Explore the vast range of titles available.

A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities can lead to instabilities towards long-range many-body orders, altogether allowing for the realization and discovery of a series of topological kagome magnets and superconductors with exotic properties. Recent progress in exploring kagome materials has revealed rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin and correlation. Here we review these key developments in this field, starting from the fundamental concepts of a kagome lattice, to the realizations of Chern and Weyl topological magnetism, to various flat-band many-body correlations, and then to the puzzles of unconventional charge-density waves and superconductivity. We highlight the connection between theoretical ideas and experimental observations, and the bond between quantum interactions within kagome magnets and kagome superconductors, as well as their relation to the concepts in topological insulators, topological superconductors, Weyl semimetals and high-temperature superconductors. These developments broadly bridge topological quantum physics and correlated many-body physics in a wide range of bulk materials and substantially advance the frontier of topological quantum matter. Recent key developments in the exploration of kagome materials are reviewed, including fundamental concepts of a kagome lattice, realizations of Chern and Weyl topological magnetism, flat-band many-body correlations, and unconventional charge-density waves and superconductivity.

Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics 1 – 4 . A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect 5 , 6 in topological materials and for the hidden phase in cuprate high-temperature superconductors 7 , 8 . However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV 3 Sb 5 , with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity. An unconventional chiral charge order is observed in a kagome superconductor by scanning tunnelling microscopy. This charge order has unusual magnetic tunability and intertwines with electronic topology.

Topological matter is known to exhibit unconventional surface states and anomalous transport owing to unusual bulk electronic topology. In this study, we use photoemission spectroscopy and quantum transport to elucidate the topology of the room temperature magnet Co₂MnGa. We observe sharp bulk Weyl fermion line dispersions indicative of nontrivial topological invariants present in the magnetic phase. On the surface of the magnet, we observe electronic wave functions that take the form of drumheads, enabling us to directly visualize the crucial components of the bulk-boundary topological correspondence. By considering the Berry curvature field associated with the observed topological Weyl fermion lines, we quantitatively account for the giant anomalous Hall response observed in this magnet. Our experimental results suggest a rich interplay of strongly interacting electrons and topology in quantum matter.

The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics 1 – 15 . Kagome magnets are predicted to support intrinsic Chern quantum phases owing to their unusual lattice geometry and breaking of time-reversal symmetry 14 , 15 . However, quantum materials hosting ideal spin–orbit-coupled kagome lattices with strong out-of-plane magnetization are lacking 16 – 21 . Here, using scanning tunnelling microscopy, we identify a new topological kagome magnet, TbMn 6 Sn 6 , that is close to satisfying these criteria. We visualize its effectively defect-free, purely manganese-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state shows distinct Landau quantization on application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk–boundary correspondence between the Chern gap and the topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn 6 Sn 6 , and may enable the observation of topological quantum phenomena in the RMn 6 Sn 6 (where R is a rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk–boundary–Berry correspondence covering real space and momentum space demonstrates a proof-of-principle method for revealing topological magnets. Scanning tunnelling microscopy is used to reveal a new topological kagome magnet with an intrinsic Chern quantum phase, which shows a distinct Landau fan structure with a large Chern gap.

A hallmark of strongly correlated quantum materials is the rich phase diagram resulting from competing and intertwined phases with nearly degenerate ground-state energies 1 , 2 . A well-known example is the copper oxides, in which a charge density wave (CDW) is ordered well above and strongly coupled to the magnetic order to form spin-charge-separated stripes that compete with superconductivity 1 , 2 . Recently, such rich phase diagrams have also been shown in correlated topological materials. In 2D kagome lattice metals consisting of corner-sharing triangles, the geometry of the lattice can produce flat bands with localized electrons 3 , 4 , non-trivial topology 5 – 7 , chiral magnetic order 8 , 9 , superconductivity and CDW order 10 – 15 . Although CDW has been found in weakly electron-correlated non-magnetic A V 3 Sb 5 ( A  = K, Rb, Cs) 10 – 15 , it has not yet been observed in correlated magnetic-ordered kagome lattice metals 4 , 16 – 21 . Here we report the discovery of CDW in the antiferromagnetic (AFM) ordered phase of kagome lattice FeGe (refs.  16 – 19 ). The CDW in FeGe occurs at wavevectors identical to that of A V 3 Sb 5 (refs.  10 – 15 ), enhances the AFM ordered moment and induces an emergent anomalous Hall effect 22 , 23 . Our findings suggest that CDW in FeGe arises from the combination of electron-correlations-driven AFM order and van Hove singularities (vHSs)-driven instability possibly associated with a chiral flux phase 24 – 28 , in stark contrast to strongly correlated copper oxides 1 , 2 and nickelates 29 – 31 , in which the CDW precedes or accompanies the magnetic order. Analysis of the antiferromagnetic ordered phase of kagome lattice FeGe suggests that charge density wave is the result of a combination of electronic-correlations-driven antiferromagnetic order and instability driven by van Hove singularities.

Chiral crystals are materials with a lattice structure that has a well-defined handedness due to the lack of inversion, mirror or other roto-inversion symmetries. Although it has been shown that the presence of crystalline symmetries can protect topological band crossings, the topological electronic properties of chiral crystals remain largely uncharacterized. Here we show that Kramers–Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin–orbit coupling and are guaranteed by structural chirality, lattice translation and time-reversal symmetry. Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. We identify representative chiral materials in 33 of the 65 chiral space groups in which Kramers–Weyl fermions are relevant to the low-energy physics. We determine that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin–orbit coupling carry non-trivial Chern numbers. Kramers–Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window.

Weyl semimetals provide the realization of Weyl fermions in solid-state physics. Among all the physical phenomena that are enabled by Weyl semimetals, the chiral anomaly is the most unusual one. Here, we report signatures of the chiral anomaly in the magneto-transport measurements on the first Weyl semimetal TaAs. We show negative magnetoresistance under parallel electric and magnetic fields, that is, unlike most metals whose resistivity increases under an external magnetic field, we observe that our high mobility TaAs samples become more conductive as a magnetic field is applied along the direction of the current for certain ranges of the field strength. We present systematically detailed data and careful analyses, which allow us to exclude other possible origins of the observed negative magnetoresistance. Our transport data, corroborated by photoemission measurements, first-principles calculations and theoretical analyses, collectively demonstrate signatures of the Weyl fermion chiral anomaly in the magneto-transport of TaAs. Anomalous conducting behavior of solids may reflect the presence of novel quantum states. Here, Zhang et al . report an increased conductivity in TaAs with a magnetic field applied along the direction of the current, which reveals an inherent property of the Weyl Fermion.

In today’s dynamic and competitive business landscape, innovation is paramount for companies striving to maintain a competitive edge. Among various innovation strategies, corporate green innovation has gained prominence as an efficient means of achieving sustainable growth. In response to the pressing need for sustainable development, this study investigates the bidirectional cointegration link between green innovation and overall corporate innovation in a panel dataset of Chinese-listed enterprises.As China emphasizes principles like \"greening\" and \"innovation\" for twenty-first-century development, this research aligns with the nation’s goal of fostering sustainable industry growth through \"green innovation”. It employs panel cointegration tests, including the Westerlund test, dynamic panel ordinary least square (DOLS), and the panel vector error correction model (VECM), using data from Chinese A-listed firms spanning from 2008 to 2020. The study reveals a robust long-term, bidirectional relationship between corporate innovation and green innovation. Notably, it demonstrates that green innovation causally impacts corporate innovation in both the short and long term. This research also conducts subsample analysis, ensuring the robustness of the main findings across both non-polluted and polluted industries. These findings provide valuable insights into how corporate innovation factors influence corporate green innovation. Consequently, they offer valuable insights for policymakers and organizations, aiding in the formulation of policies that promote environmentally friendly innovation while elevating corporate innovation standards.

Symmetry-broken three-dimensional (3D) topological Dirac semimetal systems with strong spin-orbit coupling can host many exotic Hall-like phenomena and Weyl fermion quantum transport. Here, using high-resolution angle-resolved photoemission spectroscopy, we performed systematic electronic structure studies on Cd 3 As 2 , which has been predicted to be the parent material, from which many unusual topological phases can be derived. We observe a highly linear bulk band crossing to form a 3D dispersive Dirac cone projected at the Brillouin zone centre by studying the (001)-cleaved surface. Remarkably, an unusually high in-plane Fermi velocity up to 1.5 × 10 6  ms −1 is observed in our samples, where the mobility is known up to 40,000 cm 2  V −1 s −1 , suggesting that Cd 3 As 2 can be a promising candidate as an anisotropic-hypercone (three-dimensional) high spin-orbit analogue of 3D graphene. Our discovery of the Dirac-like bulk topological semimetal phase in Cd 3 As 2 opens the door for exploring higher dimensional spin-orbit Dirac physics in a real material. Topological Dirac semimetals constitute a promising platform for the study of quantum Hall phenomena and Weyl fermion transport. Using high-resolution angle-resolved photoemission spectroscopy, Neupane et al. identify the topological bulk Dirac semimetal phase in a Cd 3 As 2 system.

Through intense research on Weyl semimetals during the past few years, we have come to appreciate that typical Weyl semimetals host many Weyl points. Nonetheless, the minimum nonzero number of Weyl points allowed in a time-reversal invariant Weyl semimetal is four. Realizing such a system is of fundamental interest and may simplify transport experiments. Recently, it was predicted that TaIrTe 4 realizes a minimal Weyl semimetal. However, the Weyl points and Fermi arcs live entirely above the Fermi level, making them inaccessible to conventional angle-resolved photoemission spectroscopy (ARPES). Here, we use pump-probe ARPES to directly access the band structure above the Fermi level in TaIrTe 4 . We observe signatures of Weyl points and topological Fermi arcs. Combined with ab initio calculation, our results show that TaIrTe 4 is a Weyl semimetal with the minimum number of four Weyl points. Our work provides a simpler platform for accessing exotic transport phenomena arising in Weyl semimetals. Weyl semimetals are interesting because they are characterized by topological invariants, but specific examples discovered to date tend to have complicated band structures with many Weyl points. Here, the authors show that TaIrTe 4 has only four Weyl points, the minimal number required by time-reversal symmetry.