is critically lacking. In this context, we exploit Sondheimer oscillations, semi-classical magnetoresistance oscillations due to  helical electronic motion, as a method to obtain l_MR in micro-devices even when l_MR>>d. This gives information on the bulk l_MR complementary to quantum oscillations, which are sensitive to all scattering processes. We extract l_MR from the Sondheimer amplitude in the topological semimetal WP₂, at elevated temperatures up to T~40K, in a range most relevant for hydrodynamic transport phenomena. Our data on µm-sized devices are in excellent agreement with experimental reports of the large bulk l_MR and thus confirm that WP₂ can be microfabricated without degradation. Indeed, the measured scattering rates match well with those of theoretically predicted electron-phonon scattering, thus supporting the notion of strong momentum exchange between electrons and phonons in WP₂ at these temperatures. These results conclusively establish Sondheimer oscillations as a quantitative probe of l_MR in micro-devices in studying non-ohmic electron flow.