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A complete electronic band theory is presented that describes the global properties of all possible band structures and materials, and can be used to predict new topological insulators and semimetals.

We report the observation of narrowband terahertz emission from a quasi-one-dimensional charge-density-wave insulator, (TaSe₄)₂I. The origin of the emitted radiation is interpreted as a phason that obtains mass due to the long-range Coulomb interaction.

3D higher-order topological insulators (HOTIs) exhibit 1D hinge states depending on extrinsic sample details, while intrinsic features of HOTIs remain unknown. Here, K.S. Lin et al. introduce the framework of spin-resolved topology to show that helical HOTIs can realize a doubled axion insulator phase with nontrivial partial axion angles.

Here the authors propose a scheme for observing axion topology in 3D photonic crystals. Exploiting gyromagnetism, they demonstrate topological switching of axionic channels of light, outlining a way to realize axion topology in Weyl semimetal domain walls.

Spin-momentum locking is a fundamental property of condensed matter systems. Here, the authors evidence parallel Weyl spin-momentum locking of multifold fermions in the chiral topological semimetal PtGa.

The hierarchy of symmetry breaking in magic-angle twisted bilayer graphene remains a topic of intense fundamental study. Here, the authors determine the spin polarization of symmetry-broken quantum Hall states and Chern insulators in MATBG using a twist-decoupled graphene probe.

The band topology of nonmagnetic crystals can be characterized by Topological Quantum Chemistry (TQC), whereas the band topology of magnetic crystals remains unexplored. Here, the authors extend TQC to the magnetic space groups to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids.

It has been predicted that the quasi-one-dimensional charge density wave material (TaSe₄)₂I hosts Kramers-Weyl fermions, but direct spectroscopic evidence of this is limited. Here, ARPES and theoretical calculations reveal signatures that may indicate the presence of Kramers-Weyl fermions.

The existence of a topological bulk-boundary correspondence for Dirac semimetals has remained an open question. Here, Wieder et al. predict one-dimensional hinge states originating from bulk three-dimensional Dirac points in solid-state Dirac semimetals, revealing condensed matter Dirac fermions to be higher-order topological.

Chern number controls the number of surface state channels in topological insulators. Here the authors propose 3D Chern insulating cubic photonic crystals with orientable and arbitrarily large Chern numbers demonstrating topologically protected photonic surface states.

AlPt is shown to be a chiral topological material with four-fold and six-fold degeneracies in the band structure. Fermi arc edge states span the whole Brillouin zone and their dispersion enables identification of the handedness of the chiral material.

Solid-state materials have emerged as a platform for probing and manipulating topological phases of matter. This Review surveys topological materials discovery in nonmagnetic crystalline solids, focusing on the role of crystal symmetry and geometry in topological material predictions.

There are areas where high-energy and condensed-matter physics can successfully overlap a prominent example being topological matter and the role of supersymmetry. Here, via anisotropic magnetoresistance, the authors investigate distortions in the Fermi surface geometry of FeRh films and provide a theoretical interpretation that considers the results within the framework of a pseudogravitational fields.