Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV3Sb5

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.

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.

Large Fermi surface in pristine kagome metal CsV3Sb5 and enhanced quasiparticle effective masses

The kagome metal CsV[Formula: see text]Sb[Formula: see text] is an ideal platform to study the interplay between topology and electron correlation. To understand the fermiology of CsV[Formula: see text]Sb[Formula: see text], intensive quantum oscillation (QO) studies at ambient pressure have been conducted. However, due to the Fermi surface reconstruction by the complicated charge density wave (CDW) order, the QO spectrum is exceedingly complex, hindering a complete understanding of the fermiology. Here, we directly map the Fermi surface of the pristine CsV[Formula: see text]Sb[Formula: see text] by measuring Shubnikov-de Haas QOs up to 29 T under pressure, where the CDW order is completely suppressed. The QO spectrum of the pristine CsV[Formula: see text]Sb[Formula: see text] is significantly simpler than the one in the CDW phase, and the detected oscillation frequencies agree well with our density functional theory calculations. In particular, a frequency as large as 8,200 T is detected. Pressure-dependent QO studies further reveal a weak but noticeable enhancement of the quasiparticle effective masses on approaching the critical pressure where the CDW order disappears, hinting at the presence of quantum fluctuations. Our high-pressure QO results reveal the large, unreconstructed Fermi surface of CsV[Formula: see text]Sb[Formula: see text], paving the way to understanding the parent state of this intriguing metal in which the electrons can be organized into different ordered states.

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.

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.

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.

Drastic magnetic-field-induced chiral current order and emergent current-bond-field interplay in kagome metals

In kagome metals, the chiral current order parameter [Formula: see text] with time-reversal-symmetry-breaking is the source of various exotic electronic states, while the method of controlling the current order and its interplay with the star-of-David bond order [Formula: see text] are still unsolved. Here, we reveal that tiny uniform orbital magnetization [Formula: see text] is induced by the chiral current order, and its magnitude is prominently enlarged under the presence of the bond order. Importantly, we derive the magnetic-field ([Formula: see text])-induced Ginzburg-Landau (GL) free energy expression [Formula: see text], which enables us to elucidate the field-induced current-bond phase transitions in kagome metals. The emergent current-bond-[Formula: see text] trilinear coupling term in the free energy, [Formula: see text], naturally explains the characteristic magnetic-field sensitive electronic states in kagome metals, such as the field-induced current order and the strong interplay between the bond and current orders. The GL coefficients of [Formula: see text] derived from the realistic multiorbital model are appropriate to explain various experiments. Furthermore, we discuss the field-induced loop current orders in the square lattice models that have been studied in cuprate superconductors.

Charge-loop current order and Z3 nematicity mediated by bond order fluctuations in kagome metals

Recent experiments on geometrically frustrated kagome metal AV3Sb5 (A = K, Rb, Cs) have revealed the emergence of the charge loop current (cLC) order near the bond order (BO) phase. However, the origin of the cLC and its interplay with other phases have been uncovered. Here, we propose a novel mechanism of the cLC state, by focusing on the BO phase common in kagome metals. The BO fluctuations in kagome metals, which emerges due to the Coulomb interaction and the electron-phonon coupling, mediate the odd-parity particle-hole condensation that gives rise to the topological current order. Furthermore, the predicted cLC+BO phase gives rise to the Z3-nematic state in addition to the giant anomalous Hall effect. The present theory predicts the close relationship between the cLC, the BO, and the nematicity, which is significant to understand the cascade of quantum electron states in kagome metals. The present scenario provides a natural understanding.

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.

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.

Underlying Mechanisms and Tunability of the Anomalous Hall Effect in NiCo2 O4 Films with Robust Perpendicular Magnetic Anisotropy

Their high tunability of electronic and magnetic properties makes transition-metal oxides (TMOs) highly intriguing for fundamental studies and promising for a wide range of applications. TMOs with strong ferrimagnetism provide new platforms for tailoring the anomalous Hall effect (AHE) beyond conventional concepts based on ferromagnets, and particularly TMOs with perpendicular magnetic anisotropy (PMA) are of prime importance for today's spintronics. This study reports on transport phenomena and magnetic characteristics of the ferrimagnetic TMO NiCo2 O4 (NCO) exhibiting PMA. The entire electrical and magnetic properties of NCO films are strongly correlated with their conductivities governed by the cation valence states. The AHE exhibits an unusual sign reversal resulting from a competition between intrinsic and extrinsic mechanisms depending on the conductivity, which can be tuned by the synthesis conditions independent of the film thickness. Importantly, skew-scattering is identified as an AHE contribution for the first time in the low-conductivity regime. Application wise, the robust PMA without thickness limitation constitutes a major advantage compared to conventional PMA materials utilized in today's spintronics. The great potential for applications is exemplified by two proposed novel device designs consisting only of NCO films that open a new route for future spintronics, such as ferrimagnetic high-density memories.

Tiny Sc Allows the Chains to Rattle: Impact of Lu and Y Doping on the Charge-Density Wave in ScV6Sn6

The kagome metals display an intriguing variety of electronic and magnetic phases arising from the connectivity of atoms on a kagome lattice. A growing number of these materials with vanadium-kagome nets host charge-density waves (CDWs) at low temperatures, including ScV6Sn6, CsV3Sb5, and V3Sb2. Curiously, only the Sc version of the RV6Sn6 materials with a HfFe6Ge6-type structure hosts a CDW (R = Gd-Lu, Y, Sc). In this study, we investigate the role of rare earth size in CDW formation in the RV6Sn6 compounds. Magnetization measurements on our single crystals of (Sc,Lu)V6Sn6 and (Sc,Y)V6Sn6 establish that the CDW is suppressed by substituting Sc by larger Lu or Y. Single-crystal X-ray diffraction reveals that compressible Sn-Sn bonds accommodate the larger rare earth atoms within loosely packed R-Sn-Sn chains without significantly expanding the lattice. We propose that Sc provides extra room in these chains crucial to CDW formation in ScV6Sn6. Our rattling chain model explains why both physical pressure and substitution by larger rare earth atoms hinder CDW formation despite opposite impacts on lattice size. We emphasize the cooperative effect of pressure and rare earth size by demonstrating that pressure further suppresses the CDW in a Lu-doped ScV6Sn6 crystal. Our model not only addresses why a CDW only forms in the RV6Sn6 materials with tiny Sc but also advances our understanding of why unusual CDWs form in the kagome metals.

Interplay of the charge density wave transition with topological and superconducting properties

Exotic phenomena due to the interplay of different quantum orders have been observed and the study of these phenomena has emerged as a new frontier in condensed matter research, especially in the two-dimensional limit. Here, we report the coexistence of charge density waves (CDWs), superconductivity, and nontrivial topology in monolayer 1H-MSe2 (M = Nb, Ta) triggered by momentum-dependent electron-phonon coupling through electron doping. At a critical electron doping concentration, new 2 × 2 CDW phases emerge with nontrivial topology, Dirac cones, and van Hove singularities. Interestingly, these 2 × 2 CDW phases are also superconducting. Our findings not only reveal a route towards realizing nontrivial electronic characters by CDW engineering, but also provide an exciting platform to modulate different quantum states at the confluence of CDWs, superconductivity, nontrivial topology, and electron-phonon coupling.

Observation of Termination-Dependent Topological Connectivity in a Magnetic Weyl Kagome Lattice

Engineering surfaces and interfaces of materials promises great potential in the field of heterostructures and quantum matter designers, with the opportunity to drive new many-body phases that are absent in the bulk compounds. Here, we focus on the magnetic Weyl kagome system Co3Sn2S2 and show how for the terminations of different samples the Weyl points connect differently, still preserving the bulk-boundary correspondence. Scanning tunneling microscopy has suggested such a scenario indirectly, and here, we probe the Fermiology of Co3Sn2S2 directly, by linking it to its real space surface distribution. By combining micro-ARPES and first-principles calculations, we measure the energy-momentum spectra and the Fermi surfaces of Co3Sn2S2 for different surface terminations and show the existence of topological features depending on the top-layer electronic environment. Our work helps to define a route for controlling bulk-derived topological properties by means of surface electrostatic potentials, offering a methodology for using Weyl kagome metals in responsive magnetic spintronics.

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.

Emergent Magnetism with Continuous Control in the Ultrahigh-Conductivity Layered Oxide PdCoO2

The current challenge to realizing continuously tunable magnetism lies in our inability to systematically change properties, such as valence, spin, and orbital degrees of freedom, as well as crystallographic geometry. Here, we demonstrate that ferromagnetism can be externally turned on with the application of low-energy helium implantation and can be subsequently erased and returned to the pristine state via annealing. This high level of continuous control is made possible by targeting magnetic metastability in the ultrahigh-conductivity, nonmagnetic layered oxide PdCoO2 where local lattice distortions generated by helium implantation induce the emergence of a net moment on the surrounding transition metal octahedral sites. These highly localized moments communicate through the itinerant metal states, which trigger the onset of percolated long-range ferromagnetism. The ability to continuously tune competing interactions enables tailoring precise magnetic and magnetotransport responses in an ultrahigh-conductivity film and will be critical to applications across spintronics.

Emergent topological quantum orbits in the charge density wave phase of kagome metal CsV3Sb5

The recently discovered kagome materials AV3Sb5 (A = K, Rb, Cs) attract intense research interest in intertwined topology, superconductivity, and charge density waves (CDW). Although the in-plane 2 × 2 CDW is well studied, its out-of-plane structural correlation with the Fermi surface properties is less understood. In this work, we advance the theoretical description of quantum oscillations and investigate the Fermi surface properties in the three-dimensional CDW phase of CsV3Sb5. We derived Fermi-energy-resolved and layer-resolved quantum orbits that agree quantitatively with recent experiments in the fundamental frequency, cyclotron mass, and topology. We reveal a complex Dirac nodal network that would lead to a π Berry phase of a quantum orbit in the spinless case. However, the phase shift of topological quantum orbits is contributed by the orbital moment and Zeeman effect besides the Berry phase in the presence of spin-orbital coupling (SOC). Therefore, we can observe topological quantum orbits with a π phase shift in otherwise trivial orbits without SOC, contrary to common perception. Our work reveals the rich topological nature of kagome materials and paves a path to resolve different topological origins of quantum orbits.

Anisotropic proximity-induced superconductivity and edge supercurrent in Kagome metal, K1-xV3Sb5

Materials with Kagome nets are of particular importance for their potential combination of strong correlation, exotic magnetism, and electronic topology. KV₃Sb₅ was discovered to be a layered topological metal with a Kagome net of vanadium. Here, we fabricated Josephson Junctions of K_1-xV₃Sb₅ and induced superconductivity over long junction lengths. Through magnetoresistance and current versus phase measurements, we observed a magnetic field sweeping direction-dependent magnetoresistance and an anisotropic interference pattern with a Fraunhofer pattern for in-plane magnetic field but a suppression of critical current for out-of-plane magnetic field. These results indicate an anisotropic internal magnetic field in K_1-xV₃Sb₅ that influences the superconducting coupling in the junction, possibly giving rise to spin-triplet superconductivity. In addition, the observation of long-lived fast oscillations shows evidence of spatially localized conducting channels arising from edge states. These observations pave the way for studying unconventional superconductivity and Josephson device based on Kagome metals with electron correlation and topology.

Observation of flat band, Dirac nodal lines and topological surface states in Kagome superconductor CsTi3Bi5

Kagome lattices of various transition metals are versatile platforms for achieving anomalous Hall effects, unconventional charge-density wave orders and quantum spin liquid phenomena due to the strong correlations, spin-orbit coupling and/or magnetic interactions involved in such a lattice. Here, we use laser-based angle-resolved photoemission spectroscopy in combination with density functional theory calculations to investigate the electronic structure of the newly discovered kagome superconductor CsTi₃Bi₅, which is isostructural to the AV₃Sb₅ (A = K, Rb or Cs) kagome superconductor family and possesses a two-dimensional kagome network of titanium. We directly observe a striking flat band derived from the local destructive interference of Bloch wave functions within the kagome lattice. In agreement with calculations, we identify type-II and type-III Dirac nodal lines and their momentum distribution in CsTi₃Bi₅ from the measured electronic structures. In addition, around the Brillouin zone centre, [Formula: see text] nontrivial topological surface states are also observed due to band inversion mediated by strong spin-orbit coupling.

High Resolution Polar Kerr Effect Studies of CsV_{3}Sb_{5}: Tests for Time-Reversal Symmetry Breaking below the Charge-Order Transition

We report high resolution polar Kerr effect measurements on CsV_{3}Sb_{5} single crystals in search of signatures of spontaneous time-reversal symmetry breaking below the charge-order transition at T^{*}≈94  K. Utilizing two different versions of zero-area loop Sagnac interferometers operating at 1550 nm wavelength, each with the fundamental attribute that without a time-reversal symmetry breaking sample at its path, the interferometer is perfectly reciprocal, we find no observable Kerr effect to within the noise floor limit of the apparatus at 30 nanoradians. Simultaneous coherent reflection ratio measurements confirm the sharpness of the charge-order transition in the same optical volume as the Kerr measurements. At finite magnetic field we observe a sharp onset of a diamagnetic shift in the Kerr signal at T^{*}, which persists down to the lowest temperature without change in trend. Since 1550 nm is an energy that was shown to capture all features of the optical properties of the material that interact with the charge-order transition, we are led to conclude that it is highly unlikely that time-reversal symmetry is broken in the charge ordered state in CsV_{3}Sb_{5}.

Abundant Lattice Instability in Kagome Metal ScV_{6}Sn_{6}

Kagome materials are emerging platforms for studying charge and spin orders. In this Letter, we have revealed a rich lattice instability in a Z_{2} kagome metal ScV_{6}Sn_{6} by first-principles calculations. Beyond verifying the sqrt[3]×sqrt[3]×3 charge density wave (CDW) order observed by the recent experiment, we further identified three more possible CDW structures, i.e., sqrt[3]×sqrt[3]×2 CDW with P6/mmm symmetry, 2×2×2 CDW with Immm symmetry, and 2×2×2 CDW with P6/mmm symmetry. The former two are more energetically favored than the sqrt[3]×sqrt[3]×3 phase, while the third one is comparable in energy. These CDW distortions involve mainly out-of-plane motions of Sc and Sn atoms, while V atoms constituting the kagome net are almost unchanged. We attribute the lattice instability to the smallness of Sc atomic radius. In contrast, such instability disappears in its sister compounds RV_{6}Sn_{6} (R is Y, or a rare-earth element), which exhibit quite similar electronic band structures to the Sc compound, because R has a larger atomic radius. Our work indicates that ScV_{6}Sn_{6} might exhibit varied CDW phases in different experimental conditions and provides insights to explore rich charge orders in kagome materials.

Observation of Electronic Nematicity Driven by the Three-Dimensional Charge Density Wave in Kagome Lattice KV3Sb5

Kagome superconductors AV₃Sb₅ (A = K, Rb, Cs) provide a fertile playground for studying intriguing phenomena, including nontrivial band topology, superconductivity, giant anomalous Hall effect, and charge density wave (CDW). Recently, a C₂ symmetric nematic phase prior to the superconducting state in AV₃Sb₅ drew enormous attention due to its potential inheritance of the symmetry of the unusual superconductivity. However, direct evidence of the rotation symmetry breaking of the electronic structure in the CDW state from the reciprocal space is still rare, and the underlying mechanism remains ambiguous. The observation shows unconventional unidirectionality, indicative of rotation symmetry breaking from six-fold to two-fold. The interlayer coupling between adjacent planes with π-phase offset in the 2 × 2 × 2 CDW phase leads to the preferred two-fold symmetric electronic structure. These rarely observed unidirectional back-folded bands in KV₃Sb₅ may provide important insights into its peculiar charge order and superconductivity.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

Anomalous enhancement of charge density wave in kagome superconductor CsV3Sb5 approaching the 2D limit

The recently discovered kagome metals AV₃Sb₅ (A = Cs, Rb, K) exhibit a variety of intriguing phenomena, such as a charge density wave (CDW) with time-reversal symmetry breaking and possible unconventional superconductivity. Here, we report a rare non-monotonic evolution of the CDW temperature (T_CDW) with the reduction of flake thickness approaching the atomic limit, and the superconducting transition temperature (T_c) features an inverse variation with T_CDW. T_CDW initially decreases to a minimum value of 72 K at 27 layers and then increases abruptly, reaching a record-high value of 120 K at 5 layers. Raman scattering measurements reveal a weakened electron-phonon coupling with the reduction of sample thickness, suggesting that a crossover from electron-phonon coupling to dominantly electronic interactions could account for the non-monotonic thickness dependence of T_CDW. Our work demonstrates the novel effects of dimension reduction and carrier doping on quantum states in thin flakes and provides crucial insights into the complex mechanism of the CDW order in the family of AV₃Sb₅ kagome metals.

Nodeless electron pairing in CsV3Sb5-derived kagome superconductors

The newly discovered kagome superconductors represent a promising platform for investigating the interplay between band topology, electronic order and lattice geometry^1-9. Despite extensive research efforts on this system, the nature of the superconducting ground state remains elusive^10-17. In particular, consensus on the electron pairing symmetry has not been achieved so far^18-20, in part owing to the lack of a momentum-resolved measurement of the superconducting gap structure. Here we report the direct observation of a nodeless, nearly isotropic and orbital-independent superconducting gap in the momentum space of two exemplary CsV₃Sb₅-derived kagome superconductors-Cs(V_0.93Nb_0.07)₃Sb₅ and Cs(V_0.86Ta_0.14)₃Sb₅-using ultrahigh-resolution and low-temperature angle-resolved photoemission spectroscopy. Remarkably, such a gap structure is robust to the appearance or absence of charge order in the normal state, tuned by isovalent Nb/Ta substitutions of V. Our comprehensive characterizations of the superconducting gap provide indispensable information on the electron pairing symmetry of kagome superconductors, and advance our understanding of the superconductivity and intertwined electronic orders in quantum materials.

Thickness-Dependent Topological Hall Effect in 2D Cr5 Si3 Nanosheets with Noncollinear Magnetic Phase

Antiferromagnets with noncollinear spin order are expected to exhibit unconventional electromagnetic response, such as spin Hall effects, chiral abnormal, quantum Hall effect, and topological Hall effect. Here, 2D thickness-controlled and high-quality Cr5 Si3 nanosheets that are compatible with the complementary metal-oxide-semiconductor technology are synthesized by chemical vapor deposition method. The angular dependence of electromagnetic transport properties of Cr5 Si3 nanosheets is investigated using a physical property measurement system, and an obvious topological Hall effect (THE) appears at a large tilted magnetic field, which results from the noncollinear magnetic structure of the Cr5 Si3 nanosheet. The Cr5 Si3 nanosheets exhibit distinct thickness-dependent perpendicular magnetic anisotropy (PMA), and the THE only emerges in the specific thickness range with moderate PMA. This work provides opportunities for exploring fundamental spin-related physical mechanisms of noncollinear antiferromagnet in ultrathin limit.

Magnetic Breakdown and Topology in the Kagome Superconductor CsV_{3}Sb_{5} under High Magnetic Field

The recently discovered layered kagome metals of composition AV_{3}Sb_{5} (A=K, Rb, Cs) exhibit a complex interplay among superconductivity, charge density wave order, topologically nontrivial electronic band structure and geometrical frustration. Here, we probe the electronic band structure underlying these exotic correlated electronic states in CsV_{3}Sb_{5} with quantum oscillation measurements in pulsed fields up to 86 T. The high-field data reveal a sequence of magnetic breakdown orbits that allows the construction of a model for the folded Fermi surface of CsV_{3}Sb_{5}. The dominant features are large triangular Fermi surface sheets that cover almost half the folded Brillouin zone. These sheets have not yet been detected in angle resolved photoemission spectroscopy and display pronounced nesting. The Berry phases of the electron orbits have been deduced from Landau level fan diagrams near the quantum limit without the need for extrapolations, thereby unambiguously establishing the nontrivial topological character of several electron bands in this kagome lattice superconductor.

Field-linear anomalous Hall effect and Berry curvature induced by spin chirality in the kagome antiferromagnet Mn3Sn

During the past two decades, it has been established that a non-trivial electron wave-function topology generates an anomalous Hall effect (AHE), which shows itself as a Hall conductivity non-linear in magnetic field. Here, we report on an unprecedented case of field-linear AHE. In Mn₃Sn, a kagome magnet, the out-of-plane Hall response, which shows an abrupt jump, was discovered to be a case of AHE. We find now that the in-plane Hall response, which is perfectly linear in magnetic field, is set by the Berry curvature of the wavefunction. The amplitude of the Hall response and its concomitant Nernst signal exceed by far what is expected in the semiclassical picture. We argue that magnetic field induces out-of-plane spin canting and thereafter gives rise to nontrivial spin chirality on the kagome lattice. In band structure, we find that the spin chirality modifies the topology by gapping out Weyl nodal lines unknown before, accounting for the AHE observed. Our work reveals intriguing unification of real-space Berry phase from spin chirality and momentum-space Berry curvature in a kagome material.

Emergent superconducting fluctuations in compressed kagome superconductor CsV3Sb5

The recent discovery of superconductivity (SC) and charge density wave (CDW) in kagome metals AV₃Sb₅ (A = K, Rb, Cs) provides an ideal playground for the study of emergent electronic orders. Application of moderate pressure leads to a two-dome-shaped SC phase regime in CsV₃Sb₅ accompanied by the destabilizing of CDW phase. Nonetheless, the nature of this pressure-tuned SC state and its interplay with the CDW are yet to be explored. Here, we perform soft point-contact spectroscopy (SPCS) measurements in CsV₃Sb₅ to investigate the evolution of superconducting order parameter with pressure. Surprisingly, we find that the superconducting gap is significantly enhanced between the two SC domes, at which the zero-resistance temperature is suppressed and the transition is remarkably broadened. Moreover, the temperature-dependence of the SC gap in this pressure range severely deviates from the conventional Bardeen-Cooper-Schrieffer (BCS) behavior, evidencing for strong Cooper pair phase fluctuations. These findings reveal the complex intertwining of the CDW with SC in the compressed CsV₃Sb₅, suggesting striking parallel to the cuprate superconductor La_2-xBa_xCuO₄. Our results point to the essential role of charge degree of freedom in the development of intertwining electronic orders, and thus provide new constraints for theories.

Electrically controlled superconductor-to-failed insulator transition and giant anomalous Hall effect in kagome metal CsV3Sb5 nanoflakes

The electronic correlations (e.g. unconventional superconductivity (SC), chiral charge order and nematic order) and giant anomalous Hall effect (AHE) in topological kagome metals AV₃Sb₅ (A = K, Rb, and Cs) have attracted great interest. Electrical control of those correlated electronic states and AHE allows us to resolve their own nature and origin and to discover new quantum phenomena. Here, we show that electrically controlled proton intercalation has significant impacts on striking quantum phenomena in CsV₃Sb₅ nanodevices mainly through inducing disorders in thinner nanoflakes and carrier density modulation in thicker ones. Specifically, in disordered thin nanoflakes (below 25 nm), we achieve a quantum phase transition from a superconductor to a "failed insulator" with a large saturated sheet resistance for T → 0 K. Meanwhile, the carrier density modulation in thicker nanoflakes shifts the Fermi level across the charge density wave (CDW) gap and gives rise to an extrinsic-intrinsic transition of AHE. With the first-principles calculations, the extrinsic skew scattering of holes in the nearly flat bands with finite Berry curvature by multiple impurities would account for the giant AHE. Our work uncovers a distinct disorder-driven bosonic superconductor-insulator transition (SIT), outlines a global picture of the giant AHE and reveals its correlation with the unconventional CDW in the AV₃Sb₅ family.

Nodeless Superconductivity in Kagome Metal CsV3Sb5 with and without Time Reversal Symmetry Breaking

The kagome metal CsV₃Sb₅ features an unusual competition between the charge-density-wave (CDW) order and superconductivity. Evidence for time reversal symmetry breaking (TRSB) inside the CDW phase has been accumulating. Hence, the superconductivity in CsV₃Sb₅ emerges from a TRSB normal state, potentially resulting in an exotic superconducting state. To reveal the pairing symmetry, we first investigate the effect of nonmagnetic impurity. Our results show that the superconducting critical temperature is insensitive to disorder, pointing to conventional s-wave superconductivity. Moreover, our measurements of the self-field critical current (I_c,sf), which is related to the London penetration depth, also confirm conventional s-wave superconductivity with strong coupling. Finally, we measure I_c,sf where the CDW order is removed by pressure and superconductivity emerges from the pristine normal state. Our results show that s-wave gap symmetry is retained, providing strong evidence for the presence of conventional s-wave superconductivity in CsV₃Sb₅ irrespective of the presence of the TRSB.

Chiral excitonic order from twofold van Hove singularities in kagome metals

Recent experiments on kagome metals AV₃Sb₅ (A=K,Rb,Cs) identify twofold van Hove singularities (TvHS) with opposite concavity near the Fermi energy, generating two approximately hexagonal Fermi surfaces - one electron-like and the other hole-like. Here we propose that a TvHS generates a novel time-reversal symmetry breaking excitonic order - arising due to bound pairs of electrons and holes located at opposite concavity van Hove singularities. We introduce a minimal model for the TvHS and investigate interaction induced many-body instabilities via the perturbative renormalisation group technique and a free energy analysis. Specialising to parameters appropriate for the kagome metals AV₃Sb₅, we construct a phase diagram comprising chiral excitons, charge density wave and a region of coexistence. We propose this as an explanation of a diverse range of experimental observations in AV₃Sb₅. Notably, the chiral excitonic state gives rise to a quantum anomalous Hall conductance, providing an appealing interpretation of the observed anomalous Hall effect in kagome metals. Possible alternative realisations of the TvHS mechanism in bilayer materials are also discussed. We suggest that TvHS open up interesting possibilities for correlated phases, enriching the set of competing ground states to include excitonic order.

Monolayer Kagome metals AV3Sb5

Recently, layered kagome metals AV₃Sb₅ (A = K, Rb, and Cs) have emerged as a fertile platform for exploring frustrated geometry, correlations, and topology. Here, using first-principles and mean-field calculations, we demonstrate that AV₃Sb₅ can crystallize in a mono-layered form, revealing a range of properties that render the system unique. Most importantly, the two-dimensional monolayer preserves intrinsically different symmetries from the three-dimensional layered bulk, enforced by stoichiometry. Consequently, the van Hove singularities, logarithmic divergences of the electronic density of states, are enriched, leading to a variety of competing instabilities such as doublets of charge density waves and s- and d-wave superconductivity. We show that the competition between orders can be fine-tuned in the monolayer via electron-filling of the van Hove singularities. Thus, our results suggest the monolayer kagome metal AV₃Sb₅ as a promising platform for designer quantum phases.

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.

Exploration of the physical properties of the newly synthesized kagome superconductor LaIr3Ga2 using different exchange-correlation functionals

LaIr₃Ga₂ is a kagome superconductor with a superconducting temperature (T_c) of 5.16 K. Here, we present the physical properties of the LaIr₃Ga₂ kagome superconductor computed via the DFT method wherein six different exchange-correlation functionals were used. The lattice parameters obtained using different functionals are reasonable, with a slight variation compared to experimental values. The bonding nature was explored. The elastic constants (C_ij), moduli (B, G, Y), and Vickers hardness (H_v) were computed to disclose the mechanical behavior. The H_v values were estimated to be 2.56-3.16 GPa using various exchange-correlation functionals, indicating the softness of the kagome material. The Pugh ratio, Poisson's ratio, and Cauchy pressure revealed the ductile nature. In addition, mechanical stability was ensured based on the estimated elastic constants. The anisotropic mechanical behavior was confirmed via different anisotropic indices. The Debye temperature (Θ_D), melting temperature (T_m), and minimum thermal conductivity (k_min) were calculated to characterize the thermal properties and predict the potential of LaIr₃Ga₂ as a thermal barrier coating material. The electronic density of states was investigated in detail. The McMillan equation was used to estimate T_c, and the electron-phonon coupling constant (λ) was calculated to explore the superconducting nature. The important optical constants were also calculated to explore its possible optoelectronic applications. The values of reflectivity in the IR-visible region are about 62% to 80%, indicating that the compound under study is suitable as a coating to reduce solar heating. The obtained parameters were compared with previously reported parameters, where available.

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.

Chern Fermi pocket, topological pair density wave, and charge-4e and charge-6e superconductivity in kagomé superconductors

The recent discovery of novel charge density wave (CDW) and pair density wave (PDW) in kagomé lattice superconductors AV₃Sb₅ (A = K, Rb, Cs) hints at unexpected time-reversal symmetry breaking correlated and topological states whose physical origin and broader implications are not understood. Here, we make conceptual advances toward a mechanism behind the striking observations and new predictions for novel macroscopic phase coherent quantum states. We show that the metallic CDW state with circulating loop currents is a doped orbital Chern insulator near van Hove filling. The emergent Chern Fermi pockets (CFPs) carry concentrated Berry curvature and orbital magnetic moment. We find that the pairing of electrons on the CFPs leads to a superconducting state with an emergent vortex-antivortex lattice and the formation of a complex triple-Q PDW. A plethora of correlated and topological states emerge, including a never-before-encountered chiral topological PDW superconductor, a loop-current pseudogap phase, and vestigial charge-4e and charge-6e superconductivity in staged melting of the vortex-antivortex lattice and hexatic liquid crystal. Our findings reveal previously unknown nature of the superconducting state of a current-carrying Chern metal, with broad implications for correlated and topological materials.

Charge Density Wave in Kagome Lattice Intermetallic ScV_{6}Sn_{6}

Materials hosting kagome lattices have drawn interest for the diverse magnetic and electronic states generated by geometric frustration. In the AV_{3}Sb_{5} compounds (A=K, Rb, Cs), stacked vanadium kagome layers give rise to unusual charge density waves (CDW) and superconductivity. Here we report single-crystal growth and characterization of ScV_{6}Sn_{6}, a hexagonal HfFe_{6}Ge_{6}-type compound that shares this structural motif. We identify a first-order phase transition at 92 K. Single crystal x-ray and neutron diffraction reveal a charge density wave modulation of the atomic lattice below this temperature. This is a distinctly different structural mode than that observed in the AV_{3}Sb_{5} compounds, but both modes have been anticipated in kagome metals. The diverse HfFe_{6}Ge_{6} family offers more opportunities to tune ScV_{6}Sn_{6} and explore density wave order in kagome lattice materials.

Discovery of conjoined charge density waves in the kagome superconductor CsV3Sb5

The electronic instabilities in CsV₃Sb₅ are believed to originate from the V 3d-electrons on the kagome plane, however the role of Sb 5p-electrons for 3-dimensional orders is largely unexplored. Here, using resonant tender X-ray scattering and high-pressure X-ray scattering, we report a rare realization of conjoined charge density waves (CDWs) in CsV₃Sb₅, where a 2 × 2 × 1 CDW in the kagome sublattice and a Sb 5p-electron assisted 2 × 2 × 2 CDW coexist. At ambient pressure, we discover a resonant enhancement on Sb L₁-edge (2s→5p) at the 2 × 2 × 2 CDW wavevectors. The resonance, however, is absent at the 2 × 2 × 1 CDW wavevectors. Applying hydrostatic pressure, CDW transition temperatures are separated, where the 2 × 2 × 2 CDW emerges 4 K above the 2 × 2 × 1 CDW at 1 GPa. These observations demonstrate that symmetry-breaking phases in CsV₃Sb₅ go beyond the minimal framework of kagome electronic bands near van Hove filling.

The kagomé metals RbTi3Bi5 and CsTi3Bi5

The kagomé metals RbTi3Bi5 and CsTi3Bi5 were synthesized both as polycrystalline powders by heating the elements in an argon atmosphere and as single crystals grown using a self-flux method. The compounds crystallize in the hexagonal crystal system isotypically to KV3Sb5 (P6/mmm, Z = 1, CsTi3Bi5: a = 5.7873(1), c = 9.2062(1) Å; RbTi3Bi5: a = 5.773(1), c = 9.065(1) Å). The titanium atoms form a kagomé net with bismuth atoms in the hexagons as well as above and below the triangles. The alkali metal atoms are coordinated by 12 bismuth atoms and form AlB2-like slabs between the kagomé layers. Magnetic susceptibility measurements with CsTi3Bi5 and RbTi3Bi5 single crystals reveal Pauli-paramagnetism and traces of superconductivity caused by CsBi2/RbBi2 impurities. Magnetotransport measurements reveal conventional Fermi liquid behavior and quantum oscillations indicative of a single dominant orbit at low temperature. DFT calculations show the characteristic metallic kagomé band structure similar to that of CsV3Sb5 with reduced band filling. A symmetry analysis of the band structure does not reveal an obvious and unique signature of a nontrivial topology.

Tunable topological Dirac surface states and van Hove singularities in kagome metal GdV6Sn6

Transition-metal-based kagome materials at van Hove filling are a rich frontier for the investigation of novel topological electronic states and correlated phenomena. To date, in the idealized two-dimensional kagome lattice, topologically Dirac surface states (TDSSs) have not been unambiguously observed, and the manipulation of TDSSs and van Hove singularities (VHSs) remains largely unexplored. Here, we reveal TDSSs originating from a ℤ₂ bulk topology and identify multiple VHSs near the Fermi level (E_F) in magnetic kagome material GdV₆Sn₆. Using in situ surface potassium deposition, we successfully realize manipulation of the TDSSs and VHSs. The Dirac point of the TDSSs can be tuned from above to below E_F, which reverses the chirality of the spin texture at the Fermi surface. These results establish GdV₆Sn₆ as a fascinating platform for studying the nontrivial topology, magnetism, and correlation effects native to kagome lattices. They also suggest potential application of spintronic devices based on kagome materials.

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 energies^1,2. 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 superconductivity^1,2. 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 electrons^3,4, non-trivial topology^5-7, chiral magnetic order^8,9, superconductivity and CDW order^10-15. 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 metals^4,16-21. 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 effect^22,23. 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 phase^24-28, in stark contrast to strongly correlated copper oxides^1,2 and nickelates^29-31, in which the CDW precedes or accompanies the magnetic order.

Disorder- and Topology-Enhanced Fully Spin-Polarized Currents in Nodal Chain Spin-Gapless Semimetals

Recently discovered high-quality nodal chain spin-gapless semimetals MF_{3} (M=Pd, Mn) feature an ultraclean nodal chain in the spin up channel residing right at the Fermi level and displaying a large spin gap leading to a 100% spin polarization of transport properties. Here, we investigate both intrinsic and extrinsic contributions to anomalous and spin transport in this class of materials. The dominant intrinsic origin is found to originate entirely from the gapped nodal chains without the entanglement of any other trivial bands. The side-jump mechanism is predicted to be negligibly small, but intrinsic skew scattering enhances the intrinsic Hall and Nernst signals significantly, leading to large values of respective conductivities. Our findings open a new material platform for exploring strong anomalous and spin transport properties in magnetic topological semimetals.

Quantum conductivity in the topological surface state in the SbV3S5 kagome lattice

We have successfully predicted the local topological bands in the frustrated kagome lattice SbV₃S₅. An important future research direction is to raise the kagome band with novel co-existing strong nonlinear dispersion and strong cohesion due to the anisotropic inner field of kagome SbV₃S₅ to the Fermi level. The Z₂ topological index of T-invariant systems provides evidence for a σ_yz near the Fermi level that determines the quantum anomalous Hall state. This shows that the quantum anomalous Hall effect (QAHE) phase of the kagome lattice SbV₃S₅ has a weak topological stability that is sensitive to weak disorder and field interactions. Neighbouring van Hove singularities near the Fermi level induced a quantum anomalous Hall conductivity and charge density wave platform.

The magnetic properties of pressurized CsV3Sb5 calculated by using a hybrid functional

Based on the hybrid functional, we find that at 0 GPa, pristine CsV₃Sb₅ has a magnetic moment of 0.28 μ_B per vanadium atom, which is suppressed at a pressure of 2.5 GPa resulting in a spin-crossover. Since the ground state of CsV₃Sb₅ with charge density wave (CDW) distortion is a non-magnetic state, the magnetic moment of V atoms in pristine CsV₃Sb₅ will be suppressed by the temperature-induced CDW transition at 94 K. The schematic evolution of magnetic moments as functions of pressure and temperature is presented. At low temperature, CsV₃Sb₅ is a rare example of materials hosting a pressure-induced magnetic moment, and we suggest that the effects of magnetic moments of V atoms should be considered for understanding its properties.

Observation of anomalous amplitude modes in the kagome metal CsV3Sb5

The kagome lattice provides a fertile platform to explore novel symmetry-breaking states. Charge-density wave (CDW) instabilities have been recently discovered in a new kagome metal family, commonly considered to arise from Fermi-surface instabilities. Here we report the observation of Raman-active CDW amplitude modes in CsV₃Sb₅, which are collective excitations typically thought to emerge out of frozen soft phonons, although phonon softening is elusive experimentally. The amplitude modes strongly hybridize with other superlattice modes, imparting them with clear temperature-dependent frequency shift and broadening, rarely seen in other known CDW materials. Both the mode mixing and the large amplitude mode frequencies suggest that the CDW exhibits the character of strong electron-phonon coupling, a regime in which phonon softening can cease to exist. Our work highlights the importance of the lattice degree of freedom in the CDW formation and points to the complex nature of the mechanism.

The mechanism of the charge density wave in kagome metals is not fully understood. Here, the authors report the observation of unusual large-frequency collective lattice excitations, or amplitude modes, in CsV₃Sb₅ in the absence of phonon mode softening, evidencing the strong electron-phonon coupling regime.

A new class of bilayer kagome lattice compounds with Dirac nodal lines and pressure-induced superconductivity

Kagome lattice composed of transition-metal ions provides a great opportunity to explore the intertwining between geometry, electronic orders and band topology. The discovery of multiple competing orders that connect intimately with the underlying topological band structure in nonmagnetic kagome metals AV₃Sb₅ (A = K, Rb, Cs) further pushes this topic to the quantum frontier. Here we report a new class of vanadium-based compounds with kagome bilayers, namely AV₆Sb₆ (A = K, Rb, Cs) and V₆Sb₄, which, together with AV₃Sb₅, compose a series of kagome compounds with a generic chemical formula (A_m-1Sb_2m)(V₃Sb)_n (m = 1, 2; n = 1, 2). Theoretical calculations combined with angle-resolved photoemission measurements reveal that these compounds feature Dirac nodal lines in close vicinity to the Fermi level. Pressure-induced superconductivity in AV₆Sb₆ further suggests promising emergent phenomena in these materials. The establishment of a new family of layered kagome materials paves the way for designer of fascinating kagome systems with diverse topological nontrivialities and collective ground states.

Structural, Thermodynamic, and Transport Properties of the Small-Gap Two-Dimensional Metal-Organic Kagomé Materials Cu3(hexaiminobenzene)2 and Ni3(hexaiminobenzene)2

Metal-organic frameworks (MOFs) provide exceptional chemical tunability and have recently been demonstrated to exhibit electrical conductivity and related functional electronic properties. The kagomé lattice is a fruitful source of novel physical states of matter, including the quantum spin liquid (in insulators) and Dirac fermions (in metals). Small-bandgap kagomé materials have the potential to bridge quantum spin liquid states and exhibit phenomena such as superconductivity but remain exceptionally rare. Here we report a structural, thermodynamic, and transport study of the two-dimensional kagomé metal-organic frameworks Ni₃(HIB)₂ and Cu₃(HIB)₂ (HIB = hexaiminobenzene). Magnetization measurements yield Curie constants of 0.989 emu K (mol Ni)^-1 Oe^-1 and 0.371 emu K (mol Cu)^-1 Oe^-1, respectively, close to the values expected for ideal S = 1 Ni²⁺ and S = ¹/₂ Cu²⁺. Weiss temperatures of -10.6 and -14.3 K indicate net weak mean field antiferromagnetic interactions between ions. Electrical transport measurements reveal that both materials are semiconducting, with gaps (E_g) of 22.2 and 103 meV, respectively. Specific heat measurements reveal a large T-linear contribution γ of 148(4) mJ mol-fu^-1 K^-2 in Ni₃(HIB)₂ with only a gradual upturn below ∼5 K and no evidence of a phase transition to an ordered state down to 0.1 K. Cu₃(HIB)₂ also lacks evidence of a phase transition above 0.1 K, with a substantial, field-dependent, magnetic contribution below ∼5 K. Despite them being superficially in agreement with the expectations of magnetic frustration and spin liquid physics, we ascribe these observations to the stacking faults found from a detailed analysis of synchrotron X-ray diffraction data. At the same time, our results demonstrate that these MOFs exhibit localized magnetism with simultaneous proximity to a metallic state, thus opening up opportunities to explore the connection between the insulating and metallic ground states of kagomé materials in a highly tunable chemical platform.