Haldane state with toroidal magnetic order

TL;DR

This paper demonstrates that a two-band model with toroidal magnetic order in 2D crystals is equivalent to the Haldane model, predicting topologically nontrivial states similar to quantum Hall effects without external magnetic fields.

Contribution

It establishes a direct equivalence between toroidal magnetic order models and the Haldane model, suggesting new physical realizations of topological states.

Findings

Crystals with toroidal order can exhibit Haldane-like topological states.

Topological quantum Hall effects can occur without external magnetic fields.

Analogous effects are predicted for quantum spin Hall states without spin-orbit coupling.

Abstract

We show that a simplified two-band model describing toroidal magnetic order in two-dimensional crystal is entirely equivalent to the well-known Haldane model of a honeycomb lattice in periodic internal magnetic field with zero total flux through the unit cell. Crystals with toroidal ordering can be considered as real physical systems which should exhibit topologically nontrivial state, predicted by Haldane, that is similar to the quantum Hall effect regime without any external magnetic field. Analogous description is formulated for quantum spin Hall effect without any spin-orbit interaction.