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Fe₃Sn₂ hosts massive Dirac fermions, owing to the underlying symmetry properties of the bilayer kagome lattice in the ferromagnetic state and the atomic spin–orbit coupling.

Two studies show evidence that single layers of a transition metal dichalcogenide are two-dimensional topological insulators.

Experiments that directly probe the quantum geometric tensor in solids have not been reported. Now, the quantum metric and spin Berry curvature—dual components of the quantum geometric tensor—have been simultaneously measured in reciprocal space.

Electrons in f orbitals can create localized states that interact strongly and drive strange metal and critical behaviour via the Kondo mechanism. Now a mechanism of geometric frustration enables similar phenomena with d electrons.

Angle-resolved photoemission spectroscopy of CaNi₂ shows a band with vanishing dispersion across the full 3D Brillouin zone that is identified with the pyrochlore flat band as well as two additional flat bands that arise from multi-orbital interference of Ni d-electrons.

A prototypical kagome metal with magnetic and topological properties is identified.

Transition metal kagome compounds have been shown to host flat bands in their bulk electronic spectrum. Here, using planar tunnelling spectroscopy supported by first-principles calculations, the authors report the signature of a novel type of flat band at the surface of antiferromagnetic kagome metal FeSn.

Employing nonlinear, time-resolved terahertz spectroscopy to study condensate dynamics on Ta₂NiSe₅—a narrow-bandgap semiconductor and putative excitonic insulator—the authors reveal enhanced terahertz reflectivity upon photoexcitation and condensation-like temperature dependence below the structural transition critical temperature.

The kagome lattice is increasingly known as a host for correlated topological electronic states. Here, Ye et al. report quantum de Haas-van Alphen oscillations of a ferromagnetic kagome material Fe3Sn2, where bulk electronic Dirac fermions are found to be modulated by rotation of the magnetic moment.

Doping a topological insulator with manganese makes it magnetic. Moreover, decreasing the concentration of Dirac fermions in a Mn-doped topological insulator with an electric field increases the strength of its magnetic characteristics—a trait that could be valuable to the use of topological insulators in the development of spintronics.

The authors develop a high-spatial-resolution photoemission technique to show variation of the energy of the Dirac point of approximately 50 meV. They also find an interplay between bulk and surface states.

The authors use high-resolution angle-resolved photoemission spectroscopy to determine the microscopic structure of three-dimensional charge order in AV₃Sb₅ (A = K, Rb, Cs) and its interplay with superconductivity.

The experimental realization of lattice-born flat bands with nontrivial topology has been elusive. Here, the authors observe topological flat bands near the Fermi level in a kagome metal CoSn, with flat bands as well as Dirac bands originating from 3d orbitals in a frustrated kagome geometry.

Flat-band materials such as kagome and moiré lattices and strongly correlated electron systems including heavy-fermion compounds exhibit strikingly similar phenomena of topology and strong correlations. This Perspective article discusses Kondo physics as the underlying theme and a route to a unified understanding.

Helical Dirac fermions are charge carriers that behave as massless relativistic particles with an intrinsic angular momentum (spin) locked to their translational momentum, a property desirable for spintronic and computing technologies. It has recently been proposed that such fermions may exist at the edges of certain types of topologically ordered insulators. Here, the realization and characterization of such a system is reported; the results reveal nearly 100 per cent spin polarization, even up to room temperature.

Moiré materials are an emerging class of strongly correlated quantum materials designed by the rotational or lattice misalignment of 2D crystals. This Review discusses how local probe techniques are uniquely positioned to elucidate the microscopic mechanisms underlying the electronic phases in moiré materials.