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Ongoing advances in superconductors continue to revolutionize technology thanks to the increasingly versatile and robust availability of lossless supercurrent. In particular high supercurrent density can lead to more efficient and compact power transmission lines, high-field magnets, as well as high-performance nanoscale radiation detectors and superconducting spintronics. Here, we report the discovery of an unprecedentedly high superconducting critical current density (17 MA/cm2 at 0 T and 7 MA/cm2 at 8 T) in 1T'-WS2, exceeding those of all reported two-dimensional superconductors to date. 1T'-WS2 features a strongly anisotropic (both in- and out-of-plane) superconducting state that violates the Pauli paramagnetic limit signaling the presence of unconventional superconductivity. Spectroscopic imaging of the vortices further substantiates the anisotropic nature of the superconducting state. More intriguingly, the normal state of 1T'-WS2 carries topological properties. The band structure obtained via angle-resolved photoemission spectroscopy and first-principles calculations points to a Z2 topological invariant. The concomitance of topology and superconductivity in 1T'-WS2 establishes it as a topological superconductor candidate, which is promising for the development of quantum computing technology.

Source data for "Observation of a linked-loop quantum state in a topological magnet" by I. Belopolski et al.

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena. Here, utilizing angle-resolved photoemission spectroscopy, we demonstrate Weyl lines with strong out-of-plane dispersion in an A-A stacked kagome magnet TbxGd1-xMn6Sn6. On the Gd rich side, the Weyl line remains nearly spin-orbit-gapless due to a remarkable cooperative interplay between Kane-Mele spin-orbit-coupling, low site symmetry and in-plane magnetic order. Under Tb substitution, the kagome Weyl line gaps due to a magnetic reorientation to out-of-plane order. Our results illustrate the magnetic moment direction as an efficient tuning knob for realizing distinct three-dimensional topological phases., Comment: 12 pages, 4 figures. Comments are welcome!

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state. Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids, magnets, the quantum Hall effect, topological insulators, Weyl semimetals and other phenomena. Here we report a remarkable linking number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet. Using state-of-the-art spectroscopic methods, we directly observe three intertwined degeneracy loops in the material's bulk Brillouin zone three-torus, $\mathbb{T}^3$. We find that each loop links each other loop twice. Through systematic spectroscopic investigation of this linked loop quantum state, we explicitly draw its link diagram and conclude, in analogy with knot theory, that it exhibits linking number $(2,2,2)$, providing a direct determination of the invariant structure from the experimental data. On the surface of our samples, we further predict and observe Seifert boundary states protected by the bulk linked loops, suggestive of a remarkable Seifert bulk-boundary correspondence. Our observation of a quantum loop link motivates the application of knot theory to the exploration of exotic properties of quantum matter., See popular summary at https://research.princeton.edu/news/electrons-crystal-exhibit-linked-and-knotted-quantum-twists

Room-temperature realization of macroscopic quantum phenomena is one of the major pursuits in fundamental physics. The quantum spin Hall state, a topological quantum phenomenon that features a two-dimensional insulating bulk and a helical edge state, has not yet been realized at room temperature. Here, we use scanning tunneling microscopy to visualize a quantum spin Hall edge state on the surface of the higher-order topological insulator Bi4Br4. We find that the atomically resolved lattice exhibits a large insulating gap of over 200meV, and an atomically sharp monolayer step edge hosts a striking in-gap gapless state, suggesting the topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent to the underlying topology. We further identify the geometrical hybridization of such edge states, which not only attests to the Z2 topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Remarkably, both the insulating gap and topological edge state are observed to persist up to 300K. Our results point to the realization of the room-temperature quantum spin Hall edge state in a higher-order topological insulator.

Superconductors with kagome lattices have been identified for over 40 years, with a superconducting transition temperature TC up to 7K. Recently, certain kagome superconductors have been found to exhibit an exotic charge order, which intertwines with superconductivity and persists to a temperature being one order of magnitude higher than TC. In this work, we use scanning tunneling microscopy (STM) to study the charge order in kagome superconductor RbV3Sb5. We observe both a 2x2 chiral charge order and nematic surface superlattices (predominantly 1x4). We find that the 2x2 charge order exhibits intrinsic chirality with magnetic field tunability. Defects can scatter electrons to introduce standing waves, which couple with the charge order to cause extrinsic effects. While the chiral charge order resembles that discovered in KV3Sb5, it further interacts with the nematic surface superlattices that are absent in KV3Sb5 but exist in CsV3Sb5.

Kagome superconductors with TC up to 7 K have been discovered for over 40 y. Recently, unconventional chiral charge order has been reported in kagome superconductor KV3Sb5, with an ordering temperature of one order of magnitude higher than the TC. However, the chirality of the charge order has not been reported in the cousin kagome superconductor CsV3Sb5, and the electronic nature of the chirality remains elusive. In this paper, we report the observation of electronic chiral charge order in CsV3Sb5 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. Cru- cially, 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􏰀/kBTC = 3.9. When further applying a c-axis magnetic field, vortex core bound states are observed within this gap, indicative of clean-limit superconductivity. Nanyang Technological University National Research Foundation (NRF) Accepted version The work at Beijing Institute of Technology was sup- ported by the National Key R&D Program of China (Grant No. 2020YFA0308800), the Natural Science Foun- dation of China (Grants No. 92065109, No. 11734003, and No. 12061131002), the Beijing Natural Science Foundation (Grant No. Z190006), and the Beijing Institute of Technology (BIT) Research Fund Program for Young Scholars (Grant No. 3180012222011). Z.W. thanks the Analysis & Testing Center at BIT for assistance in facility support. Experimental and theoretical work at Princeton University was supported by the Gordon and Betty Moore Foundation [Grants No. GBMF4547 and No. GBMF9461 (M.Z.H.)]. Y.S. was supported by the National Natural Science Foundation of China (Grant No. U2032204), and the K. C. Wong Education Foundation (Grant No. GJTD-2018-01). G.C. would like to acknowledge the support of the National Research Foundation, Singapore under its NRF Fellowship Award No. NRF-NRFF13-2021- 0010 and the Nanyang Assistant Professorship grant from Nanyang Technological University. P.D. is supported the U.S. Department of Energy (DOE), Basic Energy Sciences (BES), under Contract No. DE-SC0012311. S.S. and Y.W. were supported by the National Natural Science Foundation of China under Grants No. 11822404 and No. 11774127.

Superconductors with kagome lattices have been identified for over 40 years, with a superconducting transition temperature TC up to 7K. Recently, certain kagome superconductors have been found to exhibit an exotic charge order, which intertwines with superconductivity and persists to a temperature being one order of magnitude higher than TC. In this work, we use scanning tunneling microscopy (STM) to study the charge order in kagome superconductor RbV3Sb5. We observe both a 2×2 chiral charge order and nematic surface superlattices (predominantly 1×4). We find that the 2×2 charge order exhibits intrinsic chirality with magnetic field tunability. Defects can scatter electrons to introduce standing waves, which couple with the charge order to cause extrinsic effects. While the chiral charge order resembles that discovered in KV3Sb5, it further interacts with the nematic surface superlattices that are absent in KV3Sb5 but exist in CsV3Sb5. Nanyang Technological University National Research Foundation (NRF) Accepted version Experimental and theoretical work at Princeton University was supported by the Gordon and Betty Moore Foundation (GBMF4547 and GBMF9461; M.Z.H.). The material characterization is supported by the United States Department of Energy (US DOE) under the Basic Energy Sciences programme (grant number DOE/BES DE-FG-02-05ER46200). S.D.W. and B.R.O. acknowledge support from the University of California Santa Barbara Quantum Foundry, funded by the National Science Foundation (NSF DMR-1906325). Research reported here also made use of shared facilities of the UCSB MRSEC (NSF DMR-1720256). B.R.O. also acknowledges support from the California NanoSystems Institute through the Elings fellowship program. T.A.C. was supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1656466. H.C.L. was supported by National Natural Science Foundation of China (Grant No. 11822412 and 11774423), Ministry of Science and Technology of China (Grant No. 2018YFE0202600 and 2016YFA0300504) and Beijing Natural Science Foundation (Grant No. Z200005). Y.S. was supported by the National Natural Science Foundation of China (U2032204), and the K. C. Wong Education Foundation (GJTD-2018-01). G.C. would like to acknowledge the support of the National Research Foundation, Singapore under its NRF Fellowship Award (NRFNRFF13-2021-0010) and the Nanyang Assistant Professorship grant from Nanyang Technological University

Kagome superconductors with Tc up to 7K have been discovered over 40 years. Recently, unconventional chiral charge order has been reported in kagome superconductor KV3Sb5, with an ordering temperature of one order of magnitude higher than the TC. However, the chirality of the charge order has not been reported in the cousin kagome superconductor CsV3Sb5, and the electronic nature of the chirality remains elusive. In this letter, we report the observation of electronic chiral charge order in CsV3Sb5 via scanning tunneling microscopy (STM). We observe a 2x2 charge modulation and a 1x4 superlattice in both topographic data and tunneling spectroscopy. 2x2 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 1x4 superlattices forms 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 2x2 wave vectors with chirality, highlighting the electronic nature of the chiral charge order. STM study at 0.4K reveals a superconducting energy gap with a gap size 2{\Delta}=0.85meV, which estimates a moderate superconductivity coupling strength with 2{\Delta}/kBTc=3.9. When further applying a c-axis magnetic field, vortex core bound states are observed within this gap, indicative of clean-limit superconductivity.

Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect in topological materials and for the hidden phase in cuprate high-temperature superconductors. 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, KV3Sb5, 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. Nanyang Technological University National Research Foundation (NRF) Accepted version We thank Q Wang for stimulating discussions. Experimental and theoretical work at Princeton University was supported by the Gordon and Betty Moore Foundation (GBMF4547 and GBMF9461; M.Z.H.). The material characterization is supported by the US Department of Energy under the Basic Energy Sciences programme (grant no. DOE/BES DE-FG-02-05ER46200). S.D.W. and B.R.O. acknowledge support from the University of California Santa Barbara Quantum Foundry, funded by the National Science Foundation (NSF DMR-1906325). Research reported here also made use of shared facilities of the Materials Research Science and Engineering Center (MRSEC) at University of California Santa Barbara (NSF DMR-1720256). B.R.O. also acknowledges support from the California NanoSystems Institute through the Elings fellowship programme. R.T. is funded by the Deutsche Forschungsgemeinschaft (German Research Foundation) through project ID 258499086 – SFB 1170 and through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (ct.qmat) project ID 390858490 – EXC 2147. T.N. acknowledges supports from the European Union’s Horizon 2020 research and innovation programme (ERC-StG-Neupert-757867-PARATOP). Work at Boston College was supported by the US Department of Energy, Basic Energy Sciences grant number DE-FG02-99ER45747. T.A.C. was supported by the National Science Foundation Graduate Research Fellowship Program under grant no. DGE-1656466. Research conducted at the Center for High Energy X-ray Sciences is supported by the National Science Foundation under award DMR-1829070. G.C. would like to acknowledge the support of the National Research Foundation, Singapore under its Fellowship Award (NRF-NRFF13-2021-0010) and the Nanyang Assistant Professorship grant from Nanyang Technological University. G.X. was supported by the National Key Research and Development Program of China (2018YFA0307000) and the National Natural Science Foundation of China (11874022).

Intertwining quantum order and nontrivial topology is at the frontier of condensed matter physics. A charge density wave (CDW) like order with orbital currents has been proposed as a powerful resource for achieving the quantum anomalous Hall effect in topological materials and for the hidden phase in cuprate high-temperature superconductors. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy (STM) to discover an unconventional charge order in a kagome material KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2x2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2x2 charge modulation exhibits an intensity reversal in real-space, signaling charge ordering. At 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 CDW in the frustrated kagome lattice, which can not only lead to large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity., Orbital magnetism calculation added

Quantum states induced by single-atomic impurities are at the frontier of physics and material science. While such states have been reported in high-temperature superconductors and dilute magnetic semiconductors, they are unexplored in topological magnets which can feature spin-orbit tunability. Here we use spin-polarized scanning tunneling microscopy/spectroscopy (STM/S) to study the engineered quantum impurity in a topological magnet Co3Sn2S2. We find that each substituted In impurity introduces a striking localized bound state. Our systematic magnetization-polarized probe reveals that this bound state is spin-down polarized, in lock with a negative orbital magnetization. Moreover, the magnetic bound states of neighboring impurities interact to form quantized orbitals, exhibiting an intriguing spin-orbit splitting, analogous to the splitting of the topological fermion line. Our work collectively demonstrates the strong spin-orbit effect of the single-atomic impurity at the quantum level, suggesting that a nonmagnetic impurity can introduce spin-orbit coupled magnetic resonance in topological magnets., To appear in Nature Communications (2020), both experiment and theory included. arXiv admin note: text overlap with arXiv:2002.11783

Superconducting materials exhibiting topological properties are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. In this letter, we explore the possibility of a field-free platform for generating Majorana zero energy excitations by depositing magnetic Fe impurities on the surface of candidate topological superconductors, LiFeAs and PbTaSe2. We use scanning tunneling microscopy to probe localized states induced at the Fe adatoms on the atomic scale and at sub-Kelvin temperatures. We find that each Fe adatom generates a striking zero-energy bound state inside the superconducting gap, which do not split in magnetic fields up to 8 T, underlining a nontrivial topological origin. Our findings point to magnetic Fe adatoms evaporated on bulk superconductors with topological surface states for exploring Majorana zero modes and quantum information science under field-free conditions.

Quantum states induced by single-atomic-impurities are the current frontier of material and information science. Recently the spin-orbit coupled correlated kagome magnets are emerging as a new class of topological quantum materials, although the effect of single-atomic impurities remains unexplored. Here we use state-of-the-art scanning tunneling microscopy/spectroscopy (STM/S) to study the atomic indium impurity in a topological kagome magnet Co3Sn2S2, which is designed to support the spin-orbit quantum state. We find each impurity features a strongly localized bound state. Our systematic magnetization-polarized tunneling probe reveals its spin-down polarized nature with an unusual moment of -5uB, indicative of additional orbital magnetization. As the separation between two impurities progressively shrinks, their respective bound states interact and form quantized molecular orbital states. The molecular orbital of three neighboring impurities further exhibits an intriguing splitting owing to the combination of geometry, magnetism, and spin-orbit coupling, analogous to the splitting of the topological Weyl fermion line12,19. Our work demonstrates the quantum-level interplay between magnetism and spin-orbit coupling at an individual atomic impurity, which provides insights into the emergent impurity behavior in a topological kagome magnet and the potential of spin-orbit quantum impurities for information science.

The quantum level interplay between geometry, topology, and correlation is at the forefront of fundamental physics. Owing to the unusual lattice geometry and breaking of time-reversal symmetry, kagome magnets are predicted to support intrinsic Chern quantum phases. However, quantum materials hosting ideal spin-orbit coupled kagome lattices with strong out-of-plane magnetization have been lacking. Here we use scanning tunneling microscopy to discover a new topological kagome magnet TbMn6Sn6, which is close to satisfying the above criteria. We visualize its effectively defect-free purely Mn-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state exhibits distinct Landau quantization upon the 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 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 TbMn6Sn6, opening up an avenue for discovering topological quantum phenomena in the RMn6Sn6 (R = rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk-boundary-Berry correspondence covering real and momentum space demonstrates a proof-of-principle method revealing topological magnets., Comment: To appear in Nature (2020)

Superconducting materials exhibiting topological properties are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. In this work, we explore the possibility of a field-free platform for generating Majorana zero energy excitations by depositing magnetic Fe impurities on the surface of candidate topological superconductors, LiFeAs and PbTaSe$_2$. We use scanning tunneling microscopy to probe localized states induced at the Fe adatoms on the atomic scale and at sub-Kelvin temperatures. We find that each Fe adatom generates a striking zero-energy bound state inside the superconducting gap, which do not split in magnetic fields up to 8T, underlining a nontrivial topological origin. Our findings point to magnetic Fe adatoms evaporated on bulk superconductors with topological surface states as a new platform for exploring Majorana zero modes and quantum information science under field-free conditions., 11 pages, 3 figures

The quantum behaviour of electrons in materials lays the foundation for modern electronic and information technology. Quantum materials with novel electronic and optical properties have been proposed as the next frontier, but much remains to be discovered to actualize the promise. Here we report the first observation of topological quantum properties of chiral crystals in the RhSi family. We demonsrate that this material hosts novel phase of matter exhibiting nearly ideal topological surface properties that emerge as a consequence of the crystals' structural chirality or handedness. We also demonstrate that the electrons on the surface of this crystal show a highly unusual helicoid structure that spirals around two high-symmetry momenta signalling its topological electronic chirality. Such helicoid Fermi arcs on the surface experimentally characterize the topological charges of $\pm{2}$, which arise from the bulk chiral fermions. The existence of bulk high-fold degenerate fermions are guaranteed by the crystal symmetries, however, in order to determine the topological charge in the chiral crystals it is essential to identify and study the helical arc states. Remarkably, these topological conductors we discovered exhibit helical Fermi arcs which are of length $\pi$, stretching across the entire Brillouin zone and orders of magnitude larger than those found in all known Weyl semimetals. Our results demonstrate novel electronic topological state of matter on a structurally chiral crystal featuring helicoid Fermi arc surface states. The exotic electronic chiral fermion state realised in these materials can be used to detect a quantised photogalvanic optical response or the chiral magnetic effect and its optical version in future devices as described by G. Chang \textit{et.al.,} `Topological quantum properties of chiral crystals' Nature Mat. 17, 978-985 (2018)., Comment: 28 pages, 12 figures