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Topological insulators are now shown to be protected not only by time-reversal symmetry, but also by crystal lattice symmetry. By accounting for the crystalline symmetries, additional topological insulators can be predicted.

R.-J. Slager et al. extend the theory of multigap topology from static to non-equilibrium systems. They identify Floquet-induced non-Abelian braiding, resulting in a phase characterized by anomalous Euler class, a multi-gap topological invariant. They also find a gapped anomalous Dirac string phase. Both phases have no static counterparts and exhibit distinct boundary signatures.

Excitons can exhibit topologically non-trivial states. Here, the authors theoretically demonstrate that excitons can exhibit controllable topology and localization properties due to their geometry in organic polymers.

Non-Abelian topology allows topological charges in multi-gap systems to be converted by braiding of different band nodes. Such multi-gap effects are experimentally observed in an acoustic semimetal.

Multi-gap topology is a new avenue in topological phases of matter but it remains difficult to verify in real materials. Here, the authors predict multi-gap topologies and associated phase transitions driven by braiding processes in the phonon spectra of monolayer silicates, providing clear signatures for experimental verification.

Rare-earth mono-pnictides antiferromagnets have generated recent interest as hosts to topological states and unconventional magnetic states. Here, angle-resolved photoemission spectroscopy reveals a hidden band-structure transition within the higher-temperature antiferromagnetic state of CeBi.

Weyl points in three-dimensional systems with certain symmetry carry non-Abelian topological charges, which can be transformed via non-trivial phase factors that arise upon braiding these points inside the reciprocal space.

It is shown that tensor network states, a powerful description of correlated quantum matter, can exactly represent Euler insulators. This allows for the theoretical prediction of new interacting phases of matter relevant in experimental settings from trapped ions to monolayer silicates to acoustic metamaterials.

Sliding and twisting of van der Waals layers can produce fascinating physical phenomena. Here, authors show that moiré polar domains in bilayer hBN give rise to a topologically non-trivial winding of the polarization field, forming networks of merons and antimerons.

Magnetic splitting in an antiferromagnetic state of cubic NdBi gives rise to Fermi arcs with bands that have opposing curvature.

Weak topological insulators (WTI) remain difficult to be observed in experiments. Here, the authors discover a WTI state in RhBi₂, where the topological surface states with saddle points result in a van Hove singularity along the (100) direction near Fermi energy.

Here, the authors show that when non-collinear antiferromagnet Mn₃Sn is pumped by femtosecond laser pulses it acts as a source of picosecond current pulses that emit electro-dipole radiation in the THz range of the spectrum. The origin of these photo-currents are attributed to the photon drag effect.

Complex magnetic formations, termed ‘multi-q’ structures, can give rise to magnetic spin textures, such as skyrmions, but how they influence band structure and topology is less clear. Here, the authors use a combination of calculated and experimental data to reveal the origin of the unconventional surface state pairs that emerge for NdBi for different type-I AFM multi-q structures.