Planar Hall Plateau in Magnetic Weyl Semimetals

TL;DR

This paper reveals that the planar Hall effect (PHE) in magnetic Weyl semimetals is directly linked to the Chern number, leading to robust, quantized PHE plateaus that serve as topological signatures.

Contribution

It introduces the first connection between PHE and the global topological Chern number in magnetic Weyl semimetals, predicting quantized PHE plateaus.

Findings

PHE is proportional to the Chern number and energy tilt of Weyl points.

Quantized PHE plateaus can be observed by varying Fermi energy.

PHE plateaus are confirmed in realistic lattice models without time-reversal symmetry.

Abstract

Despite the rapid progress in the study of planar Hall effect (PHE) in recent years, all the previous works only showed that the PHE is connected to local geometric quantities, such as Berry curvature. Here, for the first time, we point out that the PHE in magnetic Weyl semimetals is directly related to a global quantity, namely, the Chern number of the Weyl point. This leads to a remarkable consequence that the PHE observation predicted here is robust against many system details, including the Fermi energy. The main difference between non-magnetic and magnetic Weyl points is that the latter breaks time-reversal symmetry T, thus generally possessing an energy tilt. Via semiclassical Boltzmann theory, we investigate the PHE in generic magnetic Weyl models with energy tilt and arbitrary Chern number. We find that by aligning the magnetic and electric fields in the same direction, the trace of the PHE conductivity contributed from Berry curvature and orbital moment is proportional to the Chern number and the energy tilt of the Weyl points, resulting in previously undiscovered quantized PHE plateau by varying Fermi energy. We further confirm the existence of PHE plateaus in a more realistic lattice model without T symmetry. By proposing a new quantized physical quantity, our work not only provides a new tool for extracting the topological character of the Weyl points but also suggests that the interplay between topology and magnetism can give rise to intriguing physics.