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

Xiangwei Huang,Chunyu Guo,Claudia Felser,Carsten Putzke,Jonas Diaz,Philip J W Moll,Chandra Shekhar,Kaustuv Manna

doi:10.1063/5.0071939

Abstract

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.

Highlights

We demonstrate a non-linear measurement scheme of the Shubnikov–de Haas effect based on Joule self-heating that builds on ideas of the 3x-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 Cobalt monosilicide (CoSi), resolving well quantum oscillations at low magnetic fields in the non-linear channel, which appear as 3rd harmonics of the current drive frequency
We explore, rather than eliminate, Joule heating in strongly quantized metals and demonstrate that it enables a robust frequency and mass determination. This alternative measurement scheme may be generally applied to metallic crystals, yet here it is tailored to micrometer-sized samples

Summary

Introduction

On practice is to find a trade-off, to increase the current to the maximal level at which selfheating is not yet suppressing the oscillatory amplitudes This sparked our curiosity: Self-heating encodes the energy dissipation landscape in a crystal and, by itself should be sensitive to Landau quantization, too. The steady-state temperature increase, DTðIÞ, naturally encodes the thermal conduction through the thin-film the conductor resides on, as it provides the dominant cooling path via heat diffusion. This non-linearity is conveniently measured via the generation of third-harmonic voltage, V3x, in a lock-in amplifier supplying a low-frequency ac-current. The main cooling channel at lowest temperatures is its internal heat conductivity, draining the heat through the electric contacts [Fig. 1(a)]

Objectives

Methods