Intertwining exotic quantum order and nontrivial topology is at the frontier of condensed matter physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . A charge density wave (CDW) like order with orbital currents has been proposed as a powerful resource for topological states in the context of the quantum anomalous Hall effect 5,6 and for the hidden matter in the pseudogap phase of cuprate superconductors 7,8 . However, the experimental realization of such topological charge order is challenging. Here we use high-resolution scanning tunnelling microscopy (STM) to discover a topological charge order in a kagome superconductor 21-25 KV3Sb5. Through both lattice-sensitive topography and electronic-sensitive spectroscopic imaging, we observe a 2×2 superlattice, consistent with the star of David deformation in the underlying kagome lattice. Spectroscopically, an energy gap opens at the Fermi level, across which the charge modulation exhibits an intensity reversal, signaling a charge ordering. The strength of charge modulations further displays a clockwise or anticlockwise chiral anisotropy, which we demonstrate can be switched by an applied magnetic field. Our observations and theoretical analysis point to a topological charge order in the frustrated kagome lattice, which not only leads to a giant anomalous Hall effect, but can also be a strong precursor of unconventional superconductivity.

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 Co 2 MnGa. 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 our samples. Our experimental results suggest a rich interplay of strongly correlated electrons and topology in this quantum magnet.The discovery of topological phases of matter has led to a new paradigm in physics, 30 which not only explores the analogs of particles relevant for high energy physics, but also 31 offers new perspectives and pathways for the application of quantum materials [1][2][3][4][5][6][7][8][9][10]. To 32 date, most topological phases have been discovered in non-magnetic materials [6][7][8], which 33 severely limits their magnetic field tunability and electronic/magnetic functionality. Iden-34 tifying and understanding electronic topology in magnetic materials will not only provide 35 indispensable information to make their existing magnetic properties more robust, but also 36 has the potential to lead to the discovery of novel magnetic response that can be used to ex-37 plore future spintronics technology. Recently, several magnets were found to exhibit a large 38 anomalous Hall response in transport, which has been linked to a large Berry curvature in 39 their electronic structures [11][12][13][14][15]. However, it is largely unclear in experiment whether the 40 Berry curvature originates from a topological band structure, such as Dirac/Weyl point or 41 line nodes, due to the lack of spectroscopic investigation. In particular, there is no direct vi-42 sualization of a topological magnetic phase demonstrating a bulk-boundary correspondence 43 with associated anomalous transport. 44Here we use angle-resolved photoemission spectroscopy (ARPES), ab initio calculation 45 and transport to explore the electronic topological phase of the ferromagnet Co 2 MnGa [10]. 46In our ARPES spectra we discover a line node in the bulk of the sample. Taken together with 47 our ab initio calculations, we conclude that we observe Weyl lines protected by crystalline 48 mirror symmetry and requiring magnetic order. In ARPES we further observe drumhead 49 surface states connecting the bulk Weyl lines, revealing a bulk-boundary correspondence in a 50 magnet. Combining our ARPES and ab initio calculation results with transport, we further 51 find that Berry curvature concentrated by the Weyl lines accounts for the giant intrinsic 52 anomal...

It has long been speculated that electronic flatband systems can be a fertile ground for hosting novel emergent phenomena including unconventional magnetism and superconductivity 1-14 . Here we use scanning tunnelling microscopy to elucidate the atomically resolved electronic states and their magnetic response in the kagome magnet 15-20 Co3Sn2S2. We observe a pronounced peak at the Fermi level, which is identified to arise from the kinetically frustrated kagome flatband. Increasing magnetic field up to ±8T, this state exhibits an anomalous magnetization-polarized Zeeman shift, dominated by an orbital moment in opposite to the field direction. Such negative magnetism can be understood as spin-orbit coupling induced quantum phase effects 21-25 tied to non-trivial flatband systems. We image the flatband peak, resolve the associated negative magnetism, and provide its connection to the Berry curvature field, showing that Co3Sn2S2 is a rare example of kagome magnet where the low energy physics can be dominated by the spinorbit coupled flatband. Our methodology of probing band-resolved ordering phenomena such as spin-orbit magnetism can also be applied in future experiments to elucidate other exotic phenomena including flatband superconductivity and anomalous quantum transport.

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Kagome superconductors with T C up to 7 K have been discovered for over 40 y. Recently, unconventional chiral charge order has been reported in kagome superconductor KV 3 Sb 5 , with an ordering temperature of one order of magnitude higher than the T C . However, the chirality of the charge order has not been reported in the cousin kagome superconductor CsV 3 Sb 5 , and the electronic nature of the chirality remains elusive. In this paper, we report the observation of electronic chiral charge order in CsV 3 Sb 5 via scanning tunneling microscopy (STM). We observe a 2 × 2 charge modulation and a 1 × 4 superlattice in both topographic data and tunneling spectroscopy. 2 × 2 charge modulation is highly anticipated as a charge order by fundamental kagome lattice models at van Hove filling, and is shown to exhibit intrinsic chirality. We find that the 1 × 4 superlattices form various small domain walls, and can be a surface effect as supported by our first-principles calculations. Crucially, we find that the amplitude of the energy gap opened by the charge order exhibits real-space modulations, and features 2 × 2 wave vectors with chirality, highlighting the electronic nature of the chiral charge order. STM study at 0.4 K reveals a superconducting energy gap with a gap size 2 = 0.85 meV, which estimates a moderate superconductivity coupling strength with 2 /k B T C = 3.9. When further applying a c-axis magnetic field, vortex core bound states are observed within this gap, indicative of clean-limit superconductivity.

Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge density wave, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to nonkagome surface layers. Here, we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifies a 2 × 2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin mapping across steps of unit cell height demonstrates the existence of spin-polarized electrons with an antiferromagnetic stacking order. We further uncover the correlation between antiferromagnetism and charge order anisotropy, highlighting the unusual magnetic coupling of the charge order. Finally, we detect a pronounced edge state within the charge order energy gap, which is robust against the irregular shape fluctuations of the kagome lattice edges. We discuss our results with the theoretically considered topological features of the kagome charge order including unconventional magnetism and bulk-boundary correspondence.