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Lattice geometry, topological electron behaviour and the competition between different possible ground states all play a role in determining the properties of materials with a kagome lattice structure. In particular, the compounds KV 3 Sb 5 , CsV 3 Sb 5 and RbV 3 Sb 5 all feature a kagome net of vanadium atoms. These materials have recently been shown to exhibit superconductivity at low temperature and an unusual charge order at high temperature, revealing a connection to the underlying topological nature of the band structure. We highlight these discoveries, place them in the context of wider research efforts in topological physics and superconductivity, and discuss the open problems for this field. Superconductivity and ordered states formed by interactions—both of which could be unconventional—have recently been observed in a family of kagome materials.

The intricate interplay between non-trivial topology and magnetism in two-dimensional materials can lead to the emergence of interesting phenomena such as the quantum anomalous Hall effect. Here we investigate the quantum transport of both bulk crystal and exfoliated MnBi 2 Te 4 flakes in a field-effect transistor geometry. For the six septuple-layer device tuned into the insulating regime, we observe a large longitudinal resistance and zero Hall plateau, which are characteristics of an axion insulator state. The robust axion insulator state occurs in zero magnetic field, over a wide magnetic-field range and at relatively high temperatures. Moreover, a moderate magnetic field drives a quantum phase transition from the axion insulator phase to a Chern insulator phase with zero longitudinal resistance and quantized Hall resistance h / e 2 , where h is Planck’s constant and e is electron charge. Our results pave the way for using even-number septuple-layer MnBi 2 Te 4 to realize the quantized topological magnetoelectric effect and axion electrodynamics in condensed matter systems. A large longitudinal resistance and zero Hall plateau—hallmarks of an axion insulator—are found in MnBi 2 Te 4 . Moreover, a moderate magnetic field drives a quantum phase transition to a Chern insulator phase with zero longitudinal resistance and quantized Hall resistance h / e 2 .

Magnetic skyrmion textures are realized mainly in non-centrosymmetric, e.g. chiral or polar, magnets. Extending the field to centrosymmetric bulk materials is a rewarding challenge, where the released helicity/vorticity degree of freedom and higher skyrmion density result in intriguing new properties and enhanced functionality. We report here on the experimental observation of a skyrmion lattice (SkL) phase with large topological Hall effect and an incommensurate helical pitch as small as 2.8 nm in metallic Gd 3 Ru 4 Al 12 , which materializes a breathing kagomé lattice of Gadolinium moments. The magnetic structure of several ordered phases, including the SkL, is determined by resonant x-ray diffraction as well as small angle neutron scattering. The SkL and helical phases are also observed directly using Lorentz-transmission electron microscopy. Among several competing phases, the SkL is promoted over a low-temperature transverse conical state by thermal fluctuations in an intermediate range of magnetic fields. Understanding and controlling the skyrmion lattice (SkL) phase facilitates its versatile applications. Here the direct observation of a SkL phase with large topological Hall effect in centrosymmetric Gd 3 Ru 4 Al 12 is reported, which is stabilized by thermal fluctuations and magnetic field without Dzyaloshinskii-Moriya interactions.

Quantum materials hosting Weyl fermions have opened a new era of research in condensed matter physics. First proposed in 1929 in the context of particle physics, Weyl fermions have yet to be observed as elementary particles. In 2015, Weyl fermions were detected as collective electronic excitations in the strong spin–orbit coupled material tantalum arsenide, TaAs. This discovery was followed by a flurry of experimental and theoretical explorations of Weyl phenomena in materials. Weyl materials naturally lend themselves to the exploration of the topological index associated with Weyl fermions and their divergent Berry curvature field, as well as the topological bulk–boundary correspondence, giving rise to protected conducting surface states. Here, we review the broader class of Weyl topological phenomena in materials, starting with the observation of emergent Weyl fermions in the bulk and Fermi arc states on the surface of the TaAs family of crystals by photoemission spectroscopy. We then discuss several exotic optical and magnetic responses observed in these materials, as well as progress in developing related chiral materials. We discuss the conceptual development of high-fold chiral fermions, which generalize Weyl fermions, and we review the observation of high-fold chiral fermion phases by taking the rhodium silicide, RhSi, family of crystals as a prime example. Lastly, we discuss recent advances in Weyl line phases in magnetic topological materials. With this Review, we aim to provide an introduction to the basic concepts underlying Weyl physics in condensed matter, and to representative materials and their electronic structures and topology as revealed by spectroscopic studies. We hope this work serves as a guide for future theoretical and experimental explorations of chiral fermions and related topological quantum systems with potentially enhanced functionalities. Weyl fermions have yet to be observed as elementary particles but can be realized in topological quantum materials. This Review discusses the theoretical and experimental discovery of emergent Weyl fermions, high-fold chiral fermions, topological Weyl lines and related Dirac phases.

Semiconductors, featuring tunable electrical transport, and magnets, featuring tunable spin configurations, form the basis of many information technologies. A long-standing challenge has been to realize materials that integrate and connect these two distinct properties. Two-dimensional (2D) materials offer a platform to realize this concept, but known 2D magnetic semiconductors are electrically insulating in their magnetic phase. Here we demonstrate tunable electron transport within the magnetic phase of the 2D semiconductor CrSBr and reveal strong coupling between its magnetic order and charge transport. This provides an opportunity to characterize the layer-dependent magnetic order of CrSBr down to the monolayer via magnetotransport. Exploiting the sensitivity of magnetoresistance to magnetic order, we uncover a second regime characterized by coupling between charge carriers and magnetic defects. The magnetoresistance within this regime can be dynamically and reversibly tuned by varying the carrier concentration using an electrostatic gate, providing a mechanism for controlling charge transport in 2D magnets. A ferromagnetic transition in CrSBr is attributed to ordering of magnetic defects, and can be electrostatically manipulated.

Magnetic skyrmions are topologically protected whirling spin texture. Their nanoscale dimensions, topologically protected stability and solitonic nature, together are promising for future spintronics applications. To translate these compelling features into practical spintronic devices, a key challenge lies in achieving effective control of skyrmion properties, such as size, density and thermodynamic stability. Here, we report the discovery of ferroelectrically tunable skyrmions in ultrathin BaTiO3/SrRuO3 bilayer heterostructures. The ferroelectric proximity effect at the BaTiO3/SrRuO3 heterointerface triggers a sizeable Dzyaloshinskii–Moriya interaction, thus stabilizing robust skyrmions with diameters less than a hundred nanometres. Moreover, by manipulating the ferroelectric polarization of the BaTiO3 layer, we achieve local, switchable and nonvolatile control of both skyrmion density and thermodynamic stability. This ferroelectrically tunable skyrmion system can simultaneously enhance the integratability and addressability of skyrmion-based functional devices.

Topological states of quantum matter have been investigated intensively in recent years in materials science and condensed matter physics. The field developed explosively largely because of the precise theoretical predictions, well-controlled materials processing, and novel characterization techniques. In this Perspective, we review recent progress in topological insulators, the quantum anomalous Hall effect, chiral topological superconductors, helical topological superconductors and Weyl semimetals. This Perspective discusses recent progress in the field of topological states in condensed matter; initiated by the quantum Hall effect, it now includes systems like topological insulators, topological superconductors, and Weyl/Dirac semimetals.

The ground-state properties of correlated electron systems can be extraordinarily sensitive to external stimuli, offering abundant platforms for functional materials. Using the multi-messenger combination of atomic force microscopy, cryogenic scanning near-field optical microscopy, magnetic force microscopy and ultrafast laser excitation, we demonstrate both ‘writing’ and ‘erasing’ of a metastable ferromagnetic metal phase in strained films of La 2/3 Ca 1/3 MnO 3 (LCMO) with nanometre-resolved finesse. By tracking both optical conductivity and magnetism at the nanoscale, we reveal how strain-coupling underlies the dynamic growth, spontaneous nanotexture and first-order melting transition of this hidden photoinduced metal. Our first-principles calculations reveal that epitaxially engineered Jahn–Teller distortion can stabilize nearly degenerate antiferromagnetic insulator and ferromagnetic metal phases. We propose a Ginzburg–Landau description to rationalize the co-active interplay of strain, lattice distortions and magnetism nano-resolved here in strained LCMO, thus guiding future functional engineering of epitaxial oxides into the regime of phase-programmable materials. A multi-messenger combination of atomic force microscopy, scanning near-field optical microscopy and magnetic force microscopy demonstrates a strain-modulated photoinduced ferromagnetic metallic state in La 2/3 Ca 1/3 MnO 3 .

Non-coplanar spin textures with scalar spin chirality can generate an effective magnetic field that deflects the motion of charge carriers, resulting in a topological Hall effect (THE)1–3. However, spin chirality fluctuations in two-dimensional ferromagnets with perpendicular magnetic anisotropy have not been considered so far. Here, we report evidence of spin chirality fluctuations by probing the THE above the Curie temperature in two different ferromagnetic ultra-thin films, SrRuO3 and V-doped Sb2Te3. The temperature, magnetic field, thickness and carrier-type dependence of the THE signal, along with Monte Carlo simulations, suggest that spin chirality fluctuations are a common phenomenon in two-dimensional ferromagnets with perpendicular magnetic anisotropy. Our results open a path for exploring spin chirality with topological Hall transport in two-dimensional magnets and beyond4–7.

Weyl fermions were originally proposed as massless Dirac fermions in relativistic quantum field theory. In solids, Weyl fermions often appear when either time-reversal symmetry or spatial-inversion symmetry is broken, which lifts the Kramer’s degeneracy of Bloch states at each crystal momentum k . Weyl fermions in solids are characterized by two novel features: spin–momentum locking and a diverging Berry curvature corresponding to a magnetic monopole forming in momentum space. These two effects bring about many novel transport phenomena, magnetic excitations and nonlinear optical effects. In this Review, we discuss some of these phenomena in various systems, in particular, the anomalous Hall effect and magnon excitation in 3D metallic ferromagnets, transition-metal-oxide semiconductors and semimetals; the quantum anomalous Hall effect, axion insulator state and magnetic skyrmions at the 2D magnetic surface of topological insulators; and nonlinear phenomena in noncentrosymmetric Weyl materials. Weyl fermions in solids exhibit unique features such as spin–momentum locking and a diverging Berry curvature corresponding to a magnetic monopole in momentum space. This Review surveys the transport phenomena, magnetic excitations and nonlinear optical effects observed in these systems.