Non-linear Shubnikov-de Haas oscillations in the self-heating regime

We demonstrate a non-linear measurement scheme of the Shubnikov–de Haas effect based on Joule self-heating that builds on ideas of the 3ω-method used in thin films. While the temperature dependence of the resistance, R(T), of clean metals at low temperatures saturates, a significant temperature dependence, dR/dT, appears at high fields due to Landau quantization. We experimentally demonstrate this effect in the semi-metal CoSi, resolving well quantum oscillations at low magnetic fields in the non-linear channel, which appear as 3rd harmonics of the current drive frequency. To ensure the dominant self-heating originates in the crystal, not at the contacts, we fabricate crystalline microbars using focused ion beam machining. These oscillations in non-linear channel encode the ratio between the dR/dT and the thermal conductivity of the material, rendering it an interesting probe in situations of the broken Wiedemann–Franz law. Our results present a quantitative methodology that is particularly suited to investigate the electronic structure of micro- and nano-materials at intermediate temperatures.