Realising Haldane's vision for a Chern insulator in buckled lattices

TL;DR

This paper demonstrates that buckled lattices like silicene can realize Haldane's Chern insulator model using simple hopping and in-plane magnetic fields, making experimental realization more feasible.

Contribution

It shows that realistic buckled lattices can implement Haldane's model with minimal conditions, bridging the gap between theory and experiment.

Findings

Silicene in an in-plane magnetic field acts as a Chern insulator.

Realization requires no exotic interactions or complex parameters.

Chern insulating behavior occurs at very small magnetic fields.

Abstract

The Chern insulator displays a quantum Hall effect with no net magnetic field. Proposed by Haldane over 20 years ago, it laid the foundation for the fields of topological order, unconventional quantum Hall effects, and topological insulators. Despite enormous impact over two decades, Haldane's original vision of a staggered magnetic field within a crystal lattice has been prohibitively difficult to realise. In fact, in the original paper Haldane stresses his idea is probably merely a toy model. I show that buckled lattices with only simple hopping terms, within in-plane magnetic fields, can realise these models, requiring no exotic interactions or experimental parameters. As a concrete example of this very broad, and remarkably simple principle, I consider silicene, a honeycomb lattice with out-of-plane sublattice anisotropy, in an in-plane magnetic field, and show that it is a Chern insulator, even at negligibly small magnetic fields, which is analogous to Haldane's original model.