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.

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The kagome lattice1, which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders2, 3,4,5,6,7,8 and, most rarely, to unconventional su-perconductivity6,9. Recently, charge sensitive probes have indicated that the kagome superconductors AV3Sb5 (A = K, Rb, Cs)9,10,11 exhibit unconventional chiral charge order12, 13,14,15,16,17,18,19, which is analogous to the long-sought-after quantum order in the Haldane model20 or Varma model21. However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV3Sb5. We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV3Sb5 and that the Tc/−2ab ratio (where Tc is the superconducting transition temperature and ab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.

Abstract:A robust zero-energy bound state (ZBS) in a superconductor, such as a Majorana or Andreev bound state, is often a consequence of non-trivial topological or symmetry related properties, and can provide indispensable information about the superconducting state. Here we use scanning tunneling microscopy/spectroscopy to demonstrate, on the atomic scale, that an isotropic ZBS emerges at the randomly distributed interstitial excess Fe sites in the superconducting Fe(Te,Se). This ZBS is localized with a short decay length of ~ 10 Å, and surprisingly robust against a magnetic field up to 8 Tesla, as well as perturbations by neighboring impurities. We find no natural explanation for the observation of such a robust zero-energy bound state, indicating a novel mechanism of impurities or an exotic pairing symmetry of the iron-based superconductivity.Main Text: Superconductivity arises from the macroscopic quantum condensation of electron pairs. The symmetry of the wave-function of these pairs is one of the most essential aspects of the microscopic pairing mechanism. Since the impurity-induced local density of states (DOS) is sensitive to the pairing symmetry, it can be used to test the symmetry of the order parameter and to probe the microscopic pairing mechanism. Being a local probe with atomic resolution, scanning tunneling microscopy/spectroscopy (STM/S) (1) has played a key role in this respect, especially in the study of high-TC cuprate superconductors (2,3).Since its discovery, new compounds of iron-based superconductor (IBSC) continue to be found. However, the pairing symmetry remains a central unresolved issue. So far,

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 KV3Sb5, CsV3Sb5 and RbV3Sb5 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.

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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.

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 of Fermi arc states on the surface of the TaAs family of crystals by photoemission spectroscopy. We then discuss some of the exotic optical and magnetic responses observed in these materials, as well as the progress in developing some of the 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.