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A hallmark of strongly correlated quantum materials is the rich phase diagram resulting from competing and intertwined phases with nearly degenerate ground-state energies

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics

Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics1–4. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect5,6 in topological materials and for the hidden phase in cuprate high-temperature superconductors7,8. 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, 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. 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.

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. National Research Foundation (NRF) Submitted/Accepted version M.Z.H. acknowledges support from the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center and Princeton University. M.Z.H. acknowledges visiting scientist support at Berkeley Lab (Lawrence Berkeley National Laboratory) during the early phases of this work. Theoretical and STM works at Princeton University was supported by the Gordon and Betty Moore Foundation (GBMF9461; GBMF4547; M.Z.H.). The theoretical work including ARPES were supported by the US DOE under the Basic Energy Sciences program (grant number DOE/BES DE-FG-02-05ER46200; M.Z.H.). T.-R.C. was supported by the Young Scholar Fellowship Program under a MOST grant for the Columbus Program, MOST111-2636-M-006-014, the Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at the National Cheng Kung University (NCKU), the National Center for Theoretical Sciences (Taiwan). The work at Rice was supported by US NSF-DMR-2100741, the Robert A. Welch Foundation under grant no. C-1839, C-2024, and No. C-1411, the U.S. Department Of Energy (DOE) grant no. DE-SC0021421 and No. DE-SC0018197, and the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant no. GBMF9470. The work at Nanyang Technological University was supported by the National Research Foundation, Singa- pore under its Fellowship Award (NRF-NRFF13-2021-0010). T.N. acknowledges support from the European Union’s Horizon 2020 research and innovation programme (ERC-StG-Neupert-757867-PARATOP). G. X. acknowledges support from the National Key Research and Development Program of China (2018YFA0307000), and the National Natural Science Foundation of China (11874022).

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization and spin-orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle-resolved photoemission spectroscopy, we directly visualize the Weyl lines with strong out-of-plane dispersion in the A-A stacked kagome magnet GdMn6Sn6. Remarkably, the Weyl lines exhibit a strong magnetization-direction tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. Our results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct three-dimensional topological phases, but also demonstrate AMn6Sn6 (A = rare earth or Li, Mg, Ca) as a versatile material family for exploring diverse emergent topological quantum responses. Nanyang Technological University National Research Foundation (NRF) Submitted/Accepted version The material characterization (ARPES) is supported by the United States Department of Energy (US DOE) under the Basic Energy Sciences program (Grant No. DOE/BES DE‐FG‐02‐05ER46200). This research used resources of the Advanced Light Source (ALS), a DOE Office of Science User Facility under contract number DE‐AC02‐05CH11231. Use of the Stanford Synchrotron Radiation Light Source (SSRL), SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract no. DE‐AC02‐76SF00515. The authors acknowledge the Paul Scherrer Institut, Villigen, Switzerland, for provision of synchrotron radiation beamtime at the ADRESS beamline of the Swiss Light Source. The authors thank Donghui Lu and Makoto Hashimoto at Beamline 5.2 of the SSRL for support. The authors thank C. Polley, J. Adell, and B. Thiagarajan at Beamline Bloch of the Max IV, Lund, Sweden, for support. The authors also want to thank J. Denlinger at Beamline 4.0.3 (MERLIN) of the ALS for support in getting the preliminary data. The authors also acknowledge the use of Princeton University's Imaging and Analysis Center, which is partially supported by the Princeton Center for Complex Materials (PCCM), a National Science Foundation (NSF)‐MRSEC program (DMR‐2011750). I.B. acknowledges the generous support of the Special Postdoctoral Researchers Program, RIKEN during the late stages of this work. T.A.C. acknowledges the support of the National Science Foundation Graduate Research Fellowship Program (DGE‐1656466). B.L. is supported by the Alfred P. Sloan Foundation, the National Science Foundation through Princeton University's Materials Research Science and Engineering Center (DMR‐2011750), and the National Science Foundation under award DMR‐2141966. G.C. would like to acknowledge the support of the National Research Foundation, Singapore, under its NRF Fellowship Award (NRF‐NRFF13‐2021‐0010), and the Nanyang Assistant Professorship grant from Nanyang Technological University. T.‐R.C. was supported by the 2030 Cross‐Generation Young Scholars Program from the National Science and Technology Council (NSTC) in Taiwan (Program No. MOST111‐2628‐M‐006‐003‐MY3), National Cheng Kung University (NCKU), Taiwan, and National Center for Theoretical Sciences, Taiwan. This research was supported, in part, by Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at NCKU. The work in Peking University was supported by CAS Interdisciplinary Innovation Team, the strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), and the National Natural Science Foundation of China (Grant Nos. 12141002 and 12225401). N.B.M.S. was partially supported by Microsoft. The work was also supported partially by the European Research Council (ERC Advanced Grant No. 742068 “TOPMAT”), the DFG through SFB 1143 (Project ID. 247310070), and the Würzburg‐Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC2147, Project ID. 390858490). M.Z.H. acknowledges the support from Lawrence Berkeley National Laboratory and the Miller Institute of Basic Research in Science at the University of California, Berkeley, in the form of a Visiting Miller Professorship during the early stage of this work.

Topological insulators with intrinsic magnetic order are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. To study these systems and their physics, people have proposed a variety of magnetic topological insulator systems, including HoSbTe, an antiferromagnetic weak topological insulator candidate. In this work, we use scanning tunneling microscopy to probe the electronic structure of HoSbTe with antiferromagnetic and ferromagnetic orders that are tuned by applying an external magnetic field. Although around the Fermi energy, we find minor differences between the quasi-particle interferences under the ferromagnetic and antiferromagnetic orders, deep inside the valance region, a new quasi-particle interference signal emerges with ferromagnetism. This observation is consistent with our first-principles calculations indicating the magnetism-driven transition of the electronic states in this spin-orbit coupled topological magnet., Comment: 13 pages, 7 figures

Kagome lattices host flat bands due to their frustrated lattice geometry, which leads to destructive quantum interference of electron wave functions. Here, we report imaging of the kagome flat band localization in real-space using scanning tunneling microscopy. We identify both the Fe3Sn kagome lattice layer and the Sn2 honeycomb layer with atomic resolution in kagome antiferromagnet FeSn. On the Fe3Sn lattice, at the flat band energy determined by the angle resolved photoemission spectroscopy, tunneling spectroscopy detects an unusual state localized uniquely at the Fe kagome lattice network. We further show that the vectorial in-plane magnetic field manipulates the spatial anisotropy of the localization state within each kagome unit cell. Our results are consistent with the real-space flat band localization in the magnetic kagome lattice. We further discuss the magnetic tuning of flat band localization under the spin-orbit coupled magnetic kagome lattice model., Comment: To appear in Communications Materials

Author(s): Wang, Z; Jiang, YX; Yin, JX; Li, Y; Wang, GY; Huang, HL; Shao, S; Liu, J; Zhu, P; Shumiya, N; Hossain, MS; Liu, H; Shi, Y; Duan, J; Li, X; Chang, G; Dai, P; Ye, Z; Xu, G; Wang, Y; Zheng, H; Jia, J; Hasan, MZ; Yao, Y | Abstract: 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. 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 2Δ=0.85meV, which estimates a moderate superconductivity coupling strength with 2Δ/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

Elucidating the symmetry of intertwined orders in exotic superconductors is at the quantum frontier. Recent surface sensitive studies of the topological kagome superconductor CsV$_3$Sb$_5$ discovered a cascade 4a$_0$ superlattice below the charge density wave (CDW) ordering temperature, which can be related to the pair density modulations in the superconducting state. If the 4a$_0$ phase is a bulk and intrinsic property of the kagome lattice, this would form a striking analogy to the stripe order and pair density wave discovered in the cuprate high-temperature superconductors, and the cascade ordering found in twisted bilayer graphene. High-resolution X-ray diffraction has recently been established as an ultra-sensitive probe for bulk translational symmetry-breaking orders, even for short-range orders at the diffusive limit. Here, combining high-resolution X-ray diffraction, scanning tunneling microscopy and scanning transmission electron microscopy, we demonstrate that the 4a$_0$ superstructure emerges uniquely on the surface and hence exclude the 4a$_0$ phase as the origin of any bulk transport or spectroscopic anomaly. Crucially, we show that our detected 2$\times$2$\times$2 CDW order breaks the bulk rotational symmetry to C2, which can be the driver for the bulk nematic orders and nematic surface superlattices including the 4a$_0$ phase. Our high-resolution data impose decisive spatial symmetry constraints on emergent electronic orders in the kagome superconductor CsV$_3$Sb$_5$.

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., Single-atomic impurities may induce novel quantum state, but they are unexplored in topological magnets. Here, the authors report spin-down polarized bound states which further interact with neighboring states to form spin-orbit split quantized orbitals in a topological magnet Co3Sn2S2.

Kagome-net, appearing in areas of fundamental physics, materials, photonic and cold-atom systems, hosts frustrated fermionic and bosonic excitations. However, it is extremely rare to find a system to study both fermionic and bosonic modes to gain insights into their many-body interplay. Here we use state-of-the-art scanning tunneling microscopy and spectroscopy to discover unusual electronic coupling to flat-band phonons in a layered kagome paramagnet. Our results reveal the kagome structure with unprecedented atomic resolution and observe the striking bosonic mode interacting with dispersive kagome electrons near the Fermi surface. At this mode energy, the fermionic quasi-particle dispersion exhibits a pronounced renormalization, signaling a giant coupling to bosons. Through a combination of self-energy analysis, first-principles calculation, and a lattice vibration model, we present evidence that this mode arises from the geometrically frustrated phonon flat-band, which is the lattice analog of kagome electron flat-band. Our findings provide the first example of kagome bosonic mode (flat-band phonon) in electronic excitations and its strong interaction with fermionic degrees of freedom in kagome-net materials., Comment: To appear in Nature Communications (2020)

A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However existing results suggest that such an enhancement is only possible when the measurement efficiency exceeds 0.5, which is difficult to achieve experimentally. We address the task of finding the global optimal feedback control for purifying a single qubit in the presence of measurement inefficiency. We use the Bloch vector length, a more physical and practical quantity than purity, to assess the quality of the state, and employ a backward iteration algorithm to find the globally optimal strategy. Our results show that a speedup is available for quantum efficiencies well below 0.5, which opens the possibility of experimental implementation in existing systems., 9 pages, 5 figures

Three types of fermions have been extensively studied in topological quantum materials: Dirac, Weyl, and Majorana fermions. Beyond the fundamental fermions in high energy physics, exotic fermions are allowed in condensed matter systems residing in three-, six- or eightfold degenerate band crossings. Here, we use angle-resolved photoemission spectroscopy to directly visualize three-doubly-degenerate bands in $\mathrm{PdS}{\mathrm{b}}_{2}$. The ultrahigh energy resolution we are able to achieve allows for the confirmation of all the sixfold degenerate bands at the $R$ point, in remarkable consistency with first-principles calculations. Moreover, we find that this sixfold degenerate crossing has quadratic dispersion as predicted by theory. Finally, we compare sixfold degenerate fermions with previously confirmed fermions to demonstrate the importance of this work: our study indicates a topological fermion beyond the constraints of high energy physics.

We present an original self-error-rejecting photonic qubit transmission scheme for both the polarization and spatial states of photon systems transmitted over collective noise channels. In our scheme, we use simple linear-optical elements, including half-wave plates, 50:50 beam splitters, and polarization beam splitters, to convert spatial-polarization modes into different time bins. By using postselection in different time bins, the success probability of obtaining the uncorrupted states approaches 1/4 for single-photon transmission, which is not influenced by the coefficients of noisy channels. Our self-error-rejecting transmission scheme can be generalized to hyperentangled N-photon systems and is useful in practical high-capacity quantum communications with photon systems in two degrees of freedom., Comment: 8 pages, 2 figures, one column

Yellow-seeded (YS) rapeseed varieties have attracted considerable interests from cultivators because of their thin seed coat and high seed oil content. However, compared with black-seeded (BS) rapeseed, little is known about the response of YS rapeseed to abiotic stresses. In this study, we characterized the cellular structures of YS varieties and BS varieties and the physiological parameters of the YS and BS seedlings subjected to high-salt and/or high-cadmium conditions. We observed larger and denser (in arrangement) oilbodies in YS than in BS varieties. The BS variety seed coat was much thicker than that of the YS variety because of the existence of a palisade layer where pigments are deposited. Either at the eighth day or 1 month after sowing, YS seedlings showed higher sensitivity to NaCl and/or CdCl2 stress than BS seedlings, as reflected by the length of roots, biomass, and a variety of physiological parameters, including MDA, chlorophyll content, and antioxidant activities. Our results suggested that the more vigorous growth of BS seedlings is likely due to the higher flavonoid content in their vegetative tissues, and the poor performance of YS seedlings under stress treatment (especially with NaCl) could be attributed to its relatively low flavonoid content. Our findings raise some points that need further investigation to obtain an in-depth understanding of the molecular mechanisms involved.

Tocopherols (Tocs) are vital scavengers of reactive oxygen species (ROS) and important seed oil quality indicators. Nitrogen (N) is one of the most important fertilizers in promoting biomass and grain yield in crop production. However, the effect of different sources and application rates of N on seed Toc contents in oilseed rape is poorly understood. In this study, pot trials were conducted to evaluate the effect of two sources of N fertilizer (urea and ammonium nitrate). Each source was applied to five oilseed rape genotypes (Zheshuang 72, Jiu-Er-1358, Zheshuang 758, Shiralee, and Pakola) at three different application rates (0.41 g/pot (N1), 0.81 g/pot (N2), and 1.20 g/pot (N3)). Results indicated that urea increased α-, γ-, and total Toc (T-Toc) more than did ammonium nitrate. N3 was proven as the most efficient application rate, which yielded high contents of γ-Toc and T-Toc. Highly significant correlations were observed between Toc isomers, T-Toc, and α-/γ-Toc ratio. These results clearly demonstrate that N sources and application rates significantly affect seed Toc contents in oilseed rape.