A hybrid topological quantum state in an elemental solid.

Topology1-3 and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three important research directions: (1) the competition between distinct interactions, as in several intertwined phases, (2) the interplay between interactions and topology that drives the phenomena in twisted layered materials and topological magnets, and (3) the coalescence of several topological orders to generate distinct novel phases. The first two examples have grown into major areas of research, although the last example remains mostly unexplored, mainly because of the lack of a material platform for experimental studies. Here, using tunnelling microscopy, photoemission spectroscopy and a theoretical analysis, we unveil a 'hybrid' topological phase of matter in the simple elemental-solid arsenic. Through a unique bulk-surface-edge correspondence, we uncover that arsenic features a conjoined strong and higher-order topology that stabilizes a hybrid topological phase. Although momentum-space spectroscopy measurements show signs of topological surface states, real-space microscopy measurements unravel a unique geometry of topologically induced step-edge conduction channels revealed on various natural nanostructures on the surface. Using theoretical models, we show that the existence of gapless step-edge states in arsenic relies on the simultaneous presence of both a non-trivial strong Z2 invariant and a non-trivial higher-order topological invariant, which provide experimental evidence for hybrid topology. Our study highlights pathways for exploring the interplay of different band topologies and harnessing the associated topological conduction channels in engineered quantum or nano-devices.

Enhancement of superconductivity and phase diagram of Ta-doped Kagome superconductor CsV3Sb5.

Kagome superconductors AV3Sb5 (A = K, Rb, and Cs) have attracted enormous interest due to the coexistence of charge density wave (CDW) order, unconventional superconductivity (SC) and anomalous Hall effect (AHE). In this paper, we reported an intensive investigation on Cs(V1-xTax)3Sb5 single crystals with systematic Ta doping. Ta was confirmed to be doped into V-site in the Kagome layer from both single crystal X-ray diffraction structural refinement and scanning transmission electron microscopy observation. The highest Ta doping level was found to be about 16%, which is more than twice as much as 7% in Nb-doped CsV3Sb5. With the increase of Ta doping, CDW order was gradually suppressed and finally vanished when the doping level reached to more than 8%. Meanwhile, superconductivity was enhanced with a maximum critical temperature (Tc) of 5.3 K, which is the highest Tc in the bulk crystal of this Kagome system at ambient pressure so far. The µ0Hc2(T) behavior demonstrates that the system is still a two-band superconductor after Ta doping. Based on the electrical transport measurement, a phase diagram was set up to exhibit the evolution of CDW and SC in the Cs(V1-xTax)3Sb5 system. These findings pave a new way to search for new superconductors with higher Tc in the AV3Sb5 family and establish a new platform for tuning and controlling the multiple orders and superconducting states.

Phonon promoted charge density wave in topological kagome metal ScV6Sn6.

Charge density wave (CDW) orders in vanadium-based kagome metals have recently received tremendous attention, yet their origin remains a topic of debate. The discovery of ScV6Sn6, a bilayer kagome metal featuring an intriguing [Formula: see text] CDW order, offers a novel platform to explore the underlying mechanism behind the unconventional CDW. Here, we combine high-resolution angle-resolved photoemission spectroscopy, Raman scattering and density functional theory to investigate the electronic structure and phonon modes of ScV6Sn6. We identify topologically nontrivial surface states and multiple van Hove singularities (VHSs) in the vicinity of the Fermi level, with one VHS aligning with the in-plane component of the CDW vector near the [Formula: see text] point. Additionally, Raman measurements indicate a strong electron-phonon coupling, as evidenced by a two-phonon mode and new emergent modes. Our findings highlight the fundamental role of lattice degrees of freedom in promoting the CDW in ScV6Sn6.

Quantum interactions in topological R166 kagome magnet.

Kagome magnet has been found to be a fertile ground for the search of exotic quantum states in condensed matter. Arising from the unusual geometry, the quantum interactions in the kagome lattice give rise to various quantum states, including the Chern-gapped Dirac fermion, Weyl fermion, flat band and van Hove singularity. Here we review recent advances in the study of the R166 kagome magnet (RT6E6, R = rare earths; T = transition metals; and E = Sn, Ge, etc) whose crystal structure highlights the transition-metal-based kagome lattice and rare-earth sublattice. Compared with other kagome magnets, the R166 family owns the particularly strong interplays between thedelectrons on the kagome site and the localizedfelectrons on the rare-earth site. In the form of spin-orbital coupling, exchange interaction and many-body effect, the quantum interactions play an essential role in the Berry curvature in both the reciprocal and real spaces of R166 family. We discuss the spectroscopic and transport visualization of the topological electrons hosted in the Mn kagome layer of RMn6Sn6and the various topological effects due to the quantum interactions, including the Chern-gap opening, the exchange-biased effect, the topological Hall effect and the emergent inductance. We hope this work serves as a guide for future explorations of quantum magnets.

Intertwining of Magnetism and Charge Ordering in Kagome FeGe.

Recent experiments report a charge density wave (CDW) in the antiferromagnet FeGe, but the nature of the charge ordering and the associated structural distortion remains elusive. We discuss the structural and electronic properties of FeGe. Our proposed ground state phase accurately captures atomic topographies acquired by scanning tunneling microscopy. We show that the 2 × 2 × 1 CDW likely results from the Fermi surface nesting of hexagonal-prism-shaped kagome states. FeGe is found to exhibit distortions in the positions of the Ge atoms instead of the Fe atoms in the kagome layers. Using in-depth first-principles calculations and analytical modeling, we demonstrate that this unconventional distortion is driven by the intertwining of magnetic exchange coupling and CDW interactions in this kagome material. The movement of Ge atoms from their pristine positions also enhances the magnetic moment of the Fe kagome layers. Our study indicates that magnetic kagome lattices provide a material candidate for exploring the effects of strong electronic correlations on the ground state and their implications for transport, magnetic, and optical responses in materials.

Spectroscopic signature of obstructed surface states in SrIn2P2.

The century-long development of surface sciences has witnessed the discoveries of a variety of quantum states. In the recently proposed "obstructed atomic insulators", symmetric charges are pinned at virtual sites where no real atoms reside. The cleavage through these sites could lead to a set of obstructed surface states with partial electronic occupation. Here, utilizing scanning tunneling microscopy, angle-resolved photoemission spectroscopy and first-principles calculations, we observe spectroscopic signature of obstructed surface states in SrIn2P2. We find that a pair of surface states that are originated from the pristine obstructed surface states split in energy by a unique surface reconstruction. The upper branch is marked with a striking differential conductance peak followed by negative differential conductance, signaling its localized nature, while the lower branch is found to be highly dispersive. This pair of surface states is in consistency with our calculational results. Our finding not only demonstrates a surface quantum state induced by a new type of bulk-boundary correspondence, but also provides a platform for exploring efficient catalysts and related surface engineering.

Causal structure of interacting Weyl fermions in condensed matter systems.

The spacetime light cone is central to the definition of causality in the theory of relativity. Recently, links between relativistic and condensed matter physics have been uncovered, where relativistic particles can emerge as quasiparticles in the energy-momentum space of matter. Here, we unveil an energy-momentum analogue of the spacetime light cone by mapping time to energy, space to momentum, and the light cone to the Weyl cone. We show that two Weyl quasiparticles can only interact to open a global energy gap if they lie in each other's energy-momentum dispersion cones-analogous to two events that can only have a causal connection if they lie in each other's light cones. Moreover, we demonstrate that the causality of surface chiral modes in quantum matter is entangled with the causality of bulk Weyl fermions. Furthermore, we identify a unique quantum horizon region and an associated 'thick horizon' in the emergent causal structure.

Kagome superconductors AV3Sb5 (A = K, Rb, Cs).

The quasi-two-dimensional kagome materials AV3Sb5 (A = K, Rb, Cs) were found to be a prime example of kagome superconductors, a new quantum platform to investigate the interplay between electron correlation effects, topology and geometric frustration. In this review, we report recent progress on the experimental and theoretical studies of AV3Sb5 and provide a broad picture of this fast-developing field in order to stimulate an expanded search for unconventional kagome superconductors. We review the electronic properties of AV3Sb5, the experimental measurements of the charge density wave state, evidence of time-reversal symmetry breaking and other potential hidden symmetry breaking in these materials. A variety of theoretical proposals and models that address the nature of the time-reversal symmetry breaking are discussed. Finally, we review the superconducting properties of AV3Sb5, especially the potential pairing symmetries and the interplay between superconductivity and the charge density wave state.

Emergent Edge Modes in Shifted Quasi-One-Dimensional Charge Density Waves.

We propose and study a two-dimensional phase of shifted charge density waves (CDW), which is constructed from an array of weakly coupled 1D CDW wires whose phases shift from one wire to the next. We show that the fully gapped bulk CDW has topological properties, characterized by a nonzero Chern number, that imply edge modes within the bulk gap. Remarkably, these edge modes exhibit spectral pseudoflow as a function of position along the edge, and are thus dual to the chiral edge modes of Chern insulators with their spectral flow in momentum space. Furthermore, we show that the CDW edge modes are stable against interwire coupling. Our predictions can be tested experimentally in quasi-1D CDW compounds such as Ta_{2}Se_{8}I.

Coexistence of Bulk-Nodal and Surface-Nodeless Cooper Pairings in a Superconducting Dirac Semimetal.

The interplay of nontrivial topology and superconductivity in condensed matter physics gives rise to exotic phenomena. However, materials are extremely rare where it is possible to explore the full details of the superconducting pairing. Here, we investigate the momentum dependence of the superconducting gap distribution in a novel Dirac material PdTe. Using high resolution, low temperature photoemission spectroscopy, we establish it as a spin-orbit coupled Dirac semimetal with the topological Fermi arc crossing the Fermi level on the (010) surface. This spin-textured surface state exhibits a fully gapped superconducting Cooper pairing structure below T_{c}∼4.5 K. Moreover, we find a node in the bulk near the Brillouin zone boundary, away from the topological Fermi arc. These observations not only demonstrate the band resolved electronic correlation between topological Fermi arc states and the way it induces Cooper pairing in PdTe, but also provide a rare case where surface and bulk states host a coexistence of nodeless and nodal gap structures enforced by spin-orbit coupling.

Optical bulk-boundary dichotomy in a quantum spin Hall insulator.

The bulk-boundary correspondence is a critical concept in topological quantum materials. For instance, a quantum spin Hall insulator features a bulk insulating gap with gapless helical boundary states protected by the underlying Z2 topology. However, the bulk-boundary dichotomy and distinction are rarely explored in optical experiments, which can provide unique information about topological charge carriers beyond transport and electronic spectroscopy techniques. Here, we utilize mid-infrared absorption micro-spectroscopy and pump-probe micro-spectroscopy to elucidate the bulk-boundary optical responses of Bi4Br4, a recently discovered room-temperature quantum spin Hall insulator. Benefiting from the low energy of infrared photons and the high spatial resolution, we unambiguously resolve a strong absorption from the boundary states while the bulk absorption is suppressed by its insulating gap. Moreover, the boundary absorption exhibits strong polarization anisotropy, consistent with the one-dimensional nature of the topological boundary states. Our infrared pump-probe microscopy further measures a substantially increased carrier lifetime for the boundary states, which reaches one nanosecond scale. The nanosecond lifetime is about one to two orders longer than that of most topological materials and can be attributed to the linear dispersion nature of the helical boundary states. Our findings demonstrate the optical bulk-boundary dichotomy in a topological material and provide a proof-of-principal methodology for studying topological optoelectronics.

Visualizing Higher-Fold Topology in Chiral Crystals.

Novel topological phases of matter are fruitful platforms for the discovery of unconventional electromagnetic phenomena. Higher-fold topology is one example, where the low-energy description goes beyond standard model analogs. Despite intensive experimental studies, conclusive evidence remains elusive for the multigap topological nature of higher-fold chiral fermions. In this Letter, we leverage a combination of fine-tuned chemical engineering and photoemission spectroscopy with photon energy contrast to discover the higher-fold topology of a chiral crystal. We identify all bulk branches of a higher-fold chiral fermion for the first time, critically important for allowing us to explore unique Fermi arc surface states in multiple interband gaps, which exhibit an emergent ladder structure. Through designer chemical gating of the samples in combination with our measurements, we uncover an unprecedented multigap bulk boundary correspondence. Our demonstration of multigap electronic topology will propel future research on unconventional topological responses.

Visualization of Tunable Weyl Line in A-A Stacking Kagome Magnets.

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, the Weyl lines are directly visualized with strong out-of-plane dispersion in the A-A stacked kagome magnet GdMn6 Sn6 . Remarkably, the Weyl lines exhibit a strong magnetization-direction-tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn6 Sn6 (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum responses.

Topological kagome magnets and superconductors.

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.

Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe.

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.

Discovery of charge density wave in a kagome lattice antiferromagnet.

A hallmark of strongly correlated quantum materials is the rich phase diagram resulting from competing and intertwined phases with nearly degenerate ground-state energies1,2. 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 superconductivity1,2. 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 electrons3,4, non-trivial topology5-7, chiral magnetic order8,9, superconductivity and CDW order10-15. Although CDW has been found in weakly electron-correlated non-magnetic AV3Sb5 (A = K, Rb, Cs)10-15, it has not yet been observed in correlated magnetic-ordered kagome lattice metals4,16-21. 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 AV3Sb5 (refs. 10-15), enhances the AFM ordered moment and induces an emergent anomalous Hall effect22,23. 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 phase24-28, in stark contrast to strongly correlated copper oxides1,2 and nickelates29-31, in which the CDW precedes or accompanies the magnetic order.

Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator.

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics1,2. The quantum spin Hall phase3-6 is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature 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 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical hybridization of such edge states, which not only supports the Z2 topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Our results further encourage the exploration of high-temperature transport quantization of the putative topological phase reported here.

The Magnetic Genome of Two-Dimensional van der Waals Materials.

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.