Roton pair density wave in a strong-coupling kagome superconductor

Quasi-Homoepitaxial Growth of Highly Strained Alkali-Metal Ultrathin Films on Kagome Superconductors

Applying lattice strain to thin films, a critical factor to tailor their properties such as stabilizing a structural phase unstable at ambient pressure, generally necessitates heteroepitaxial growth to control the lattice mismatch with substrate. Therefore, while homoepitaxy, the growth of thin film on a substrate made of the same material, is a useful method to fabricate high-quality thin films, its application to studying strain-induced structural phases is limited. Contrary to this general belief, here the quasi-homoepitaxial growth of Cs and Rb thin films is reported with substantial in-plane compressive strain. This is achieved by utilizing the alkali-metal layer existing in bulk crystal of kagome metals AV3Sb5 (A = Cs and Rb) as a structural template. The angle-resolved photoemission spectroscopy measurements reveal the formation of metallic quantum well states and notable thickness-dependent quasiparticle lifetime. Comparison with density functional theory calculations suggests that the obtained thin films crystalize in the face-centered cubic structure, which is typically stable only under high pressure in bulk crystals. These findings provide a useful approach for synthesizing highly strained thin films by quasi-homoepitaxy, and pave the way for investigating many-body interactions in Fermi liquids with tunable dimensionality.

Conventional superconductivity in the doped kagome superconductor Cs(V0.86Ta0.14)3Sb5 from vortex lattice studies

A hallmark of unconventional superconductors is a complex electronic phase diagram where intertwined orders of charge-spin-lattice degrees of freedom compete and coexist. While the kagome metals such as CsV3Sb5 also exhibit complex behavior, involving coexisting charge density wave order and superconductivity, much is unclear about the microscopic origin of the superconducting pairing. We study the vortex lattice in the superconducting state of Cs(V0.86Ta0.14)3Sb5, where the Ta-doping suppresses charge order and enhances superconductivity. Using small-angle neutron scattering, a strictly bulk probe, we show that the vortex lattice exhibits a strikingly conventional behavior. This includes a triangular symmetry with a period consistent with 2e-pairing, a field dependent scattering intensity that follows a London model, and a temperature dependence consistent with a uniform superconducting gap. Our results suggest that optimal bulk superconductivity in Cs(V1-xTax)3Sb5 arises from a conventional Bardeen-Cooper-Schrieffer electron-lattice coupling, different from spin fluctuation mediated unconventional copper- and iron-based superconductors.

Nanoscale Visualization of Symmetry-Breaking Electronic Orders and Magnetic Anisotropy in a Kagome Magnet YMn6Sn6

A kagome lattice hosts a plethora of quantum states arising from the interplay between nontrivial topology and electron correlations. The recently discovered kagome magnet RMn6Sn6 (R represents a rare-earth element) is believed to showcase a kagome band closely resembling textbook characteristics. Here, we report the characterization of local electronic states and their magnetization response in YMn6Sn6 via scanning tunneling microscopy measurements under vector magnetic fields. Our spectroscopic maps reveal a spontaneously trimerized kagome electronic order in YMn6Sn6, where the 6-fold rotational symmetry is disrupted while translational symmetry is maintained. Further application of an external magnetic field demonstrates a strong coupling of the YMn6Sn6 kagome band to the field, which exhibits an energy shift discrepancy under different field directions, implying the existence of magnetization-response anisotropy and anomalous g factors. Our findings establish YMn6Sn6 as an ideal platform for investigating kagome-derived orbital magnetic moment and correlated magnetic topological states.

Discovery of a long-ranged charge order with 1/4 Ge1-dimerization in an antiferromagnetic Kagome metal

Exotic quantum states arise from the interplay of various degrees of freedom such as charge, spin, orbital, and lattice. Recently, a short-ranged charge order (CO) was discovered deep inside the antiferromagnetic phase of Kagome magnet FeGe, exhibiting close relationships with magnetism. Despite extensive investigations, the CO mechanism remains controversial, mainly because the short-ranged behavior hinders precise identification of CO superstructure. Here, combining multiple experimental techniques, we report the observation of a long-ranged CO in high-quality FeGe samples, which is accompanied with a first-order structural transition. With these high-quality samples, the distorted 2 × 2 × 2 CO superstructure is characterized by a strong dimerization along the c-axis of 1/4 of Ge1-sites in Fe3Ge layers, and in response to that, the 2 × 2 in-plane charge modulations are induced. Moreover, we show that the previously reported short-ranged CO might be related to large occupational disorders at Ge1-site, which upsets the equilibrium of the CO state and the ideal 1 × 1 × 1 structure with very close energies, inducing nanoscale coexistence of these two phases. Our study provides important clues for further understanding the CO properties in FeGe and helps to identify the CO mechanism.

Large oscillatory thermal hall effect in kagome metals

The thermal Hall effect recently provided intriguing probes to the ground state of exotic quantum matters. These observations of transverse thermal Hall signals lead to the debate on the fermionic versus bosonic origins of these phenomena. The recent report of quantum oscillations (QOs) in Kitaev spin liquid points to a possible resolution. The Landau level quantization would most likely capture only the fermionic thermal transport effect. However, the QOs in the thermal Hall effect are generally hard to detect. In this work, we report the observation of a large oscillatory thermal Hall effect of correlated Kagome metals. We detect a 180-degree phase change of the oscillation and demonstrate the phase flip as an essential feature for QOs in the thermal transport properties. More importantly, the QOs in the thermal Hall channel are more profound than those in the electrical Hall channel, which strongly violates the Wiedemann-Franz (WF) law for QOs. This result presents the oscillatory thermal Hall effect as a powerful probe to the correlated quantum materials.

Evidence of a distinct collective mode in Kagome superconductors

The collective modes of the superconducting order parameter fluctuation can provide key insights into the nature of the superconductor. Recently, a family of superconductors has emerged in non-magnetic kagome materials AV3Sb5 (A = K, Rb, Cs), exhibiting fertile emergent phenomenology. However, the collective behaviors of Cooper pairs have not been studied. Here, we report a distinct collective mode in CsV3-xTaxSb5 using scanning tunneling microscope/spectroscopy. The spectral line-shape is well-described by one isotropic and one anisotropic superconducting gap, and a bosonic mode due to electron-mode coupling. With increasing x, the two gaps move closer in energy, merge into two isotropic gaps of equal amplitude, and then increase synchronously. The mode energy decreases monotonically to well below 2 Δ and survives even after the charge density wave order is suppressed. We propose the interpretation of this collective mode as Leggett mode between different superconducting components or the Bardasis-Schrieffer mode due to a subleading superconducting component.

Van Hove annihilation and nematic instability on a kagome lattice

A nematic phase breaks the point-group symmetry of the crystal lattice and is known to emerge in correlated materials. Here we report the observation of an intra-unit-cell nematic order and associated Fermi surface deformation in the kagome metal ScV6Sn6. Using scanning tunnelling microscopy and scanning tunnelling spectroscopy, we reveal a stripe-like nematic order breaking the crystal rotational symmetry within the kagome lattice itself. Moreover, we identify a set of Van Hove singularities adhering to the kagome-layer electrons, which appear along one direction of the Brillouin zone and are annihilated along other high-symmetry directions, revealing rotational symmetry breaking. Via detailed spectroscopic maps, we further observe an elliptical deformation of the Fermi surface, which provides direct evidence for an electronically mediated nematic order. Our work not only bridges the gap between electronic nematicity and kagome physics but also sheds light on the potential mechanism for realizing symmetry-broken phases in correlated electron systems.

Optical manipulation of the charge-density-wave state in RbV3Sb5

Broken time-reversal symmetry in the absence of spin order indicates the presence of unusual phases such as orbital magnetism and loop currents1-4. The recently discovered kagome superconductors AV3Sb5 (where A is K, Rb or Cs)5,6 display an exotic charge-density-wave (CDW) state and have emerged as a strong candidate for materials hosting a loop current phase. The idea that the CDW breaks time-reversal symmetry7-14 is, however, being intensely debated due to conflicting experimental data15-17. Here we use laser-coupled scanning tunnelling microscopy to study RbV3Sb5. By applying linearly polarized light along high-symmetry directions, we show that the relative intensities of the CDW peaks can be reversibly switched, implying a substantial electro-striction response, indicative of strong nonlinear electron-phonon coupling. A similar CDW intensity switching is observed with perpendicular magnetic fields, which implies an unusual piezo-magnetic response that, in turn, requires time-reversal symmetry breaking. We show that the simplest CDW that satisfies these constraints is an out-of-phase combination of bond charge order and loop currents that we dub a congruent CDW flux phase. Our laser scanning tunnelling microscopy data open the door to the possibility of dynamic optical control of complex quantum phenomenon in correlated materials.

Atomically Thin Kagome-Structured Co9Te16 Achieved through Self-Intercalation and Its Flat Band Visualization

Kagome materials have recently garnered substantial attention due to the intrinsic flat band feature and the stimulated magnetic and spin-related many-body physics. In contrast to their bulk counterparts, two-dimensional (2D) kagome materials feature more distinct kagome bands, beneficial for exploring novel quantum phenomena. Herein, we report the direct synthesis of an ultrathin kagome-structured Co-telluride (Co9Te16) via a molecular beam epitaxy (MBE) route and clarify its formation mechanism from the Co-intercalation in the 1T-CoTe2 layers. More significantly, we unveil the flat band states in the ultrathin Co9Te16 and identify the real-space localization of the flat band states by in situ scanning tunneling microscopy/spectroscopy (STM/STS) combined with first-principles calculations. A ferrimagnetic order is also predicted in kagome-Co9Te16. This work should provide a novel route for the direct synthesis of ultrathin kagome materials via a metal self-intercalation route, which should shed light on the exploration of the intriguing flat band physics in the related systems.

Plasmons in the Kagome metal CsV3Sb5

Plasmon polaritons, or plasmons, are coupled oscillations of electrons and electromagnetic fields that can confine the latter into deeply subwavelength scales, enabling novel polaritonic devices. While plasmons have been extensively studied in normal metals or semimetals, they remain largely unexplored in correlated materials. In this paper, we report infrared (IR) nano-imaging of thin flakes of CsV3Sb5, a prototypical layered Kagome metal. We observe propagating plasmon waves in real-space with wavelengths tunable by the flake thickness. From their frequency-momentum dispersion, we infer the out-of-plane dielectric functionϵ c that is generally difficult to obtain in conventional far-field optics, and elucidate signatures of electronic correlations when compared to density functional theory (DFT). We propose correlation effects might have switched the real part ofϵ c from negative to positive values over a wide range of middle-IR frequencies, transforming the surface plasmons into hyperbolic bulk plasmons, and have dramatically suppressed their dissipation.

Annealing-Tunable Charge Density Wave in the Magnetic Kagome Material FeGe

The unprecedented phenomenon that a charge density wave (CDW) emerges inside the antiferromagnetic (AFM) phase indicates an unusual CDW mechanism associated with magnetism in FeGe. Here, we demonstrate that both the CDW and magnetism of FeGe can be effectively tuned through postgrowth annealing treatments. Instead of the short-range CDW reported earlier, a long-range CDW order is realized below 110 K in single crystals annealed at 320 °C for over 48 h. The CDW and AFM transition temperatures appear to be inversely correlated with each other. The onset of the CDW phase significantly reduces the critical field of the spin-flop transition, whereas the CDW transition remains stable against minor variations in magnetic orders such as annealing-induced magnetic clusters and spin-canting transitions. Single-crystal x-ray diffraction measurements reveal substantial disorder on the Ge1 site, which is characterized by displacement of the Ge1 atom from the Fe_{3}Ge layer along the c axis and can be reversibly modified by the annealing process. The observed annealing-tunable CDW and magnetic orders can be well understood in terms of disorder on the Ge1 site. Our study provides a vital starting point for the exploration of the unconventional CDW mechanism in FeGe and of kagome materials in general.

Strain-induced long-range charge-density wave order in the optimally doped Bi2Sr2-xLaxCuO6 superconductor

The mechanism of high-temperature superconductivity in copper oxides (cuprate) remains elusive, with the pseudogap phase considered a potential factor. Recent attention has focused on a long-range symmetry-broken charge-density wave (CDW) order in the underdoped regime, induced by strong magnetic fields. Here by 63,65Cu-nuclear magnetic resonance, we report the discovery of a long-range CDW order in the optimally doped Bi2Sr2-xLaxCuO6 superconductor, induced by in-plane strain exceeding ∣ε∣ = 0.15 %, which deliberately breaks the crystal symmetry of the CuO2 plane. We find that compressive/tensile strains reduce superconductivity but enhance CDW, leaving superconductivity to coexist with CDW. The findings show that a long-range CDW order is an underlying hidden order in the pseudogap state, not limited to the underdoped regime, becoming apparent under strain. Our result sheds light on the intertwining of various orders in the cuprates.

Low-energy electronic structure in the unconventional charge-ordered state of ScV6Sn6

Kagome vanadates AV3Sb5 display unusual low-temperature electronic properties including charge density waves (CDW), whose microscopic origin remains unsettled. Recently, CDW order has been discovered in a new material ScV6Sn6, providing an opportunity to explore whether the onset of CDW leads to unusual electronic properties. Here, we study this question using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). The ARPES measurements show minimal changes to the electronic structure after the onset of CDW. However, STM quasiparticle interference (QPI) measurements show strong dispersing features related to the CDW ordering vectors. A plausible explanation is the presence of a strong momentum-dependent scattering potential peaked at the CDW wavevector, associated with the existence of competing CDW instabilities. Our STM results further indicate that the bands most affected by the CDW are near vHS, analogous to the case of AV3Sb5 despite very different CDW wavevectors.

Three-dimensional hidden phase probed by in-plane magnetotransport in kagome metal CsV3Sb5 thin flakes

Transition metal compounds with kagome structure have been found to exhibit a variety of exotic structural, electronic, and magnetic orders. These orders are competing with energies very close to each other, resulting in complex phase transitions. Some of the phases are easily observable, such as the charge density wave (CDW) and the superconducting phase, while others are more challenging to identify and characterize. Here we present magneto-transport evidence of a new phase below ~ 35 K in the kagome topological metal CsV3Sb5 (CVS) thin flakes between the CDW and the superconducting transition temperatures. This phase is characterized by six-fold rotational symmetry in the in-plane magnetoresistance (MR) and is connected to the orbital current order in CVS. Furthermore, the phase is characterized by a large in-plane negative magnetoresistance, which suggests the existence of a three-dimensional, magnetic field-tunable orbital current ordered phase. Our results highlight the potential of magneto-transport to reveal the interactions between exotic quantum states of matter and to uncover the symmetry of such hidden phases.

Crystal structure, properties and pressure-induced insulator-metal transition in layered kagome chalcogenides

Layered materials with kagome lattice have attracted a lot of attention due to the presence of nontrivial topological bands and correlated electronic states with tunability. In this work, we investigate a unique van der Waals (vdW) material system,A2M3X4(A= K, Rb, Cs;M= Ni, Pd;X= S, Se), where transition metal kagome lattices, chalcogen honeycomb lattices and alkali metal triangular lattices coexist simultaneously. A notable feature of this material is that each Ni/Pd atom is positioned in the center of four chalcogen atoms, forming a local square-planar environment. This crystal field environment results in a low spin stateS= 0 of Ni2+/Pd2+. A systematic study of the crystal growth, crystal structure, magnetic and transport properties of two representative compounds, Rb2Ni3S4and Cs2Ni3Se4, has been carried out on powder and single crystal samples. Both compounds exhibit nonmagneticp-type semiconducting behavior, closely related to the particular chemical environment of Ni2+ions and the alkali metal intercalated vdW structure. Additionally, Cs2Ni3Se4undergoes an insulator-metal transition (IMT) in transport measurements under pressure up to 87.1 GPa without any structural phase transition, while Rb2Ni3S4shows the tendency to be metalized.

Two-Dimensional Ultrathin Fe3Sn2 Kagome Metal with Defect-Dependent Magnetic Property

Two-dimensional (2D) Fe3Sn2, which is a room-temperature ferromagnetic kagome metal, has potential applications in spintronic devices. However, the systematic synthesis and magnetic study of 2D Fe3Sn2 single crystals have rarely been reported. Here we have synthesized 2D hexagonal and triangular Fe3Sn2 nanosheets by controlling the amount of FeCl2 precursors in the chemical vapor deposition (CVD) method. It is found that the hexagonal Fe3Sn2 nanosheets exist with Fe vacancy defects and show no obvious coercivity. While the triangular Fe3Sn2 nanosheet has obvious hysteresis loops at room temperature, its coercivity first increases and then remains stable with an increase in temperature, which should result from the competition of the thermal activation mechanism and spin direction rotation mechanism. A first-principles calculation study shows that the Fe vacancy defects in Fe3Sn2 can increase the distances between Fe atoms and weaken the ferromagnetism of Fe3Sn2. The resulting 2D Fe3Sn2 nanosheets provide a new choice for spintronic devices.

Temperature-Driven Rotation Symmetry-Breaking States in an Atomic Kagome Metal KV3Sb5

Kagome lattice AV3Sb5 has attracted tremendous interest because it hosts correlated and topological physics. However, an in-depth understanding of the temperature-driven electronic states in AV3Sb5 is elusive. Here we use scanning tunneling microscopy to directly capture the rotational symmetry-breaking effect in KV3Sb5. Through both topography and spectroscopic imaging of defect-free KV3Sb5, we observe a charge density wave (CDW) phase transition from an a0 × a0 atomic lattice to a robust 2a0 × 2a0 superlattice upon cooling the sample to 60 K. An individual Sb-atom vacancy in KV3Sb5 further gives rise to the local Friedel oscillation (FO), visible as periodic charge modulations in spectroscopic maps. The rotational symmetry of the FO tends to break at the temperature lower than 40 K. Moreover, the FO intensity shows an obvious competition against the intensity of the CDW. Our results reveal a tantalizing electronic nematicity in KV3Sb5, highlighting the multiorbital correlation in the kagome lattice framework.

Superconducting diode effect and interference patterns in kagome CsV3Sb5

The interplay among frustrated lattice geometry, non-trivial band topology and correlation yields rich quantum states of matter in kagome systems1,2. A series of recent members in this family, AV3Sb5 (A = K, Rb or Cs), exhibit a cascade of symmetry-breaking transitions3, involving the 3Q chiral charge ordering4-8, electronic nematicity9,10, roton pair density wave11 and superconductivity12. The nature of the superconducting order is yet to be resolved. Here we report an indication of dynamic superconducting domains with boundary supercurrents in intrinsic CsV3Sb5 flakes. The magnetic field-free superconducting diode effect is observed with polarity modulated by thermal histories, suggesting that there are dynamic superconducting order domains in a spontaneous time-reversal symmetry-breaking background. Strikingly, the critical current exhibits double-slit superconductivity interference patterns when subjected to an external magnetic field. The characteristics of the patterns are modulated by thermal cycling. These phenomena are proposed as a consequence of periodically modulated supercurrents flowing along certain domain boundaries constrained by fluxoid quantization. Our results imply a time-reversal symmetry-breaking superconducting order, opening a potential for exploring exotic physics, for example, Majorana zero modes, in this intriguing topological kagome system.

Inhomogeneous high temperature melting and decoupling of charge density waves in spin-triplet superconductor UTe2

Charge, spin and Cooper-pair density waves have now been widely detected in exotic superconductors. Understanding how these density waves emerge - and become suppressed by external parameters - is a key research direction in condensed matter physics. Here we study the temperature and magnetic-field evolution of charge density waves in the rare spin-triplet superconductor candidate UTe2 using scanning tunneling microscopy/spectroscopy. We reveal that charge modulations composed of three different wave vectors gradually weaken in a spatially inhomogeneous manner, while persisting to surprisingly high temperatures of 10-12 K. We also reveal an unexpected decoupling of the three-component charge density wave state. Our observations match closely to the temperature scale potentially related to short-range magnetic correlations, providing a possible connection between density waves observed by surface probes and intrinsic bulk features. Importantly, charge density wave modulations become suppressed with magnetic field both below and above superconducting Tc in a comparable manner. Our work points towards an intimate connection between hidden magnetic correlations and the origin of the unusual charge density waves in UTe2.

Formation and Manipulation of Diatomic Rotors at the Symmetry-Breaking Surfaces of a Kagome Superconductor

Construction of diatomic rotors, which is crucial for artificial nanomachines, remains challenging due to surface constraints and limited chemical design. Here we report the construction of diatomic Cr-Cs and Fe-Cs rotors where a Cr or Fe atom switches around a Cs atom at the Sb surface of the newly discovered kagome superconductor CsV3Sb5. The switching rate is controlled by the bias voltage between the rotor and scanning tunneling microscope (STM) tip. The spatial distribution of rates exhibits C2 symmetry, possibly linked to the symmetry-breaking charge orders of CsV3Sb5. We have expanded the rotor construction to include different transition metals (Cr, Fe, V) and alkali metals (Cs, K). Remarkably, designed configurations of rotors are achieved through STM manipulation. Rotor orbits and quantum states are precisely controlled by tuning the inter-rotor distance. Our findings establish a novel platform for the controlled fabrication of atomic motors on symmetry-breaking quantum materials, paving the way for advanced nanoscale devices.

Colossal c-Axis Response and Lack of Rotational Symmetry Breaking within the Kagome Planes of the CsV_{3}Sb_{5} Superconductor

The kagome materials AV_{3}Sb_{5} (A=K, Rb, Cs) host an intriguing interplay between unconventional superconductivity and charge-density waves. Here, we investigate CsV_{3}Sb_{5} by combining high-resolution thermal-expansion, heat-capacity, and electrical resistance under strain measurements. We directly unveil that the superconducting and charge-ordered states strongly compete, and that this competition is dramatically influenced by tuning the crystallographic c axis. In addition, we report the absence of additional bulk phase transitions within the charge-ordered state, notably associated with rotational symmetry breaking within the kagome planes. This suggests that any breaking of the C_{6} invariance occurs via different stacking of C_{6}-symmetric kagome patterns. Finally, we find that the charge-density-wave phase exhibits an enhanced A_{1g}-symmetric elastoresistance coefficient, whose large increase at low temperature is driven by electronic degrees of freedom.

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.

Tunable vortex bound states in multiband CsV3Sb5-derived kagome superconductors

Vortices and bound states offer an effective means of comprehending the electronic properties of superconductors. Recently, surface-dependent vortex core states have been observed in the newly discovered kagome superconductors CsV3Sb5. Although the spatial distribution of the sharp zero energy conductance peak appears similar to Majorana bound states arising from the superconducting Dirac surface states, its origin remains elusive. In this study, we present observations of tunable vortex bound states (VBSs) in two chemically-doped kagome superconductors Cs(V1-xTrx)3Sb5 (Tr = Ta or Ti), using low-temperature scanning tunneling microscopy/spectroscopy. The CsV3Sb5-derived kagome superconductors exhibit full-gap-pairing superconductivity accompanied by the absence of long-range charge orders, in contrast to pristine CsV3Sb5. Zero-energy conductance maps demonstrate a field-driven continuous reorientation transition of the vortex lattice, suggesting multiband superconductivity. The Ta-doped CsV3Sb5 displays the conventional cross-shaped spatial evolution of Caroli-de Gennes-Matricon bound states, while the Ti-doped CsV3Sb5 exhibits a sharp, non-split zero-bias conductance peak (ZBCP) that persists over a long distance across the vortex. The spatial evolution of the non-split ZBCP is robust against surface effects and external magnetic field but is related to the doping concentrations. Our study reveals the tunable VBSs in multiband chemically-doped CsV3Sb5 system and offers fresh insights into previously reported Y-shaped ZBCP in a non-quantum-limit condition at the surface of kagome superconductor.

Violation of emergent rotational symmetry in the hexagonal Kagome superconductor CsV3Sb5

Superconductivity is caused by electron pairs that are canonically isotropic, whereas some exotic superconductors are known to exhibit non-trivial anisotropy stemming from unconventional pairings. However, superconductors with hexagonal symmetry, the highest rotational symmetry allowed in crystals, exceptionally have strong constraint that is called emergent rotational symmetry (ERS): anisotropic properties should be very weak especially near the critical temperature Tc even for unconventional pairings such as d-wave states. Here, we investigate superconducting anisotropy of the recently-found hexagonal Kagome superconductor CsV3Sb5, which is known to exhibit various intriguing phenomena originating from its undistorted Kagome lattice formed by vanadium atoms. Based on calorimetry performed under accurate two-axis field-direction control, we discover a combination of six- and two-fold anisotropies in the in-plane upper critical field. Both anisotropies, robust up to very close to Tc, are beyond predictions of standard theories. We infer that this clear ERS violation with nematicity is best explained by multi-component nematic superconducting order parameter in CsV3Sb5 intertwined with symmetry breakings caused by the underlying charge-density-wave order.

Artificial kagome lattices of Shockley surface states patterned by halogen hydrogen-bonded organic frameworks

Artificial electronic kagome lattices may emerge from electronic potential landscapes using customized structures with exotic supersymmetries, benefiting from the confinement of Shockley surface-state electrons on coinage metals, which offers a flexible approach to realizing intriguing quantum phases of matter that are highly desired but scarce in available kagome materials. Here, we devise a general strategy to construct varieties of electronic kagome lattices by utilizing the on-surface synthesis of halogen hydrogen-bonded organic frameworks (XHOFs). As a proof of concept, we demonstrate three XHOFs on Ag(111) and Au(111) surfaces, which correspondingly deliver regular, breathing, and chiral breathing diatomic-kagome lattices with patterned potential landscapes, showing evident topological edge states at the interfaces. The combination of scanning tunnelling microscopy and noncontact atomic force microscopy, complemented by density functional theory and tight-binding calculations, directly substantiates our method as a reliable and effective way to achieve electronic kagome lattices for engineering quantum states.

Intertwined Van Hove Singularities as a Mechanism for Loop Current Order in Kagome Metals

Recent experiments on kagome metals AV_{3}Sb_{5} (A=Cs,Rb,K) indicated spontaneous time-reversal symmetry breaking in the charge density wave state in the absence of static magnetization. The loop current order (LCO) is proposed as its cause, but a microscopic model explaining the emergence of LCO through electronic correlations has not been firmly established. We show that the coupling between van Hove singularities with distinct mirror symmetries is a key ingredient to generate LCO ground state. By constructing an effective model, we find that when multiple van Hove singularities with opposite mirror eigenvalues are close in energy, the nearest-neighbor electron repulsion favors a ground state with coexisting LCO and charge bond order. It is then demonstrated that this mechanism applies to the kagome metals AV_{3}Sb_{5}. Our findings provide an intriguing mechanism of LCO and pave the way for a deeper understanding of complex quantum phenomena in kagome systems.

Chemical Rules for Stacked Kagome and Honeycomb Topological Semimetals

The chemical rules for predicting and understanding topological states in stacked kagome and honeycomb lattices are studied in both analytical and numerical ways. Starting with a minimal five-band tight-binding model, all the topological states are sorted into five groups, which are determined by the interlayer and intralayer hopping parameters. Combined with the model, an algorithm is designed to obtain a series of experimentally synthesized topological semimetals with kagome and honeycomb layers, i.e., IAMX family (IA = Alkali metal element, M = Rare earth metal element, X = Carbon group element), in the inorganic crystal structure database. A follow-up high-throughput calculation shows that IAMX family materials are all nodal-line semimetals and they will be Weyl semimetals after taking spin-orbit coupling into consideration. To have further insights into the topology of the IAMX family, a detailed chemical rule analysis is carried out on the high-throughput calculations, including the lattice constants of the structure, intralayer and interlayer couplings, bond strengths, electronegativity, and so on, which are consistent with the tight-binding model. This study provides a way to discover and modulate topological properties in stacked kagome and honeycomb crystals and offers candidates for studying topology-related properties like topological superconductors and axion insulators.

Distance-Dependent Evolution of Electronic States in Kagome-Honeycomb Lateral Heterostructures in FeSn

In this work, we demonstrate the formation and electronic influence of lateral heterointerfaces in FeSn containing Kagome and honeycomb layers. Lateral heterostructures offer spatially resolved property control, enabling the integration of dissimilar materials and promoting phenomena not typically observed in vertical heterostructures. Using the molecular beam epitaxy technique, we achieve a controllable synthesis of lateral heterostructures in the Kagome metal FeSn. With scanning tunneling microscopy/spectroscopy in conjunction with first-principles calculations, we provide a comprehensive understanding of the bonding motif connecting the Fe3Sn-terminated Kagome and Sn2-terminated honeycomb surfaces. More importantly, we reveal a distance-dependent evolution of the electronic states in the vicinity of the heterointerfaces. This evolution is significantly influenced by the orbital character of the flat bands. Our findings suggest an approach to modulate the electronic properties of the Kagome lattice, which should be beneficial for the development of future quantum devices.

Atomically precise engineering of spin-orbit polarons in a kagome magnetic Weyl semimetal

Atomically precise defect engineering is essential to manipulate the properties of emerging topological quantum materials for practical quantum applications. However, this remains challenging due to the obstacles in modifying the typically complex crystal lattice with atomic precision. Here, we report the atomically precise engineering of the vacancy-localized spin-orbit polarons in a kagome magnetic Weyl semimetal Co3Sn2S2, using scanning tunneling microscope. We achieve the step-by-step repair of the selected vacancies, leading to the formation of artificial sulfur vacancies with elaborate geometry. We find that that the bound states localized around these vacancies undergo a symmetry dependent energy shift towards Fermi level with increasing vacancy size. As the vacancy size increases, the localized magnetic moments of spin-orbit polarons become tunable and eventually become itinerantly negative due to spin-orbit coupling in the kagome flat band. These findings provide a platform for engineering atomic quantum states in topological quantum materials at the atomic scale.

Competing itinerant and local spin interactions in kagome metal FeGe

The combination of a geometrically frustrated lattice, and similar energy scales between degrees of freedom endows two-dimensional Kagome metals with a rich array of quantum phases and renders them ideal for studying strong electron correlations and band topology. The Kagome metal, FeGe is a noted example of this, exhibiting A-type collinear antiferromagnetic (AFM) order at TN ≈ 400 K, then establishes a charge density wave (CDW) phase coupled with AFM ordered moment below TCDW ≈ 110 K, and finally forms a c-axis double cone AFM structure around TCanting ≈ 60 K. Here we use neutron scattering to demonstrate the presence of gapless incommensurate spin excitations associated with the double cone AFM structure of FeGe at temperatures well above TCanting and TCDW that merge into gapped commensurate spin waves from the A-type AFM order. Commensurate spin waves follow the Bose factor and fit the Heisenberg Hamiltonian, while the incommensurate spin excitations, emerging below TN where AFM order is commensurate, start to deviate from the Bose factor around TCDW, and peaks at TCanting. This is consistent with a critical scattering of a second order magnetic phase transition with decreasing temperature. By comparing these results with density functional theory calculations, we conclude that the incommensurate magnetic structure arises from the nested Fermi surfaces of itinerant electrons and the formation of a spin density wave order.

Atomistic Origin of Diverse Charge Density Wave States in CsV_{3}Sb_{5}

Kagome metals AV_{3}Sb_{5} (A=K, Rb, or Cs) exhibit intriguing charge density wave (CDW) instabilities, which interplay with superconductivity and band topology. However, despite firm observations, the atomistic origins of the CDW phases, as well as hidden instabilities, remain elusive. Here, we adopt our newly developed symmetry-adapted cluster expansion method to construct a first-principles-based effective Hamiltonian of CsV_{3}Sb_{5}, which not only reproduces the established inverse star of David (ISD) phase, but also predict a series of D_{3h}-n states under mild tensile strains. With such atomistic Hamiltonians, the microscopic origins of different CDW states are revealed as the competition of the second-nearest neighbor V-V pairs versus the first-nearest neighbor V-V and V-Sb couplings. Interestingly, the effective Hamiltonians also reveal the existence of ionic Dzyaloshinskii-Moriya interaction in the high-symmetry phase of CsV_{3}Sb_{5} and drives the formation of noncollinear CDW patterns. Our work thus not only deepens the understanding of the CDW formation in AV_{3}Sb_{5}, but also demonstrates that the effective Hamiltonian is a suitable approach for investigating CDW mechanisms, which can be extended to various CDW systems.

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.

π Phase Interlayer Shift and Stacking Fault in the Kagome Superconductor CsV_{3}Sb_{5}

The stacking degree of freedom is a crucial factor in tuning material properties and has been extensively investigated in layered materials. The kagome superconductor CsV_{3}Sb_{5} was recently discovered to exhibit a three-dimensional CDW phase below T_{CDW}∼94  K. Despite the thorough investigation of in-plane modulation, the out-of-plane modulation has remained ambiguous. Here, our polarization- and temperature-dependent Raman measurements reveal the breaking of C_{6} rotational symmetry and the presence of three distinct domains oriented at approximately 120° to each other. The observations demonstrate that the CDW phase can be naturally explained as a 2c staggered order phase with adjacent layers exhibiting a relative π phase shift. Further, we discover a first-order structural phase transition at approximately 65 K and suggest that it is a stacking order-disorder phase transition due to stacking fault, supported by the thermal hysteresis behavior of a Cs-related phonon mode. Our findings highlight the significance of the stacking degree of freedom in CsV_{3}Sb_{5} and offer structural insights to comprehend the entanglement between superconductivity and CDW.

Resonant x-ray diffraction measurements in charge ordered kagome superconductors KV3Sb5and RbV3Sb5

We report on (resonant) x-ray diffraction experiments on the normal state properties of kagome-lattice superconductors KV3Sb5and RbV3Sb5. We have confirmed previous reports indicating that the charge density wave (CDW) phase is characterized by a doubling of the unit cell in all three crystallographic directions. By monitoring the temperature dependence of Bragg peaks associated with the CDW phase, we ascertained that it develops gradually over several degrees, as opposed to CsV3Sb5, where the CDW peak intensity saturates promptly just below the CDW transition temperature. Analysis of symmetry modes indicates that this behavior arises due to lattice distortions linked to the formation of CDWs. These distortions occur abruptly in CsV3Sb5, while they progress more gradually in RbV3Sb5and KV3Sb5. In contrast, the amplitude of the mode leading to the crystallographic symmetry breaking fromP6/mmmtoFmmmappears to develop more gradually in CsV3Sb5as well. Diffraction measurements close to the V K edge and the Sb L1edge show no sensitivity to inversion- or time-symmetry breaking, which are claimed to be associated with the onset of the CDW phase. The azimuthal angle dependence of the resonant diffraction intensity observed at the Sb L1edge is associated with the difference in the population of unoccupied states and the anisotropy of the electron density of certain Sb ions.

Correlated order at the tipping point in the kagome metal CsV3Sb5

Spontaneously broken symmetries are at the heart of many phenomena of quantum matter and physics more generally. However, determining the exact symmetries that are broken can be challenging due to imperfections such as strain, in particular when multiple electronic orders are competing. This is exemplified by charge order in some kagome systems, where evidence of nematicity and flux order from orbital currents remains inconclusive due to contradictory measurements. Here we clarify this controversy by fabricating highly symmetric samples of a member of this family, CsV3Sb5, and measuring their transport properties. We find that a measurable anisotropy is absent at any temperature in the unperturbed material. However, a pronounced in-plane transport anisotropy appears when either weak magnetic fields or strains are present. A symmetry analysis indicates that a perpendicular magnetic field can indeed lead to in-plane anisotropy by inducing a flux order coexisting with more conventional bond order. Our results provide a unifying picture for the controversial charge order in kagome metals and highlight the need for materials control at the microscopic scale in the identification of broken symmetries.

Charge-4e superconductivity and chiral metal in 45°-twisted bilayer cuprates and related bilayers

The material realization of charge-4e/6e superconductivity (SC) is a big challenge. Here, we propose to realize charge-4e SC in maximally-twisted homobilayers, such as 45∘-twisted bilayer cuprates and 30∘-twisted bilayer graphene, referred to as twist-bilayer quasicrystals (TB-QC). When each monolayer hosts a pairing state with the largest pairing angular momentum, previous studies have found that the second-order interlayer Josephson coupling would drive chiral topological SC (TSC) in the TB-QC. Here we propose that, above the Tc of the chiral TSC, either charge-4e SC or chiral metal can arise as vestigial phases, depending on the ordering of the total- and relative-pairing-phase fields of the two layers. Based on a thorough symmetry analysis to get the low-energy effective Hamiltonian, we conduct a combined renormalization-group and Monte-Carlo study and obtain the phase diagram, which includes the charge-4e SC and chiral metal phases.

Evidence for Quantum Stripe Ordering in a Triangular Optical Lattice

Understanding strongly correlated quantum materials, such as high-T_{c} superconductors, iron-based superconductors, and twisted bilayer graphene systems, remains as one of the outstanding challenges in condensed matter physics. Quantum simulation with ultracold atoms in particular optical lattices, which provide orbital degrees of freedom, is a powerful tool to contribute new insights to this endeavor. Here, we report the experimental realization of an unconventional Bose-Einstein condensate of ^{87}Rb atoms populating degenerate p orbitals in a triangular optical lattice, exhibiting remarkably long coherence times. Using time-of-flight spectroscopy, we observe that this state spontaneously breaks the rotational symmetry and its momentum spectrum agrees with the theoretically predicted coexistence of exotic stripe and loop-current orders. Like certain strongly correlated electronic systems with intertwined orders, such as high-T_{c} cuprate superconductors, twisted bilayer graphene, and the recently discovered chiral density-wave state in kagome superconductors AV_{3}Sb_{5} (A=K, Rb, Cs), the newly demonstrated quantum state, in spite of its markedly different energy scale and the bosonic quantum statistics, exhibits multiple symmetry breakings at ultralow temperatures. These findings hold the potential to enhance our comprehension of the fundamental physics governing these intricate quantum materials.

Toward large-scale, ordered and tunable Majorana-zero-modes lattice on iron-based superconductors

Majorana excitations are the quasiparticle analog of Majorana fermions in solid materials. Typical examples are the Majorana zero modes (MZMs) and the dispersing Majorana modes. When probed by scanning tunneling spectroscopy, the former manifest as a pronounced conductance peak locating precisely at zero-energy, while the latter behaves as constant or slowly varying density of states. The MZMs obey non-abelian statistics and are believed to be building blocks for topological quantum computing, which is highly immune to the environmental noise. Existing MZM platforms include hybrid structures such as topological insulator, semiconducting nanowire or 1D atomic chains on top of a conventional superconductor, and single materials such as the iron-based superconductors (IBSs) and 4Hb-TaS2. Very recently, ordered and tunable MZM lattice has also been realized in IBS LiFeAs, providing a scalable and applicable platform for future topological quantum computation. In this review, we present an overview of the recent local probe studies on MZMs. Classified by the material platforms, we start with the MZMs in the iron-chalcogenide superconductors where FeTe0.55Se0.45and (Li0.84Fe0.16)OHFeSe will be discussed. We then review the Majorana research in the iron-pnictide superconductors as well as other platforms beyond the IBSs. We further review recent works on ordered and tunable MZM lattice, showing that strain is a feasible tool to tune the topological superconductivity. Finally, we give our summary and perspective on future Majorana research.

Chiral charge density wave induced by mirror symmetry breaking in kagome metal

Kagome lattice provides a distinctive platform to investigate various correlated electron orders. Recently, an unconventional charge density wave (CDW) with novel chirality is observed in the kagome metalAV3Sb5(A= K, Rb, Cs), and the origin of which is still unclear. Here, using a tight-binding model and the mean-field method, we calculate the electron order in the quasi-two-dimensional kagome lattice with 1/3 electron filling, and show that the chiral CDW emerges under a set of parameters withC6rotational symmetry but without mirror symmetry. Physically, the reason why we choose this set of parameters is based on the possible tangential distortion of the kagome lattice. Our results provide a fresh insight to understand the microscopic origin of the unconventional CDW inAV3Sb5.

Magnetism in AV_{3}Sb_{5} (A=Cs, Rb, and K): Origin and Consequences for the Strongly Correlated Phases

The V-based kagome systems AV_{3}Sb_{5} (A=Cs, Rb, and K) are unique by virtue of the intricate interplay of nontrivial electronic structure, topology, and intriguing fermiology, rendering them to be a playground of many mutually dependent exotic phases like charge-order and superconductivity. Despite numerous recent studies, the interconnection of magnetism and other complex collective phenomena in these systems has yet not arrived at any conclusion. Using first-principles tools, we demonstrate that their electronic structures, complex fermiologies and phonon dispersions are strongly influenced by the interplay of dynamic electron correlations, nontrivial spin-polarization and spin-orbit coupling. An investigation of the first-principles-derived intersite magnetic exchanges with the complementary analysis of q dependence of the electronic response functions and the electron-phonon coupling indicate that the system conforms as a frustrated spin cluster, where the occurrence of the charge-order phase is intimately related to the mechanism of electron-phonon coupling, rather than the Fermi-surface nesting.

Surface-independent CO2 and CO reduction on two-dimensional kagome metal KV3Sb5

Two-dimensional kagome metals possess rich band structure characteristics, including Dirac points, flat bands, and van Hove singularities, because of their special geometric structures. Furthermore, kagome metals AV3Sb5 (A = K, Rb, and Cs) have garnered significant attention due to their nontrivial topological electronic structures. In this study, we theoretically demonstrate that the KV3Sb5 (001) surface is conducive to CO2 and CO reduction. The thermodynamic stability and electrochemical states of various surface types are investigated. The reaction paths reveal that the product is identical on different surfaces, and the free energy profiles exhibit low onset potentials. This paper elucidates the effect of two-dimensional topological kagome metals on CO2 and CO reduction.

Visualizing symmetry-breaking electronic orders in epitaxial Kagome magnet FeSn films

Kagome lattice hosts a plethora of quantum states arising from the interplay of topology, spin-orbit coupling, and electron correlations. Here, we report symmetry-breaking electronic orders tunable by an applied magnetic field in a model Kagome magnet FeSn consisting of alternating stacks of two-dimensional Fe3Sn Kagome and Sn2 honeycomb layers. On the Fe3Sn layer terminated FeSn thin films epitaxially grown on SrTiO3(111) substrates, we observe trimerization of the Kagome lattice using scanning tunneling microscopy/spectroscopy, breaking its six-fold rotational symmetry while preserving the translational symmetry. Such a trimerized Kagome lattice shows an energy-dependent contrast reversal in dI/dV maps, which is significantly enhanced by bound states induced by Sn vacancy defects. This trimerized Kagome lattice also exhibits stripe modulations that are energy-dependent and tunable by an applied in-plane magnetic field, indicating symmetry-breaking nematicity from the entangled magnetic and charge degrees of freedom in antiferromagnet FeSn.

Direct observation of the collective modes of the charge density wave in the kagome metal CsV3Sb5

A recently discovered group of kagome metals AV[Formula: see text]Sb[Formula: see text] (A = K, Rb, Cs) exhibit a variety of intertwined unconventional electronic phases, which emerge from a puzzling charge density wave phase. Understanding of this charge-ordered parent phase is crucial for deciphering the entire phase diagram. However, the mechanism of the charge density wave is still controversial, and its primary source of fluctuations-the collective modes-has not been experimentally observed. Here, we use ultrashort laser pulses to melt the charge order in CsV[Formula: see text]Sb[Formula: see text] and record the resulting dynamics using femtosecond angle-resolved photoemission. We resolve the melting time of the charge order and directly observe its amplitude mode, imposing a fundamental limit for the fastest possible lattice rearrangement time. These observations together with ab initio calculations provide clear evidence for a structural rather than electronic mechanism of the charge density wave. Our findings pave the way for a better understanding of the unconventional phases hosted on the kagome lattice.

Superconducting, Topological, and Transport Properties of Kagome Metals CsTi3Bi5 and RbTi3Bi5

The recently discovered ATi3Bi5 (A=Cs, Rb) exhibit intriguing quantum phenomena including superconductivity, electronic nematicity, and abundant topological states. ATi3Bi5 present promising platforms for studying kagome superconductivity, band topology, and charge orders in parallel with AV3Sb5. In this work, we comprehensively analyze various properties of ATi3Bi5 covering superconductivity under pressure and doping, band topology under pressure, thermal conductivity, heat capacity, electrical resistance, and spin Hall conductivity (SHC) using first-principles calculations. Calculated superconducting transition temperature (Tc) of CsTi3Bi5 and RbTi3Bi5 at ambient pressure are about 1.85 and 1.92 K. When subject to pressure, Tc of CsTi3Bi5 exhibits a special valley and dome shape, which arises from quasi-two-dimensional compression to three-dimensional isotropic compression within the context of an overall decreasing trend. Furthermore, Tc of RbTi3Bi5 can be effectively enhanced up to 3.09 K by tuning the kagome van Hove singularities (VHSs) and flat band through doping. Pressures can also induce abundant topological surface states at the Fermi energy (EF) and tune VHSs across EF. Additionally, our transport calculations are in excellent agreement with recent experiments, confirming the absence of charge density wave. Notably, SHC of CsTi3Bi5 can reach up to 226ℏ ·(e· Ω ·cm)-1 at EF. Our work provides a timely and detailed analysis of the rich physical properties for ATi3Bi5, offering valuable insights for further experimental verifications and investigations in this field.

Superconductivity and phase transitions in Kagome compound Pd3P2S8from first-principles calculation

Pd3P2S8is a semiconductor that contains Kagome lattices, which exhibits various physical phenomena. Structural searches of Pd3P2S8in the pressure range from 0 to 120 GPa have revealed two phases of the space groupP3‾m1(designated asP3‾m1-1 andP3‾m1-2) and two phases of the space groupC2/m(designated asC2/m-1 andC2/m-2), with all butC2/m-2 phase being dynamically stable. Electron-phonon calculations combined with Bardeen-Cooper-Schrieffer's argument have shown that both phases are superconductors. Notably, theP3‾m1-1 phase undergoes a semiconductor-to-superconductor transition, with superconducting critical temperature (Tc) increasing up to a maximum of 9.13 K at 70 GPa. BothC2/m-1 andP3‾m1-2 phases exhibit superconductivity at 0 GPa. Our calculations demonstrate several new superconducting phases of Pd3P2S8, providing a pathway and platform for exploring superconductivity in materials with Kagome lattices and expanding the options for studying such lattices.

Discovery and construction of surface kagome electronic states induced by p-d electronic hybridization in Co3Sn2S2

Kagome-lattice materials possess attractive properties for quantum computing applications, but their synthesis remains challenging. Herein, based on the compelling identification of the two cleavable surfaces of Co3Sn2S2, we show surface kagome electronic states (SKESs) on a Sn-terminated triangular Co3Sn2S2 surface. Such SKESs are imprinted by vertical p-d electronic hybridization between the surface Sn (subsurface S) atoms and the buried Co kagome-lattice network in the Co3Sn layer under the surface. Owing to the subsequent lateral hybridization of the Sn and S atoms in a corner-sharing manner, the kagome symmetry and topological electronic properties of the Co3Sn layer is proximate to the Sn surface. The SKESs and both hybridizations were verified via qPlus non-contact atomic force microscopy (nc-AFM) and density functional theory calculations. The construction of SKESs with tunable properties can be achieved by the atomic substitution of surface Sn (subsurface S) with other group III-V elements (Se or Te), which was demonstrated theoretically. This work exhibits the powerful capacity of nc-AFM in characterizing localized topological states and reveals the strategy for synthesis of large-area transition-metal-based kagome-lattice materials using conventional surface deposition techniques.

Flat bands, non-trivial band topology and rotation symmetry breaking in layered kagome-lattice RbTi3Bi5

A representative class of kagome materials, AV3Sb5 (A = K, Rb, Cs), hosts several unconventional phases such as superconductivity, [Formula: see text] non-trivial topological states, and electronic nematic states. These can often coexist with intertwined charge-density wave states. Recently, the discovery of the isostructural titanium-based single-crystals, ATi3Bi5 (A = K, Rb, Cs), which exhibit similar multiple exotic states but without the concomitant charge-density wave, has opened an opportunity to disentangle these complex states in kagome lattices. Here, we combine high-resolution angle-resolved photoemission spectroscopy and first-principles calculations to investigate the low-lying electronic structure of RbTi3Bi5. We demonstrate the coexistence of flat bands and several non-trivial states, including type-II Dirac nodal lines and [Formula: see text] non-trivial topological surface states. Our findings also provide evidence for rotational symmetry breaking in RbTi3Bi5, suggesting a directionality to the electronic structure and the possible emergence of pure electronic nematicity in this family of kagome compounds.