The kagome lattice, a geometric arrangement of interconnected hexagons and triangles, has emerged as a fertile ground for exploring novel quantum phenomena. Its inherent geometric frustration leads to unique electronic band structures featuring Dirac fermions, flat bands, and Van Hove singularities (VHSs). This distinctive band structure can interact with various exotic electronic instabilities, as evidenced in several kagome metal families. For instance, Fe-, Mn-, and Co-based kagome magnets exhibit topological flat bands, Dirac and Weyl fermions, and Fermi arcs. The non-magnetic V-based AV₃Sb₅ (A = Cs, K, Rb) kagome metals have garnered significant attention due to their superconductivity and various symmetry-breaking states, including charge density waves (CDWs) potentially linked to loop current orders. The RV₆Sn₆ (166 family) bilayer kagome metals, where R is a rare-earth ion, offer a tunable platform to investigate Fermi surface instabilities. Similar to AV₃Sb₅, the vanadium atoms in RV₆Sn₆ are non-magnetic, but magnetism can be tuned by selecting the rare-earth element R. ScV₆Sn₆ stands out among these metals due to the reported charge density wave (CDW) state below T_CDW ≈ 92 K. Unlike the CDW in AV₃Sb₅, which connects the M points (satisfying the nesting condition between VHSs at M), the charge order (CO) in ScV₆Sn₆ connects the K points, time-reversal invariant points where Dirac nodes form. The CO in ScV₆Sn₆, like in AV₃Sb₅, is three-dimensional but with a different wave vector Q* = (1/3, 1/3, 1/3) rotated 30 degrees. Previous studies have indicated time-reversal symmetry breaking and an anomalous Hall effect, both coinciding with the CO phase, despite the absence of spin magnetism. This study uses scanning tunneling microscopy/spectroscopy (STM/S) and angle-resolved photoemission spectroscopy (ARPES) to investigate the electronic structure and CO formation in ScV₆Sn₆, aiming to understand its origin and spectroscopic fingerprint and compare it to the extensively studied CDW in AV₃Sb₅.

Extensive research has been conducted on kagome metals, exploring their unique electronic properties stemming from the kagome lattice structure. Studies on Fe-based kagome magnets have revealed the presence of Dirac fermions, flat bands, and Fermi arcs [6-15]. Similarly, Mn-based kagome magnets have shown topological magnon bands and complex magnetic phases [16-21], while Co-based systems have demonstrated Weyl fermions and a giant anomalous Hall effect [22-25]. The AV3Sb5 family of kagome metals has been a focus of intense investigation due to the emergence of superconductivity and charge density waves [28-41], with theoretical work suggesting a connection between these phenomena and loop current orders [42]. The discovery of the RV6Sn6 family provided a new platform to explore Fermi surface instabilities [43-48], where the non-magnetic vanadium atoms allow for the tuning of magnetic properties via the rare-earth element R [49-51]. Previous work on ScV6Sn6 reported a charge density wave at approximately 92 K [46], exhibiting distinct characteristics from the CDWs observed in AV3Sb5, including a different wave vector and potential time-reversal symmetry breaking [52, 53]. However, detailed spectroscopic fingerprints of the charge order in ScV6Sn6 remained largely unexplored.

Single crystals of ScV₆Sn₆ were grown using a flux-based method, characterized by a kink in magnetization measurements at the onset of charge order. STM/S measurements were conducted on ultra-high vacuum (UHV)-cleaved crystals at 4.5 K using a customized Unisoku USM1300 STM system. Spectroscopic data were acquired using a lock-in technique. ARPES measurements were performed at the QMSC beamline of the Canadian Light Source and at SSRL Beamline 5-2, with single crystals cleaved in-situ at 20 K. Energy and angular resolutions were better than 20 meV and 0.1°, respectively. Density-functional theory (DFT) calculations were performed using the Vienna ab-initio Simulation Package (VASP) for ScV₆Sn₆ and Wien2k for TbV₆Sn₆, employing the generalized gradient approximation (GGA) for exchange-correlation interactions. For ScV₆Sn₆, a plane-wave basis set with a 300 eV cutoff was used, and the Brillouin zone was sampled with a 21 × 21 × 10 k-mesh. Surface states were simulated using slabs of 8 kagome layers. For TbV₆Sn₆, a full-potential linear augmented plane wave (FP-LAPW) method was utilized, treating 4f electrons as non-magnetic core states.

STM topographs revealed a √3 × √3 R30° superstructure consistent with the in-plane component of the bulk CO wavevector. Unlike the C₂-symmetric CDW state in AV₃Sb₅, ScV₆Sn₆ showed no evidence of rotation symmetry breaking. dI/dV spectra showed a partial gap (Δ_CO = 20 meV) at the Fermi level. Surprisingly, dI/dV maps revealed a spatial phase shift (contrast inversion) in charge modulations at energies significantly higher than Δ_CO, attributed to another spectral gap. ARPES measurements showed similarities between ScV₆Sn₆ and TbV₆Sn₆ (lacking CO), suggesting a non-Fermi-surface nesting mechanism for the CO in ScV₆Sn₆. Temperature-dependent ARPES revealed band reconstruction near the K point, consistent with DFT calculations of surface states under the bulk CDW wavevector. This reconstruction involves a spectral weight shift towards the Fermi level near the K point. DFT calculations of bulk states did not predict states near the H point at the Fermi level, meaning that the band reconstruction near K is unlikely to result from bulk band folding. STM topographs obtained at different bias voltages revealed charge modulation contrast reversal at positive energies, which was also confirmed by dI/dV maps, suggesting another spectral gap, and distinct behavior from the CO contrast inversion near the Fermi level seen in AV₃Sb₅. The CO in ScV₆Sn₆ showed a surprising surface termination dependence, being clearly observed on the kagome termination but not on the Sn^2- termination.

The findings challenge the prevailing understanding of CO formation in kagome metals. The similarity of the electronic structure of ScV₆Sn₆ and TbV₆Sn₆, despite the presence of CO in the former and its absence in the latter, strongly suggests that Fermi surface nesting of VHSs is not the primary driver of CO formation in ScV₆Sn₆. The observed contrast inversion at energies much higher than the Fermi level gap, along with the absence of rotation symmetry breaking, further underscores the distinct nature of the CO in ScV₆Sn₆ compared to its counterparts in AV₃Sb₅. The K point in the Brillouin zone seems crucial, as it's connected by the CO wave vector, exhibits phonon softening, and plays a significant role in stabilizing the √3 × √3 CDW order according to theoretical studies. The presence of a Dirac point near the Fermi level at K in ScV₆Sn₆ may be the key factor driving the CO formation, along with structural instabilities at K. The observation of multiple spectral gaps in ScV₆Sn₆ highlights a frequently overlooked aspect of charge-ordered systems.

This research provides a comprehensive understanding of the charge order in ScV₆Sn₆, demonstrating its unique characteristics compared to other kagome metals. The findings suggest a novel mechanism for CO formation driven by the proximity of a Dirac node at K and structural instabilities, rather than Fermi surface nesting of VHSs at M. This study offers insights into the diverse mechanisms of charge order formation in kagome materials and suggests a new guiding principle for searching for similar COs in other materials based on similar electronic and structural features.

The study primarily focused on surface sensitive techniques, and the bulk properties might differ from the surface-specific findings. Furthermore, the DFT calculations used approximations that might not capture all the complex interactions within the material. While the authors propose a mechanism for the CO based on the Dirac node near K, further theoretical and experimental investigations are needed to fully confirm this.