Hourglass Fermions

TL;DR

This paper introduces a new topological phase in band insulators arising from nonsymmorphic spatial symmetries, featuring hourglass-shaped surface fermions and novel quantum effects, exemplified in KHgX materials.

Contribution

It reveals a new topological phase protected by nonsymmorphic symmetries, characterized by hourglass fermions and a non-Abelian polarization theory, expanding the understanding of topological materials.

Findings

Discovery of hourglass fermions protected by nonsymmorphic symmetries.

Identification of KHgX as a material hosting these exotic surface states.

Proposal of a non-Abelian polarization framework for bulk topology.

Abstract

Spatial symmetries in crystals are distinguished by whether they preserve the spatial origin. We show how this basic geometric property gives rise to a new topology in band insulators. We study spatial symmetries that translate the origin by a fraction of the lattice period, and find that these nonsymmorphic symmetries protect a novel surface fermion whose dispersion is shaped like an hourglass; surface bands connect one hourglass to the next in an unbreakable zigzag pattern. These exotic fermions are materialized in the large-gap insulators: KHgX (X=As,Sb,Bi), which we propose as the first material class whose topology relies on nonsymmorphic symmetries. Beside the hourglass fermion, another surface of KHgX manifests a 3D generalization of the quantum spin Hall effect, which has only been observed in 2D crystals. To describe the bulk topology of nonsymmorphic crystals, we propose a non-Abelian generalization of the geometric theory of polarization. Our nontrivial topology originates from an inversion of the rotational quantum numbers, which we propose as a fruitful criterion in the search for topological materials.