# Unconventional Topological Hall Effect in Skyrmion Crystals Caused by the Topology of the Lattice

## TL;DR

This paper predicts and explains an unconventional topological Hall effect in skyrmion crystals, linking it to the lattice topology and mapping it onto the quantum Hall effect, revealing quantized conductivities and sign changes.

## Contribution

It introduces a novel understanding of the topological Hall effect in skyrmion crystals by relating it to the quantum Hall effect through lattice topology considerations.

## Key findings

- Quantized Hall conductivity with steps of 2e^2/h and 1e^2/h
- Sign change of conductivity at van Hove singularity
- Mapping of THE onto QHE in skyrmion crystals

## Abstract

The hallmark of a skyrmion crystal (SkX) is the topological Hall effect (THE). In this Article, we predict and explain an unconventional behavior of the topological Hall conductivity in SkXs. In simple terms, the spin texture of the skyrmions causes an inhomogeneous emergent magnetic field whose associated Lorentz force acts on the electrons. By making the emergent field homogeneous, the THE is mapped onto the quantum Hall effect (QHE). Consequently, each electronic band of the SkX is assigned to a Landau level. This correspondence of THE and QHE allows to explain the unconventional behavior of the THE of electrons in SkXs. For example, a skyrmion crystal on a triangular lattice exhibits a quantized topological Hall conductivity with steps of $2 \cdot e^2/h$ below and with steps of $1 \cdot e^2/h$ above the van Hove singularity. On top of this, the conductivity shows a prominent sign change at the van Hove singularity. These unconventional features are deeply connected to the topology of the structural lattice.