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 3 omega-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. (c) 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http:// creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0071939

Automated summary

We demonstrate a non-linear measurement scheme of the Shubnikov-de Haas effect based on Joule self-heating, showing the significant temperature dependence due to Landau quantization effects at high fields. The experimental results in CoSi highlight the ability to resolve quantum oscillations at low magnetic fields in the non-linear channel, providing valuable insights into the electronic structure of micro- and nano-materials.