Charge Density Waves and Electronic Properties of Superconducting Kagome Metals

A Femtosecond Electron-Based Versatile Microscopy for Visualizing Carrier Dynamics in Semiconductors Across Spatiotemporal and Energetic Domains

Carrier dynamics detection in different dimensions (space, time, and energy) with high resolutions plays a pivotal role in the development of modern semiconductor devices, especially in low-dimensional, high-speed, and ultrasensitive devices. Here, a femtosecond electron-based versatile microscopy is reported that combines scanning ultrafast electron microscopy (SUEM) imaging and time-resolved cathodoluminescence (TRCL) detection, which allows for visualizing and decoupling different dynamic processes of carriers involved in surface and bulk in semiconductors with unprecedented spatiotemporal and energetic resolutions. The achieved spatial resolution is better than 10 nm, and the temporal resolutions for SUEM imaging and TRCL detection are ≈500 fs and ≈4.5 ps, respectively, representing state-of-the-art performance. To demonstrate its unique capability, the surface and bulk carrier dynamics involved in n-type gallium arsenide (GaAs) are directly tracked and distinguished. It is revealed, in real time and space, that hot carrier cooling, defect trapping, and interband-/defect-assisted radiative recombination in the energy domain result in ordinal super-diffusion, localization, and sub-diffusion of carriers at the surface, elucidating the crucial role of surface states on carrier dynamics. The study not only gives a comprehensive physical picture of carrier dynamics in GaAs, but also provides a powerful platform for exploring complex carrier dynamics in semiconductors for promoting their device performance.

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.

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.

Control of Polarity in Kagome-NiAs Bismuthides

A 2×2×1 superstructure of the P63/mmc NiAs structure is reported in which kagome nets are stabilized in the octahedral transition metal layers of the compounds Ni0.7Pd0.2Bi, Ni0.6Pt0.4Bi, and Mn0.99Pd0.01Bi. The ordered vacancies that yield the true hexagonal kagome motif lead to filling of trigonal bipyramidal interstitial sites with the transition metal in this family of "kagome-NiAs" type materials. Further ordering of vacancies within these interstitial layers can be compositionally driven to simultaneously yield kagome-connected layers and a net polarization along the c axes in Ni0.9Bi and Ni0.79Pd0.08Bi, which adopt Fmm2 symmetry. The polar and non-polar materials exhibit different electronic transport behaviour, reflecting the tuneability of both structure and properties within the NiAs-type bismuthide materials family.

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.

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.

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.

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.

Anharmonic strong-coupling effects at the origin of the charge density wave in CsV3Sb5

The formation of charge density waves is a long-standing open problem, particularly in dimensions higher than one. Various observations in the vanadium antimonides discovered recently further underpin this notion. Here, we study the Kagome metal CsV3Sb5 using polarized inelastic light scattering and density functional theory calculations. We observe a significant gap anisotropy with 2 Δ max / k B T CDW ≈ 20 , far beyond the prediction of mean-field theory. The analysis of the A1g and E2g phonons, including those emerging below TCDW, indicates strong phonon-phonon coupling, presumably mediated by a strong electron-phonon interaction. Similarly, the asymmetric Fano-type lineshape of the A1g amplitude mode suggests strong electron-phonon coupling below TCDW. The large electronic gap, the enhanced anharmonic phonon-phonon coupling, and the Fano shape of the amplitude mode combined are more supportive of a strong-coupling phonon-driven charge density wave transition than of a Fermi surface instability or an exotic mechanism in CsV3Sb5.

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.

Structural approach to charge density waves in low-dimensional systems: electronic instability and chemical bonding

The charge density wave (CDW) instability, usually occurring in low-dimensional metals, has been a topic of interest for longtime. However, some very fundamental aspects of the mechanism remain unclear. Recently, a plethora of new CDW materials, a substantial fraction of which is two-dimensional or even three-dimensional, has been prepared and characterised as bulk and/or single-layers. As a result, the need for revisiting the primary mechanism of the instability, based on the electron-hole instability established more than 50 years ago for quasi-one-dimensional (quasi-1D) conductors, has clearly emerged. In this work, we consider a large number of CDW materials to revisit the main concepts used in understanding the CDW instability, and emphasise the key role of the momentum dependent electron-phonon coupling in linking electronic and structural degrees of freedom. We argue that for quasi-1D systems, earlier weak coupling theories work appropriately and the energy gain due to the CDW and the concomitant periodic lattice distortion (PLD) remains primarily due to a Fermi surface nesting mechanism. However, for materials with higher dimensionality, intermediate and strong coupling regimes are generally at work and the modification of the chemical bonding network by the PLD is at the heart of the instability. We emphasise the need for a microscopic approach blending condensed matter physics concepts and state-of-the-art first-principles calculations with quite fundamental chemical bonding ideas in understanding the CDW phenomenon in these materials.

Co3X8 (X = Cl and Br): multiple phases and magnetic properties of the Kagome lattice

The unique magnetic properties of two-dimensional (2D) materials have demonstrated huge potential for applications in nanodevices and spintronics. In this work, we propose a new Kagome lattice, Co3X8 (X = Cl and Br), based on density functional theory (DFT) calculation. We find that Co/X in Co3X8 has spontaneous movement in the lattice, resulting in 156- and 12-phases of Co3X8 and diverse magnetic and electronic properties. We show that the magnetic and electronic properties of Co3X8 can be engineered by strain, and the magnetic properties of Co3X8 are highly related to the spontaneous movement of X. Moreover, the transmission property of 12-Co3X8 shows clear angle-dependent features due to the symmetry breaking as caused by the spontaneous movement of X. Our findings may provide not only a possible Kagome lattice with unique properties, but also a strategy for designing nanodevices and for spintronics.

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.

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.

Condensation of preformed charge density waves in kagome metals

Charge density wave (CDW) is a spontaneous spatial modulation of charges in solids whose general microscopic descriptions are yet to be completed. Kagome metals of AV3Sb5 (A = K, Rb, Cs) provide a chance to realize CDW intertwined with dimensional effects as well as their special lattice. Here, based on a state-of-the-art molecular dynamics simulation, we propose that their phase transition to CDW is a condensation process of incoherently preformed charge orders. Owing to unavoidable degeneracy in stacking charge orders, phases of preformed orders on each layer are shown to fluctuate between a limited number of states with quite slower frequencies than typical phonon vibrations until reaching their freezing temperature. As the size of interfacial alkali atom increases, the fluctuations are shown to counterbalance the condensation of orderings, resulting in a maximized transition temperature for RbV3Sb5. Our results resolve controversial observations on their CDWs, highlighting a crucial role of their interlayer interactions.

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.

Softening of a flat phonon mode in the kagome ScV6Sn6

Geometrically frustrated kagome lattices are raising as novel platforms to engineer correlated topological electron flat bands that are prominent to electronic instabilities. Here, we demonstrate a phonon softening at the kz = π plane in ScV6Sn6. The low energy longitudinal phonon collapses at ~98 K and q = [Formula: see text] due to the electron-phonon interaction, without the emergence of long-range charge order which sets in at a different propagation vector qCDW = [Formula: see text]. Theoretical calculations corroborate the experimental finding to indicate that the leading instability is located at [Formula: see text] of a rather flat mode. We relate the phonon renormalization to the orbital-resolved susceptibility of the trigonal Sn atoms and explain the approximately flat phonon dispersion. Our data report the first example of the collapse of a kagome bosonic mode and promote the 166 compounds of kagomes as primary candidates to explore correlated flat phonon-topological flat electron physics.

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.

Alternative Structure Model of Correlated Charge Density Wave in Monolayer 1T-Nb(Ta)Se2

The putative Mott charge density wave (CDW) phases of monolayer 1T-NbSe2 and 1T-TaSe2 have attracted a lot of recent interest due to the unexpected orbital texture of their Mott-Hubbard states and the superstructure related to an exotic possibility of a quantum spin liquid with a spinon Fermi surface. The origins of the orbital texture and the superstructure have been, however, elusive. We find by using density functional theory calculations that these CDW phases can have an alternative metastable structure, an anion (Se) centered cluster, in contrast to the prevailing model of a cation (Nb or Ta) centered David star cluster. This structure can be stabilized by the charge transfer from the bilayer graphene/SiC substrate used commonly in the experiments. The anion-centered structure has a similar electronic band structure of a charge transfer insulator to that of DS clusters but naturally explains the orbital texture of the upper Hubbard band from simply its atomic structure. Moreover, this band structure exhibits a Fermi surface nesting to possibly break the symmetry spontaneously into a 3 × 3 -R30° superstructure observed experimentally. The resulting ground state of the superstructure is shown to be a trivial band insulator, in contrast to exotic proposals. This result emphasizes the huge structural flexibility of these heteroexpitaxial monolayers, for which careful studies on atomic structures and interactions with substrates are highly requested.

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.

Tunable Van Hove Singularity without Structural Instability in Kagome Metal CsTi_{3}Bi_{5}

In kagome metal CsV_{3}Sb_{5}, multiple intertwined orders are accompanied by both electronic and structural instabilities. These exotic orders have attracted much recent attention, but their origins remain elusive. The newly discovered CsTi_{3}Bi_{5} is a Ti-based kagome metal to parallel CsV_{3}Sb_{5}. Here, we report angle-resolved photoemission experiments and first-principles calculations on pristine and Cs-doped CsTi_{3}Bi_{5} samples. Our results reveal that the van Hove singularity (vHS) in CsTi_{3}Bi_{5} can be tuned in a large energy range without structural instability, different from that in CsV_{3}Sb_{5}. As such, CsTi_{3}Bi_{5} provides a complementary platform to disentangle and investigate the electronic instability with a tunable vHS in kagome metals.

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}.

Optimized superconductivity in the vicinity of a nematic quantum critical point in the kagome superconductor Cs(V1-xTix)3Sb5

CsV3Sb5 exhibits superconductivity at Tc = 3.2 K after undergoing intriguing two high-temperature transitions: charge density wave order at ~98 K and electronic nematic order at Tnem ~ 35 K. Here, we investigate nematic susceptibility in single crystals of Cs(V1-xTix)3Sb5 (x = 0.00-0.06) where double-dome-shaped superconducting phase diagram is realized. The nematic susceptibility typically exhibits the Curie‒Weiss behaviour above Tnem, which is monotonically decreased with x. Moreover, the Curie‒Weiss temperature is systematically suppressed from ~30 K for x = 0 to ~4 K for x = 0.0075, resulting in a sign change at x = ~0.009. Furthermore, the Curie constant reaches a maximum at x = 0.01, suggesting drastically enhanced nematic susceptibility near a putative nematic quantum critical point (NQCP) at x = ~0.009. Strikingly, Tc is enhanced up to ~4.1 K with full Meissner shielding realized at x = ~0.0075-0.01, forming the first superconducting dome near the NQCP. Our findings directly point to a vital role of nematic fluctuations in enhancing the superconducting properties of Cs(V1-xTix)3Sb5.

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.

Intertwining of Magnetism and Charge Ordering in Kagome FeGe

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

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.

Exploring the Charge Density Wave Phase of 1T-TaSe_{2}: Mott or Charge-Transfer Gap?

1T-TaSe_{2} is widely believed to host a Mott metal-insulator transition in the charge density wave (CDW) phase according to the spectroscopic observation of a band gap that extends across all momentum space. Previous investigations inferred that the occurrence of the Mott phase is limited to the surface only of bulk specimens, but recent analysis on thin samples revealed that the Mott-like behavior, observed in the monolayer, is rapidly suppressed with increasing thickness. Here, we report combined time- and angle-resolved photoemission spectroscopy and theoretical investigations of the electronic structure of 1T-TaSe_{2}. Our experimental results confirm the existence of a state above E_{F}, previously ascribed to the upper Hubbard band, and an overall band gap of ∼0.7  eV at Γ[over ¯]. However, supported by density functional theory calculations, we demonstrate that the origin of this state and the gap rests on band structure modifications induced by the CDW phase alone, without the need for Mott correlation effects.

Testing electron-phonon coupling for the superconductivity in kagome metal CsV3Sb5

In crystalline materials, electron-phonon coupling (EPC) is a ubiquitous many-body interaction that drives conventional Bardeen-Cooper-Schrieffer superconductivity. Recently, in a new kagome metal CsV₃Sb₅, superconductivity that possibly intertwines with time-reversal and spatial symmetry-breaking orders is observed. Density functional theory calculations predicted weak EPC strength, λ, supporting an unconventional pairing mechanism in CsV₃Sb₅. However, experimental determination of λ is still missing, hindering a microscopic understanding of the intertwined ground state of CsV₃Sb₅. Here, using 7-eV laser-based angle-resolved photoemission spectroscopy and Eliashberg function analysis, we determine an intermediate λ=0.45-0.6 at T = 6 K for both Sb 5p and V 3d electronic bands, which can support a conventional superconducting transition temperature on the same magnitude of experimental value in CsV₃Sb₅. Remarkably, the EPC on the V 3d-band enhances to λ~0.75 as the superconducting transition temperature elevated to 4.4 K in Cs(V_0.93Nb_0.07)₃Sb₅. Our results provide an important clue to understand the pairing mechanism in the kagome superconductor CsV₃Sb₅.

Electric Control of 2D Van Hove Singularity in Oxide Ultra-Thin Films

Divergent density of states (DOS) can induce extraordinary phenomena such as significant enhancement of superconductivity and unexpected phase transitions. Moreover, van Hove singularities (VHSs) lead to divergent DOS in 2D systems. Despite recent interest in VHSs, only a few controllable cases have been reported to date. In this work, by utilizing an atomically ultra-thin SrRuO₃ film, the electronic structure of a 2D VHS is investigated with angle-resolved photoemission spectroscopy and transport properties are controlled. By applying electric fields with alkali metal deposition and ionic-liquid gating methods, the 2D VHS and the sign of the charge carrier are precisely controlled. Use of a tunable 2D VHS in an atomically flat oxide film could serve as a new strategy to realize infinite DOS near the Fermi level, thereby allowing efficient tuning of electric properties.

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.

Order-disorder charge density wave instability in the kagome metal (Cs,Rb)V3Sb5

The origin of the charge density wave phases in the kagome metal compound AV₃Sb₅ is still under great scrutiny. Here, we combine diffuse and inelastic x-ray scattering to identify a 3-dimensional precursor of the charge order at the L point that condenses into a CDW through a first order phase transition. The quasi-elastic critical scattering indicates that the dominant contribution to the diffuse precursor is the elastic central peak without phonon softening. However, the inelastic spectra show a small broadening of the Einstein-type phonon mode on approaching T_CDW. Our results point to the situation where the Fermi surface instability at the L point is of order-disorder type with critical growth of quasi-static domains. The experimental data indicate that the CDW consists on an alternating Star of David and trihexagonal distortions and its dynamics goes beyond the classical weak-coupling scenario and is discussed within strong-electron phonon coupling and non-adiabatic models.

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.

Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV3Sb5

The recently discovered kagome superconductors AV₃Sb₅ (A = K, Rb, Cs) exhibit unusual charge-density-wave (CDW) orders with time-reversal and rotational symmetry breaking. One of the most crucial unresolved issues is identifying the symmetry of the superconductivity that develops inside the CDW phase. Theory predicts a variety of unconventional superconducting symmetries with sign-changing and chiral order parameters. Experimentally, however, superconducting phase information in AV₃Sb₅ is still lacking. Here we report the impurity effects in CsV₃Sb₅ using electron irradiation as a phase-sensitive probe of superconductivity. Our magnetic penetration depth measurements reveal that with increasing impurities, an anisotropic fully-gapped state changes to an isotropic full-gap state without passing through a nodal state. Furthermore, transport measurements under pressure show that the double superconducting dome in the pressure-temperature phase diagram survives against sufficient impurities. These results support that CsV₃Sb₅ is a non-chiral, anisotropic s-wave superconductor with no sign change both at ambient and under pressure.

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.

Charge order landscape and competition with superconductivity in kagome metals

In the kagome metals AV₃Sb₅ (A = K, Rb, Cs), three-dimensional charge order is the primary instability that sets the stage for other collective orders to emerge, including unidirectional stripe order, orbital flux order, electronic nematicity and superconductivity. Here, we use high-resolution angle-resolved photoemission spectroscopy to determine the microscopic structure of three-dimensional charge order in AV₃Sb₅ and its interplay with superconductivity. Our approach is based on identifying an unusual splitting of kagome bands induced by three-dimensional charge order, which provides a sensitive way to refine the spatial charge patterns in neighbouring kagome planes. We found a marked dependence of the three-dimensional charge order structure on composition and doping. The observed difference between CsV₃Sb₅ and the other compounds potentially underpins the double-dome superconductivity in CsV₃(Sb,Sn)₅ and the suppression of T_c in KV₃Sb₅ and RbV₃Sb₅. Our results provide fresh insights into the rich phase diagram of AV₃Sb₅.

Orbital-Hybridization-Driven Charge Density Wave Transition in CsV3 Sb5 Kagome Superconductor

Owing to its inherent non-trivial geometry, the unique structural motif of the recently discovered kagome topological superconductor AV₃ Sb₅ (A = K, Rb, Cs) is an ideal host of diverse topologically non-trivial phenomena, including giant anomalous Hall conductivity, topological charge order, charge density wave (CDW), and unconventional superconductivity. Despite possessing a normal-state CDW order in the form of topological chiral charge order and diverse superconducting gaps structures, it remains unclear how fundamental atomic-level properties and many-body effects including Fermi surface nesting, electron-phonon coupling, and orbital hybridization contribute to these symmetry-breaking phenomena. Here, the direct participation of the V3d-Sb5p orbital hybridization in mediating the CDW phase transition in CsV₃ Sb₅ is reported. The combination of temperature-dependent X-ray absorption and first-principles studies clearly indicates the inverse Star-of-David structure as the preferred reconstruction in the low-temperature CDW phase. The results highlight the critical role that Sb orbitals play and establish orbital hybridization as the direct mediator of the CDW states and structural transition dynamics in kagome unconventional superconductors. This is a significant step toward the fundamental understanding and control of the emerging correlated phases from the kagome lattice through the orbital interactions and provides promising approaches to novel regimes in unconventional orders and topology.

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.