Orbital origin of negative magnetoresistance and planar Hall effect in Weyl electron systems

The galvanomagnetic effect is used for not only determining the transport properties such as mobility of electric carrier in materials but also for exploring non-trivial phenomena in topological materials, including Weyl and Dirac electron systems. In recent years, the observability of chiral anomaly was proposed in these systems with non-trivial Berry curvature. In these scenarios, the negative longitudinal magnetoresistance (MR) and planar Hall effect (PHE) with the period π arise as consequences of the chiral anomaly. These phenomena have been observed in varieties of materials and regarded as evidence of a non-trivial electric state. From the other viewpoint, the Fermi surfaces in actual materials are difficult to approximate with spheres or ellipsoids. Although the conventional semiclassical transport theory based on the Boltzmann equation has been a powerful tool for analyzing MR, it has not been extended enough for applying to the complicated Fermi surface in actual materials. Recently, it was suggested that the Gaussian curvature, which reflects the local effective mass on the Fermi surface, can determine the signs of magnetoresistance. This result highlights the importance of fine structures on the Fermi surface in analyzing MR in general materials.
In this time, we calculated the MR and PHE of the Weyl electron system based on the semiclassical method without assuming the Berry curvature. First, we found that the PHE in this system can arise with the period π due to the multiple masses on the Fermi surfaces. In the classical viewpoint, a multiple carrier system naturally indicates such angular dependence of PHE. Second, negative longitudinal MR was also estimated by considering the local effective mass on the Fermi surface. We found that this magnetoresistance originates from negative Gaussian curvature locating on the Fermi surface in the vicinity of degenerated points (Weyl points). These results indicate that the PHE and the negative longitudinal MR, which have been referred to as the evidence of the non-trivial Berry curvature, can arise just from the structure on the Fermi surface. In addition, we calculate the temperature dependence of the amplitude of PHE in this system. We found some non-monotonic dependence or a sign change in low temperature range, which are also observed in actual materials. This behavior can be explained by the contributions from thermally excited carriers with different types of curvature.
Our results suggest that the non-trivial magneto-transport characteristics are possibly explained by extending the framework of semiclassical electro-transport theory and make it more suitable to the actual materials in contrast to the previous understanding. Notably, we cannot neglect the effects of the fine structures of the Fermi surface when we analyze the observed MR.