Hybrid-order topology in two-dimensional nonsymmorphic antiferromagnets

TL;DR

This paper introduces a theoretical model of hybrid-order topology in 2D nonsymmorphic antiferromagnets, showing how boundary geometry influences topological edge and corner states, with potential for termination-controlled topological phases.

Contribution

It reveals a symmetry-based mechanism for duality between first- and second-order topological phases in magnetic nonsymmorphic systems, controlled by boundary termination.

Findings

Nonsymmorphic screw symmetry protects gapless edge states on certain boundaries.

Broken screw symmetry at specific terminations leads to gapped edges and corner states.

Lattice perturbations can gap edge modes while preserving corner states.

Abstract

We theoretically demonstrate hybrid-order topology in a two-dimensional nonsymmorphic antiferromagnet. Utilizing a generic antiferromagnetic Dirac model with a symmetry-allowed, momentum-dependent spin-density-wave (SDW) mass, we show that a single bulk insulating phase exhibits distinct topological boundary manifestations governed solely by the termination geometry. For screw-compatible edges, nonsymmorphic screw symmetry protects gapless first-order edge states. In contrast, for a $45^\circ$ diamond-shaped termination, the screw symmetry is broken at the boundary, resulting in gapped edges. However, the finite geometry still preserves magnetic mirror symmetries $\mathcal{M}_x\mathcal{T}$ and $\mathcal{M}_y\mathcal{T}$, which enforce an alternating pattern of edge masses, thereby binding zero-dimensional corner states. This second-order phase is characterized by a quantized quadrupole moment, with corner states pinned to zero energy by the chiral symmetry. We further demonstrate that explicit lattice perturbations can selectively gap the first-order edge modes while robustly preserving the corner states. Our work establishes a symmetry-based route to a termination-controlled duality between first- and second-order topology in magnetic nonsymmorphic systems.