Realizing Hopf Insulators in Dipolar Spin Systems
Abstract
The Hopf insulator is a weak topological insulator characterized by an insulating bulk with conducting edge states protected by an integer-valued linking number invariant. The state exists in three-dimensional two-band models. We demonstrate that the Hopf insulator can be naturally realized in lattices of dipolar-interacting spins, where spin exchange plays the role of particle hopping. The long-ranged, anisotropic nature of the dipole-dipole interactions allows for the precise detail required in the momentum-space structure, while different spin orientations ensure the necessary structure of the complex phases of the hoppings. Our model features robust gapless edge states at both smooth edges, as well as sharp edges obeying a certain crystalline symmetry, despite the breakdown of the two-band picture at the latter. In a companion manuscript [2105.10504], we provide a specific experimental blueprint for implementing our proposal using ultracold polar molecules of KRb.
Cite
@article{arxiv.1901.08597,
title = {Realizing Hopf Insulators in Dipolar Spin Systems},
author = {Thomas Schuster and Felix Flicker and Ming Li and Svetlana Kotochigova and Joel E. Moore and Jun Ye and Norman Y. Yao},
journal= {arXiv preprint arXiv:1901.08597},
year = {2021}
}
Comments
6 + 7 pages, 3 figures. See companion manuscript arxiv:2105.10504 for additional numerics and a detailed experimental proposal for realizing the Hopf insulator