Quantum skyrmion Hall effect

TL;DR

This paper introduces the quantum skyrmion Hall effect, a topologically quantized transport phenomenon of magnetic skyrmions, extending the magnetic quantum Hall effect to skyrmion systems with potential theoretical models and lattice realizations.

Contribution

It proposes the quantum skyrmion Hall effect as a new topological transport phenomenon, generalizing the magnetic quantum Hall effect to magnetic skyrmions with a theoretical framework and lattice model.

Findings

Quantized Hall conductivity proportional to topological invariant Q.

Identification of a lattice model realizing the effect without external electric field.

Outline of a field theory for composite electric and magnetic charges.

Abstract

We consider the problem of magnetic charges in $(2+1)$ dimensions for a torus geometry in real-space, subjected to an inverted Lorentz force due to an external electric field applied normal to the surface of the torus. We compute the Hall conductivity associated with transport of these charges for the case of negligible gapless excitations and global $\mathrm{U}(1)$ charge conservation symmetry, and find it is proportional to an integer-valued topological invariant $\mathcal{Q}$, corresponding to a magnetic quantum Hall effect (MQHE). We identify a lattice model realizing this physics in the absence of an external electric field. Based on this, we identify a generalization of the MQHE to be quantized transport of magnetic skyrmions, the quantum skyrmion Hall effect (QSkHE), with a $\mathrm{U}(1)$ easy-plane anisotropy of magnetic skyrmions and effective conservation of charge associated with magnetic skyrmions yielding incompressibility, provided a hierarchy of energy scales is respected. As the lattice model may be characterized both by a total Chern number and the topological invariant $\mathcal{Q}$, we furthermore outline a possible field theory for electric charges, magnetic charges, and correlations between magnetic and electric charges approximated as composite particles, on a two-torus, to handle the scenario of intermediate-strength correlations between electric and magnetic charges modeled as composite particles. We map this problem to a generalized $(4+1)$D theory of the quantum Hall effect for the composite particles.