# Gyrotropic Hall effect in Berry-curved materials

## TL;DR

This paper investigates the gyrotropic Hall effect in noncentrosymmetric metals, highlighting its dependence on Berry curvature and potential as a topological material identifier, especially in Weyl semimetals.

## Contribution

It provides a comprehensive theoretical framework for the gyrotropic Hall effect, including intrinsic and extrinsic mechanisms, and links the effect to topological properties in Weyl semimetals.

## Key findings

- The gyrotropic Hall tensor trace relates to a topological Berry charge.
- Polycrystals of gyrotropic Weyl semimetals exhibit strong optical activity.
- The effect vanishes in ordinary metals, serving as a topological signature.

## Abstract

We study the ac Hall response induced by passage of dc transport current in two- and three-dimensional metals with gyrotropic point groups -- the gyrotropic Hall effect -- and consider the phenomenon of current-induced optical activity in noncentrosymmetric metals as a physical application of our theory. While the effect is expected to be present in single crystals of any noncentrosymmetric metal, we expect it to be strongest in enantiomorphic Weyl semimetals. Using the semiclassical kinetic equation approach we present several mechanisms underlying the gyrotropic Hall effect. Amongst them, the intrinsic mechanism is determined by the Berry curvature dipole, while extrinsic impurity-induced processes are related to skew scattering and side jump phenomena. In general, the intrinsic and extrinsic contributions can be of similar magnitude. We discuss the gyrotropic Hall effect for all frequencies of practical interest, from the DC transport limit, to optical frequencies. We show that for frequencies that are small compared to relevant band splittings, the trace of the gyrotropic Hall tensor in three-dimensional materials is proportional to a topological, quantized Berry charge, and therefore is robust in gyrotropic Weyl systems. This implies that polycrystals of strongly gyrotropic Weyl semimetals will demonstrate strong current-induced optical activity, whereas the response vanishes for polycrystalline ordinary metals. Therefore, the current-induced optical activity can be considered a valuable tool in identifying the topological nature of a material.