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The topological character of electrons in semimetals subtly influences their bulk properties, leading typically to weak experimental signatures. Here, Moll et al. report a distinctive anomaly in the magnetic torque upon entering quantum limit state in the Weyl semimetal NbAs, which only appears due to the presence of Weyl fermions.

The anomalous Hall effect has been observed in high-quality epitaxial thin films of non-collinear antiferromagnet Mn₃Pt, and can be switched on and off using an electric field.

The author demonstrates that laser-driven ultracold Fermi gases can exhibit color-orbit-like coupling with SU(3) symmetry. This leads to color-like oscillations and other quantum-chromodyamics-like phenomena in an atomic physics laboratory.

Arising from singularity on the surface of Poincaré sphere, topology-protected phase for co-polarized light enables 2π phase modulation, which complements the classical cross-polarized Pancharatnam-Berry phase and expands the versatility of flat optics.

The nonlinear Hall effect is observed in bilayer WTe₂ in the absence of a magnetic field, providing a direct measure of the dipole moment of the Berry curvature.

In the magneto-optical Kerr effect, light incident on a magnetic material is reflected with a shifted polarization, the size of the shift characterized by the Kerr angle. Here, Kato et al introduce a topological magneto-optical Kerr effect, where the presence of skyrmions, a type of topological spin texture, leads to a significant enhancement of the Kerr signal.

Here, the authors study topology in spin-orbit coupled 87Rb atoms by using time domain spectroscopy and quantum state tomography. They measure full quantum state to extract the Berry phase of the system and show signatures of a half-integer Chern index.

The spins in quantum magnets couple to each other through an exchange interaction. Here, the authors show that a weak coupling between neighbouring spins called the Dzyaloshinskii–Moriya interaction can give rise to topological behaviour in the archetypal quantum magnet strontium copper borate.

Direct measurement of the Berry curvature and the quantum metric of photonic modes in a high-finesse planar microcavity is achieved, enabling quantitative prediction of the independently measured anomalous Hall drift.

The anomalous Hall effect (AHE) occurs in ferromagnets caused by intrinsic and extrinsic mechanisms. Here, Yoo et al. report large anomalous Hall conductivity and Hall angle at the interface between a ferromagnet La_0.7Sr_0.3MnO₃ and a semimetallic SrIrO₃, due to the interplay between correlated physics and topological phenomena.

An analysis of T cell responses in people with amyotrophic lateral sclerosis shows that the C9orf72 antigen is a key target of autoimmune responses in the disease, and identifies C9orf72 epitopes that are recognized.

The accidental band-crossing origin of Weyl nodes paired with the absence of sizeable band gaps hampers the exploitation of low-energy relativistic quasiparticles in Weyl semimetals. In a gate-tunable high-quality tellurene film, quantum Hall measurements unveil a topologically non-trivial π Berry phase caused by unconventional Weyl nodes in these tellurium two-dimensional sheets.

Although dissipation is often detrimental to the observation of topological effects, a photonic molecule driven at several incommensurate frequencies is shown to be a candidate system for quantized topological transport in synthetic dimensions.

Magnetically intercalated transition metal dichalcogenides provide a platform to study the interplay of magnetism, electronic band structures, and correlations. Here the authors demonstrate a nearly magnetization-free anomalous Hall effect, collinear antiferromagnetism and non-Fermi liquid behavior in V_1/3NbS₂.

A continuous mesoscale space-time crystal phase is reported from a nematic liquid crystal driven by light.

Using torque magnetometry, the thermodynamic signatures of bosonic Landau level transitions are observed in a layered superconductor, owing to the formation of Cooper pairs with finite momentum.

The transport behavior of the carriers residing in the lowest Landau level is hard to observe in most topological materials. Here, Liu et al. report a surprising angular dependence of the interlayer magnetoresistivity and Hall conductivity arising from the lowest Landau level under high magnetic field in type II Weyl semimetal YbMnBi₂.

High-harmonic generation from the Dirac-like surface state of a topological insulator is separated from bulk contributions and continuously tuned by the carrier-envelope phase of the driving lightwave.

Optical spin–orbit coupling is known to occur in open systems such as helical waveguides. Here, the authors enable spin–orbit coupling of light confined to a closed path within an asymmetric optical microcavity and demonstrate a non-cyclic Berry phase acquired in a non-Abelian evolution.

Sr_1−yMn_1−zSb₂ (y, z < 0.1) is reported to be a magnetic topological semimetal exhibiting nearly massless relativistic fermions.

In acoustic systems, quantum spin Hall physics is rarely observed because the crucial ingredient spin-orbit coupling is missing. Here, the authors construct an acoustic crystal with synthetic spin-orbit coupling and observe gapless helical boundary states as well as spin flipping effect.

Responses to high-intensity mid-infrared laser light are theoretically investigated in the Haldane system. It is found that the primary electronic response, optical tunnelling and high-harmonic emission are sensitive to the topological phase of matter.

When performing interferometry-based magnetometry, there is generally a trade-off between sensitivity and range. Here, instead, the authors demonstrate a geometric-phase-based protocol which allows a 400-fold enhancement in static magnetic field range with a single NV-centre without reducing sensitivity.

Exploiting the intrinsic response of magic-angle twisted bilayer graphene to resonant terahertz radiation, the interplay between electron interactions and quantum geometry is studied in such flat-band systems.

Snake states describe electron trajectories that curve along an interface where the charge is inverted. Here, the authors investigate electronic transport in a ballistic graphene p–n junction and observe striking conductance oscillations that are a signature of these unusual states.

The quark structure of the f₀(980) hadron is still unknown after 50 years of its discovery. Here, the CMS Collaboration reports a measurement of the elliptic flow of the f₀(980) state in proton-lead collisions at a nucleon-nucleon centre-of-mass energy of 8.16 TeV, providing strong evidence that the state is an ordinary meson.

Potential electronic applications of graphene rely on controlling its spin-dependent properties. Here, the authors use spin-resolved photoemission spectroscopy to demonstrate how Au-intercalation produces gapped one-dimensional quasi-freestanding graphene on Fe(110) with tunable Fermi surface spin texture.

Unconventional topological states emerge in anisotropic perovskite microcavities via strong photonic Rashba-Dresselhaus coupling, enabling synthetic gauge fields and non-zero Berry curvature for advanced topological photonics and spinoptronics.

While topological states are often characterized by their global properties related to the topological invariants, the introduced real-space topological markers provide new insights to these states.

Polycrystalline thin films of elemental bismuth exhibit a room-temperature nonlinear transverse voltage due to geometric effects of surface electrons that is tunable and can be extended to efficient high-harmonic generation at terahertz frequencies.

Superlattices, with a length scale and structure that differs from the parent lattice of the host material, are well-known to allow for remarkable new electronic and magnetic properties. Here, Xie et al. synthesize Cr_1/4TaS₂, and find that it exhibits an unusual anomalous Hall effect below the Néel temperature even in stoichiometric high-quality crystals.

The connection between the topological properties of the ground state and non-equilibrium dynamics remains obscure. Here, Tarnowski et al. define and measure a linking number between static and dynamical vortices, which directly corresponds to the ground-state Chern number.

Manipulating the topological phases of quantum materials is necessary to fully leverage their potential for future electronics. Here, the authors experimentally demonstrate the controllable transition from a weak to a strong topological insulator phase through the in-situ application of high strain.

Exploitation of the valley electronic structure of transition metal dichalcogenides with exciton–polaritons is an elusive challenge. Now, valley-polarized exciton–polaritons in monolayers of MoS₂ have been demonstrated.

Experimental systems in which non-trivial topology is driven by spontaneous symmetry breaking are rare. Now, topological gaps resulting from two excitonic condensates have been demonstrated in a three-dimensional material.

Photonic metasurfaces can be used to control the polarization, phase and amplitude of light. Nonlinear metasurfaces enable giant nonlinear optical chirality, realization of the geometric Berry phase, wavefront engineering, and optical switching and modulation, and hold potential for on-chip applications.

This study explores reentrant topological behaviors in a 1D system of interacting fermionic atoms trapped in an optical lattice obtained by overlapping two commensurable superlattices. It reveals a series of trivial-topological transitions and a spin-density wave pattern influenced by the lattice’s structure and atomic interactions, which could be observed in cold-atom experiments in future experimental setups.

The quantum phase of a magnetic spin carrier can be electrically controlled via the Aharonov–Casher effect. Here, the authors isolate and handle the geometric-phase component independently from the dynamical one, allowing geometric manipulation of electron spins in a semiconductor ring array.

Manipulation of topology of the electronic structure is highly desirable for practical applications of topological materials. Here the authors demonstrate tuning and annihilation of Weyl nodes in momentum space by means of the Zeeman effect in a strongly correlated topological semimetal Ce₃Bi₄Pd₃.

The anomalous Hall effect is usually associated with ferromagnets but a large anomalous Hall response can be found in topologically non-trivial half-Heusler antiferromagnets thanks to Berry phase effects associated with symmetry breaking.

6G communication requires high-speed and advanced functionalities on-chip. Here the authors demonstrate broadband phototunable topological waveguide and demultiplexing chip with record single-channel 160 Gbit/s communication link and excellent channel isolation for 300 GHz band.