Exotic antiferromagnetic magnons on a Möbius strip: Topology-induced symmetry breaking

Topological effects in solid-state systems are largely enabled by symmetry properties, typicallyarising from interactions. On the other hand, the impact of real-space topology beyond what is normallyderivable from a periodic boundary condition has been overlooked. Recent studies of non-trivial real-spacetopological structures (such as Möbius strips) primarily focused on local curvature effects under a continuousgeometry, while it remains mysterious if there are any residual effects solely attributed to the non-trivialboundary condition even in the absence of local curvature. Here, using antiferromagnetic (AFM) magnons on aMöbius strip, we demonstrate a hitherto unknown mechanism dubbed topology-induced symmetry breaking,wherein certain local symmetry preserved by the Hamiltonian is broken in the excited eigenstates due totopological constraints. The AFM magnons exhibit linear polarization of the Néel vector devoid of chirality andform two non-degenerate branches that cannot be smoothly connected to or be decomposed by the circularly-polarized magnons commonly seen in AFM materials. Only one branch of the exotic magnons supportsstanding-wave formation on the Möbius strip while the other does not, owing to its spectral shift incurred by theboundary condition. Our findings not only showcase the significant influence of real-space topology on thephysical nature of magnons but also inspire new research directions in the broad pursuit of topological effectsin physics.