Transition-metal based kagome materials, characterized by their corner-sharing triangle lattice structure, provide a unique platform for investigating correlated and topological phenomena. These include quantum spin liquids, unconventional superconductivity, Dirac/Weyl semimetals, and charge density wave (CDW) order. These phenomena arise from the kagome lattice's inherent properties: geometric spin frustration, flat bands, Dirac cones, and van Hove singularities (VHSs) at varying electron fillings. The AV3Sb5 (A=K, Rb, Cs) family of kagome metals, featuring vanadium kagome nets, exhibits a Z2 topological band structure and superconductivity (Tc max of 2.5 K at ambient pressure), along with CDW order (TCDW = 78–103 K). Evidence suggests unconventional superconductivity, potentially driven by electronic interactions. The multiple VHSs near the Fermi level are believed to be crucial in mediating these exotic phenomena. Van Hove singularities (VHSs), arising from saddle points in the band dispersion, are classified as conventional or higher-order. Higher-order VHSs display flat dispersion along one direction, resulting in a power-law divergent density of states (DOS) in 2D. Kagome lattice VHSs also exhibit sublattice features: sublattice-pure (p-type) and sublattice-mixed (m-type). These sublattice characteristics affect the local and non-local Coulomb interactions. Understanding the nature of these VHSs is crucial to unraveling the correlated behavior in AV3Sb5, but this understanding has remained elusive until now. This research addresses the lack of understanding regarding the nature of VHSs in AV3Sb5. The study uses a combination of advanced experimental and theoretical techniques to directly probe the electronic structure of CsV3Sb5, providing detailed insights into the VHSs and their role in the material's unusual properties.

Extensive research has been conducted on kagome lattice materials due to their unique electronic properties and potential for novel phenomena. Studies on materials such as Herbertsmithite (ZnCu3(OH)6Cl2), showcasing its potential for quantum spin liquid behavior, have laid the foundation for understanding kagome lattice systems [1, 8-11]. Theoretical works exploring the Hubbard model on kagome lattices have predicted the existence of various magnetic phases and instabilities, highlighting the importance of electronic correlations [2, 3, 12-16]. Experimental observations of Dirac fermions and flat bands in kagome metals like FeSn have further emphasized the rich physics of these materials [6]. The recent discovery of the AV3Sb5 family has sparked significant interest, with several studies reporting unconventional superconductivity, charge density waves, and symmetry breaking transitions [26-38]. However, a complete understanding of the interplay between these phenomena and the underlying electronic structure, particularly the role of van Hove singularities, has been missing. This gap in knowledge motivates the current study.

This work employs a multi-faceted approach combining experimental techniques and theoretical calculations to thoroughly investigate the electronic structure of CsV3Sb5. Single crystals of CsV3Sb5 were grown using a self-flux method, ensuring high-quality samples for experimental analysis. The chemical composition was verified using energy-dispersive X-ray spectroscopy (EDS). Angle-resolved photoemission spectroscopy (ARPES) measurements were conducted at the SIS beamline of the Swiss Light Source, using a Scienta-Omicron DA30L analyzer with 78 eV photons. This enabled the mapping of the electronic band structure with high energy and momentum resolution. Polarization-dependent ARPES measurements were performed using circularly and linearly polarized light to selectively probe orbitals with specific symmetries, aiding in the identification of the orbital character of the VHSs. First-principles density functional theory (DFT) calculations were performed using the VASP code [1-3], employing the projector-augmented wave method and the generalized gradient approximation (GGA) with the PBE functional. A plane-wave basis set with a cutoff energy of 500 eV was used, along with a 9 x 9 x 5 k-mesh for Brillouin zone sampling. The experimentally determined crystal structure of CsV3Sb5 was used in the calculations. This theoretical approach provided a complementary perspective on the electronic structure, enabling comparison with experimental findings and detailed analysis of VHS properties. The theoretical calculations were crucial in identifying the VHSs and their character, such as p-type or m-type. The calculations also were done with and without spin-orbit coupling (SOC) to establish the impact of SOC on the electronic structure.

The combined ARPES and DFT analysis revealed the presence of four distinct VHSs in the vicinity of the Fermi level (EF) in CsV3Sb5, all originating from vanadium 3d orbitals. Three VHSs were found around the M point below EF, with two being conventional p-type (sublattice-pure) and one exhibiting a remarkable flat dispersion along the MK direction, indicative of a higher-order p-type nature. A fourth VHS, identified through DFT calculations, is a conventional m-type (sublattice-mixed) located slightly above EF. Polarization-dependent ARPES measurements allowed for the determination of the orbital character of the VHSs. The specific orbital contributions to each VHS were identified. VHS1, VHS2, and VHS3 were assigned to d yz, d xz, and d xy orbitals, respectively. The observation of weaker intensity in the flat-top region of the VHS1 band under horizontal linear polarization is attributed to matrix element effects. The theoretical analysis confirmed the p-type nature of VHS1, VHS2, and VHS3, originating from the A sublattice, and the m-type nature of VHS4, exhibiting a mixed contribution from sublattices B and C. This detailed sublattice characterization of the VHSs is crucial in understanding the interaction mechanisms. The study also investigated the Dirac cones around the K point. Characteristic intensity modulations were observed in the ARPES data under varying polarization conditions, reflecting sublattice interference and providing experimental evidence for the chirality of the kagome-derived Dirac fermions. The observed intensity patterns were successfully reproduced through spectral simulations based on sublattice interference. The proximity of three VHSs (VHS1, VHS2, VHS4) to the Fermi level points to their key role in driving the correlated electronic states in AV3Sb5.

The findings provide a detailed understanding of the complex interplay between the electronic structure and correlated phenomena in CsV3Sb5. The presence of multiple VHSs near the Fermi level, particularly the higher-order VHS1, is significant. The higher-order VHS1 is associated with a large, power-law divergent density of states, suggesting a potential driving force for nematic order. The conventional p-type VHS2, exhibiting strong Fermi surface nesting, could be responsible for the observed 2 × 2 bond CDW instability, although the role of phonon interactions in CDW formation remains a topic of ongoing debate. The coexistence of p-type and m-type VHSs derived from multi-orbital interactions could lead to competition between various pairing instabilities and the emergence of diverse electronic orders. This suggests a pathway for tuning the properties of AV3Sb5 through techniques like carrier doping or pressure, offering potential for controlling and manipulating correlated phases.

This study provides a comprehensive understanding of the electronic structure of CsV3Sb5, identifying four VHSs with distinct sublattice and higher-order characteristics. The detailed orbital and sublattice analysis of these VHSs, combined with the investigation of Dirac cone chirality, lays a strong foundation for understanding the correlated phenomena observed in this family of kagome metals. Future research directions should focus on exploring the effects of external parameters such as pressure and doping on these VHSs and their impact on the interplay of superconductivity, CDW order, and other correlated phases. Further theoretical and experimental investigations can refine the understanding of the interplay between these phenomena and guide the design of novel kagome materials with tunable properties.

The study primarily focuses on CsV3Sb5. While the findings are expected to be relevant to other AV3Sb5 compounds (A=K, Rb), further investigations are needed to confirm the universality of these observations across the family. Additionally, the theoretical calculations utilize the density functional theory (DFT), which might not fully capture the correlation effects influencing the electronic properties. More advanced theoretical methods that incorporate electron-electron interactions more accurately would further enhance the comprehension of the complex electronic structure of these materials.