Quantum oscillations, Magnetic breakdown and thermal Hall effect in Co$_3$Sn$_2$S$_2$

TL;DR

This paper investigates the Fermi surface, quantum oscillations, and Hall effects in Co$_3$Sn$_2$S$_2$, revealing magnetic breakdown phenomena and analyzing the anomalous Wiedemann-Franz law's validity in this Weyl semimetal.

Contribution

It provides detailed experimental and theoretical analysis of the Fermi surface and magnetic breakdown in Co$_3$Sn$_2$S$_2$, and examines the anomalous thermal Hall effect and Wiedemann-Franz law deviations.

Findings

Observation of magnetic breakdown between hole and electron pockets.

Agreement of angle-dependent frequencies with DFT calculations.

Temperature-dependent deviations from the Wiedemann-Franz law.

Abstract

Co$_3$Sn$_2$S$_2$ is a ferromagnetic semi-metal with Weyl nodes in its band structure and a large anomalous Hall effect below its Curie temperature of 177 K. We present a detailed study of its Fermi surface and examine the relevance of the anomalous transverse Wiedemann Franz law to it. We studied Shubnikov-de Haas oscillations along two orientations in single crystals with a mobility as high as $2.7\times$10$^3$ cm$^2$V$^{-1}$s$^{-1}$ subject to a magnetic field as large as $\sim$ 60 T. The angle dependence of the frequencies is in agreement with density functional theory (DFT) calculations and reveals two types of hole pockets (H1, H2) and two types of electron pockets (E1, E2). An additional unexpected frequency emerges at high magnetic field. We attribute it to magnetic breakdown between the hole pocket H2 and the electron pocket E2, since it is close to the sum of the E2 and H2 fundamental frequencies. By measuring the anomalous thermal and electrical Hall conductivities, we quantified the anomalous transverse Lorenz ratio, which is close to the Sommerfeld ratio ($L_0=\frac{\pi^2}{3}\frac{k_B^2}{e^2}$) below 100 K and deviates downwards at higher temperatures. This finite temperature deviation from the anomalous Wiedemann-Franz law is a source of information on the distance between the sources and sinks of the Berry curvature and the chemical potential.