Nature of charge density wave in kagome metal ScV6Sn6

Kagome lattice materials offer a fertile ground to discover novel quantum phases of matter, ranging from unconventional superconductivity and quantum spin liquids to charge orders of various profiles. However, understanding the genuine origin of the quantum phases in kagome materials is often challenging, owing to the intertwined atomic, electronic, and structural degrees of freedom. Here, we combine angle-resolved photoemission spectroscopy, phonon mode calculation, and chemical doping to elucidate the driving mechanism of the root3*root3 charge order in a newly discovered kagome metal ScV6Sn6. In contrast to the case of the archetype kagome system AV3Sb5 (A= K, Rb, Cs), the van Hove singularities in ScV6Sn6 remain intact across the charge order transition, indicating a marginal role of the electronic instability from the V kagome lattice. Instead, we identified a three-dimensional band with dominant planar Sn character opening a large charge order gap of 260 meV and strongly reconstructing the Fermi surface. Our complementary phonon dispersion calculations further emphasize the role of the structural components other than the V kagome lattice by revealing the unstable planar Sn and Sc phonon modes associated to the root3*root3 phase. Finally, in the constructed phase diagram of Sc(V1-xCrx)6Sn6, the charge order remains robust in a wide doping range x = 0 ~ 0.10 against the Fermi level shift up to ~ 120 meV, further making the electronic scenarios such as Fermi surface or saddle point nesting unlikely. Our multimodal investigations demonstrate that the physics of ScV6Sn6 is fundamentally different from the canonical kagome metal AV3Sb5, uncovering a new mechanism to induce symmetry-breaking phase transition in kagome lattice materials.

excitation e/2, 33 analogous to the fractional spin excitations in kagome quantum spin liquids. 36In this respect, exploring a new kagome system hosting diverse forms of charge order is highly desired, yet has been missing so far.
To this end, we turn our attention to the newly discovered kagome compound ScV6Sn6 hosting the novel √3×√3 charge order below TCO » 92 K (Fig. 1j). 37The ScV6Sn6 belongs to the large family of HfFe6Ge6-type '166' kagome metals (Fig. 1c) with a prospect to tune the charge order by broad chemical substitutions. 16However, the origin and nature of the √3×√3 charge order in ScV6Sn6 have remained to be understood.3][34] The ScV6Sn6 shares the partially filled V kagome lattice with the AV3Sb5, so it is tempting to suggest that the same vHS instability of AV3Sb5 also contributes to the charge order in ScV6Sn6.On the other side, the X-ray refinement of the charge order structure revealed the dominant displacement of the Sc and Sn atoms, while the displacement within the V kagome lattice is marginal. 37Moreover, the √3×√3 charge order is not generally observed in RV6Sn6 series (R = Sc, Y, and rare earth elements), suggesting that extrinsic factors specific to ScV6Sn6 may play a role.
In this work, we established the origin of the √3 × √3 charge order in ScV6Sn6 by comprehensively mapping its electronic structure, phonon dispersion, and phase diagram.Our multimodal approaches coherently point toward that the √3×√3 charge order in ScV6Sn6 is tied to the structural components other than the V kagome lattice and is thus fundamentally different from the 2×2 charge order in AV3Sb5 originating from the intrinsic electronic instability of V kagome plane.
We start with the basic characterizations of ScV6Sn6.Our transport measurements revealed a sudden change in electrical resistivity around TCO » 92 K, signaling a symmetry-breaking phase transition (Fig. 1f).X-ray diffraction measurements detected commensurate superlattice peaks in the low-temperature phase consistent with the √3×√3 charge ordering (Fig. 1d).Both the abrupt drop in the diffraction peak intensity at TCO (Fig. 1e) and the small thermal hysteresis in resistivity (Fig. 1f) are indicative of the first-order nature of the transition.Overall, our transport and diffraction characterizations of ScV6Sn6 are in close agreement with the original report. 37re discussing the detailed electronic structure of ScV6Sn6, we briefly remark on the possible surface terminations of the 166 kagome materials.As shown in Fig. 1c, the unit cell of ScV6Sn6 consists of one ScSn2 layer, one hexagonal Sn2 layer, and two V3Sn kagome layers; this HfFe6Ge6-type 166 structure can expose complex surface terminations upon cleaving.We note that previous studies on the 166 kagome materials yield inconsistent interpretations on the surface terminations (Supplementary Section 1).To resolve this issue, we performed spatially-resolved ARPES and XPS experiments on ScV6Sn6 using micro-focused synchrotron radiation (Fig. 1k,l).
As summarized in Fig. 1m-o, we clearly identified three different surface domains characterized by dramatically different valence band structures and Sn 4d3/2, 4d5/2 core level spectra (D1, D2, and D3 domains, respectively).By comparing the ARPES and XPS spectra at each domain to the slab DFT calculations of various geometries, we unambiguously assigned the D1, D2, and D3 domains to the ScSn2, V3Sn, and Sn2 surface terminations, respectively (Supplementary Section 2,3).Below we focus on the results obtained on the V3Sn termination (D2), which best represents the bulk electronic structure of ScV6Sn6 based on the slab calculation (Supplementary Section 3).
Figure 2 displays our analysis of the low-energy electronic structure of ScV6Sn6.Similar to the case of AV3Sb5, we identified multiple kagome-derived vHSs near the Fermi level.In Fig. 2a-c, we present a three-dimensional stack of the ARPES spectra measured at the vicinity of M point (see the momentum positions of the cut 1-4 in Fig. 2j).From these plots, one can comprehensively understand the dispersions along both the G-M-G (see solid lines in the cut 4) and the K-M-K direction (see dashed lines across the cut 1 to 4).As shown in Fig. 2a,b, we identified two bands having electron-like character along the K-M-K direction and hole-like character along the G-M-G direction; these bands thus form saddle point structures or vHSs at the M point as predicted from the model kagome lattice dispersion (see also schematics in Fig. 2g,h).As shown in Fig. 2c, we also observed one additional vHS with inverted concavity, i.e., hole-like dispersion along the K-M-K and electron-like dispersion along the G-M-G direction (see schematics in Fig. 2i).The density functional theory (DFT) calculations in Fig. 2d-f closely reproduce the experimental results, revealing that the three vHSs in Fig. 2a-c respectively originate from the dxy, dxz, and dz2 local orbital degrees of freedom in the V kagome lattice (Supplementary Section 4).In the kagome lattice, the sublattice character of vHS -pure (p) or mixed (m) sublattice characteris also a topic of great interest, which critically determines the relevance of the on-site and longrange Coulomb interactions and the leading electronic instabilities. 3,4,23By analyzing the sublattice weight distribution near the M point, we revealed that all three vHSs in ScV6Sn6 are p-type vHs having pure sublattice character (Supplementary Section 5).In sum, our analysis provides the complete characterizations of the dispersions, orbital characters, and sublattice types of the vHSs in ScV6Sn6.
Notably, the dxy and dz2 vHS of ScV6Sn6 locate very close to the Fermi level at -0.02 ± 0.01 eV and -0.03 ± 0.02 (Fig. 2a,c), while the dxz vHS is positioned at higher binding energy » -0.40 ± 0.03 eV (Fig. 2b).The former vHSs contribute to the diverging density of states at the Fermi level and can in principle promote various electronic instabilities including the charge orderings.
This scenario indeed applies to the case of AV3Sb5, where the vHSs at the Fermi level develop charge order gaps and directly contribute to the stabilization of the 2×2 charge order. 21,22,38,39To test this scenario in ScV6Sn6, we tracked the temperature evolution of the vHSs across the √3×√3 charge order transition.Comparing the ARPES dispersions in the normal (Fig. 2k,m) and chargeordered states (Fig. 2l,n), we observed that all vHSs in ScV6Sn6 stay surprisingly unaltered across TCO, despite the fact that the vHS momentum (i.e., M point) lies at the folded Brillouin zone boundary of the √3×√3 charge order (see the schematics in Fig. 2j).This observation indicates that in stark contrast to the case of AV3Sb5, the intrinsic electronic instability of the V kagome lattice plays a marginal role in driving the √3×√3 charge order in ScV6Sn6.
After ruling out the vHS, we explore the electronic structure of ScV6Sn6 in the extended momentum range (Fig. 3), to identify the bands actually relevant to the √3×√3 charge order transition.Fig. 3a,b display the Fermi surfaces of ScV6Sn6 measured at the normal and chargeordered state, respectively.The major reconstruction of the Fermi surface across TCO is apparent from our data: the circular intensity pattern centered at Γ % in the normal state is modified to the starshaped pattern in the charge-ordered state as highlighted with the cyan and orange guidelines.To better understand this change, we also present the corresponding energy-momentum dispersions along the Γ % -M ' direction in Fig. 3e,f.In the normal state dispersion (Fig. 3e), we observe a large electron pocket centered at Γ % , which constructs the circular intensity pattern in the normal state Fermi surface (Fig. 3a).Below TCO (Fig. 3f), this electron band bends toward the higher binding energy and develops a substantial charge order gap at the Fermi level.This opening of the charge order gap depletes the intensity in the Fermi surface along the Γ % -M ' direction and explains the starshaped Fermi surface observed in the charge-ordered state (Fig. 3b).The momentum position of the charge order gap is at about two-thirds of the Γ % -M ' direction, which excellently matches with the folded Brillouin zone boundary of the √3×√3 phase (see Fig. 2j).We note that the band renormalization and charge order gap is also observed in other surface terminations supporting their bulk origin (see Supplementary Fig. S7 for the charge order gaps measured in the D1 termination).As shown in Fig 3g,h, our DFT calculations closely capture the experimental results, reproducing the large electron pocket at Γ % in the normal state (Fig. 3g) and opening of the charge order gap DCO » 260 meV across the Fermi level in the charge order state (Fig. 3h).Notably, the magnitude of the charge order gap in ScV6Sn6 is significantly larger than the DCO » 80 meV of AV3Sb5 despite the comparable TCO in two systems. 21,22portantly, this large electron pocket at Γ % , which is closely tied to the √3×√3 charge order, has dominant planar Sn character (i.e., Sn(1) in Fig. 1c).To illustrate this, we present the DFT band structure of ScV6Sn6 in Fig. 4a, along with the V and Sn(1) orbital-projected calculations in Fig. 4b,c.The corresponding Fermi surfaces are also shown in the insets.In the V orbital-projected calculation (Fig. 4b), multiple Dirac bands at K ' and van Hove singularities at M ' originating from the V kagome lattice can be clearly identified.Overall, the V spectral weights dominate the Fermi surface near the zone boundary.In contrast, the Fermi surface near the zone center Γ % has dominant Sn(1) orbital character, as shown in the inset of Fig. 4c.We emphasize that it is this Sn(1) band at Γ % that develops the charge order gap and reconstructs the Fermi surface across TCO (Fig. 3), while the V kagome bands near K ' and M ' remain unaltered across TCO (Fig. 2).
Our results thus highlight that the √3× √3 charge order of ScV6Sn6 is tied to the structural components other than the V kagome lattice, especially to the planar Sn atoms.
The above conclusion from the electronic sector is further supported by our phonon mode calculations presented in Fig. 4d-g.As shown in Fig. 4d, the phonon dispersions of ScV6Sn6 display the continuum of unstable phonon modes centered at H, consistent with the √3×√3 reconstruction in ScV6Sn6 at low temperature.By projecting the phonon density of states to the Sc, V, and Sn(1), Sn(2), Sn(3) sites in the unit cell, we revealed that the unstable phonon modes are associated with the structural distortions involving the planar Sn(1) and Sc sites, while the contribution from the V kagome layer is negligible (Fig. 4e).This result not only explains our observation of the large charge order gap on the Sn(1) bands (Fig. 3) and the marginal change of the V kagome bands (Fig. 2), but also is fully consistent with the X-ray refined charge order structure of ScV6Sn6 that revealed the dominant distortions in the Sn(1) and Sc sites. 37It is also instructive to compare the phonon modes of ScV6Sn6 to those of the CsV3Sb5 shown in Fig. 4f,g.
In stark contrast to the case of ScV6Sn6, the unstable phonon modes of CsV3Sb5 at M and L (associated with the 2×2 charge order) accompany the dominant displacement of the V atoms, and reflect the intrinsic electronic instability from the V kagome layers (Supplementary Fig. S10). 40nally, we construct the phase diagram of Sc(V1-xCrx)6Sn6 series to understand the evolution of charge order with carrier doping (Fig. 5).The charge order phase remains robust in the wide-doping range, up to doping x » 0.10 charges per V atom.In the framework of the virtual crystal approximation (Supplementary Fig. S11), this indicates that the charge order phase remains stable up to the order of 120 meV Fermi level shift, further making the electronic scenarios sensitive to the Fermi level, such as the Fermi surface or vHS nesting, unlikely.We note that the response of the charge order to carrier doping is again highly different in CsV3Sb5, where the charge order rapidly vanishes after the x » 0.02 ~ 0.03 charge doping per V atom, regardless of the doping methods. 31,41 summary, the present work elucidates the origin of the √3×√3 charge order in the newly discovered kagome metal ScV6Sn6.Our comprehensive characterizations of the electronic structure, phonon dispersion, and phase diagram coherently emphasize the essential role of the structural degrees of freedom other than the V kagome lattice in driving the charge order.In this context, the nature of the √3×√3 charge order in ScV6Sn6 is fundamentally different from the 2×2 charge order in the archetype kagome metal AV3Sb5, where the electronic instability in the V kagome lattice plays a major role.As discussed in the introduction, the true charge disproportionation phases in the kagome lattice can support the exotica of physics, including the fractionalization of elementary particles.Our study thus emphasizes that the search for new kagome quantum materials hosting various types of genuine charge orders should be continued.

Single crystal synthesis and characterization.
Single crystals of ScV6Sn6 and Sc(V1-xCrx)6Sn6 doping series were grown by typical self-flux methods.Scandium pieces (99.9 % Research Chemicals), Vanadium pieces (99.7 % Alfa Aeser), and Sn ingot (99.99 % Alfa Aeser) were put in the Alumina crucible with frit disc, then sealed in Ar-gas purged evacuated quartz tube.Ampule was heated at 1100 °C for 24 hrs, then slow cooled to 800 °C with 1~2°C/hr cooling ratio.To remove the flux, ampule was centrifuged at 800 °C.V and Cr ratios of the doping series were confirmed using energy dispersive spectroscopy.Electrical Resistivity measurements was performed with Physical Properties Measurement System (PPMS, Quantum design) using a conventional 4 probe method.The X-ray diffraction measurements were conducted using Cu Kα1 source (λ = 1.54 Å) and 6-axis diffractometer.We identified (1/3 1/3 19/3), The data in Fig. 2 are acquired with 129 eV photons, while the data in Fig. 3 are measured with 115 eV photons.All normal state (charge-ordered state) data in the main text is obtained at 120 K (6 K) using linear horizontal light polarization, unless specified.We refer to Supplementary Fig. S8 for the data measured in finer temperature steps.

Spatially-resolved ARPES and XPS experiments.
The real-space mappings of the valence band structure and core level spectra were conducted at Beamline 7.0.2(MAESTRO) of the Advanced Light Source.To resolve the complex surface domains of ScV6Sn6, we used the micro-focused synchrotron of lateral dimension 30 × 30 µm 2 .The domain dependent ARPES and XPS spectra are compared to the slab DFT calculations of various geometries, to assign the atomic termination layer to each domain (Supplementary Section 2,3).DFT calculations.DFT calculations were performed using the Vienna AB initio Simulation Package software. 42,43The generalized-gradient approximation Perdew-Burke-Ernzerhof exchange-correlation functional was chosen to calculate the exchange-correlation energy. 44The pseudopotential was defined based on the projector augmented-wave method. 45VASPKIT software was used for pre-and post-processing of DFT calculated information. 46For the bulk band calculation of ScV6Sn6, we used the lattice parameters (a, b, c) = (5.456Å, 5.456 Å, 9.230 Å) which is obtained by relaxing the reported single crystal refinement data. 37Relaxation is performed at the 350 eV kinetic energy cutoff that fully covers the atomic energy.The static electronic structure was calculated using a G-centered k-point mesh, 15ⅹ15ⅹ8 for the normal state structure and 8ⅹ8ⅹ3 for the charge ordered structure.We present the overall band dispersion of ScV6Sn6 in the normal state with and without spin-orbit coupling in Supplementary Fig. S9a.Supplementary Fig. S9b displays the unfolded DFT band dispersion in the charge ordered state.To understand the termination-dependence of the valence band and core level spectra, we performed the slab DFT calculation on all possible charge neutral slab configurations of ScV6Sn6 relaxed at the 350 eV kinetic cutoff energy (Supplementary Section 2,3).Γ-centered 11ⅹ11ⅹ1 k-point mesh were used for the slab band calculation.Each slab has 20 atomic layers and the vacuum was fixed at 20 Å.
DFPT calculations.Phonon dispersions were computed within the density functional perturbation theory (DFPT) framework.Input parameters were generated from the 3ⅹ3ⅹ2 supercell using Phonopy software. 47,48We compared the phonon modes of two kagome metals, ScV6Sn6 and CsV3Sb5.Various smearing factors 0.10, 0.125, 0.15, 0.175, and 0.20 were tested for both compounds.We present the smearing factor-dependent phonon dispersions in Supplementary Fig. S10.c, Experimentally identified vHS dispersions in ScV6Sn6 using ARPES.The cut 1-4 in a-c plot the ARPES spectra measured perpendicular to the K-M-K direction, with the cut 1 crossing the K point and the cut 4 crossing the M point (see panel j for the exact momentum positions of cut 1-4).We identified three coexisting vHS in ScV6Sn6 as marked with black, orange, and cyan guidelines in a-c, respectively.d-e, Corresponding DFT band structures of ScV6Sn6 for comparison with the ARPES spectra in ac.The fat bands in d-f represent the spectral weight of the dxy, dxz, and dz2 local orbitals, respectively.g-i, Schematics of the saddle point dispersions or vHSs.The concavity of vHS is identical for dxy and dxz vHS, while it becomes opposite for the dz2 vHS.j, Schematics of the pristine (grey hexagons) and the √3×√3 folded (cyan hexagons) in-plane Brillouin zones of the ScV6Sn6.Dashed and solid orange arrows represent the reciprocal lattice vectors.k-n, Temperature dependence of the vHSs across the charge order transition.The cyan and black dashed lines are guide for the eye for the dz2 and dxy vHS dispersions near the Fermi level, respectively.All data were collected with 129 eV photons, measuring the kz » 0 high-symmetry plane of the three-dimensional Brillouin zone.

Figure 1 |
Figure 1 | Novel charge orders in kagome metal.a, Prototypical electronic structure of the kagome lattice featuring the Dirac point, vHS, and flat band.Inset displays the lattice structure.b,c, Crystal structure of kagome metals CsV3Sb5 (a) and ScV6Sn6 (b) sharing the same V kagome plane.d,e, Temperature-dependent X-ray diffraction profile and integrated peak area of the (2/3, 2/3, 20/3) charge order peak in ScV6Sn6, respectively.f, Temperature-dependence of the in-plane resistivity of ScV6Sn6 around the charge order transition.g-j, Various types of charge orders predicted from the extended Hubbard model on kagome lattice.k,l, Real space mapping of the ARPES and Sn 4d XPS intensity of the ScV6Sn6 sample.Three different surface domains (D1, D2, and D3) with dramatically different ARPES and XPS spectra were identified.The representative D1, D2, and D3 domain positions are marked in k,l.m-o, ARPES (Top panel) and XPS (bottom panel) spectra of ScV6Sn6 on D1, D2, and D3 domains, respectively.The dashed cyan and orange boxes in m-o represent the area where the ARPES and XPS intensities are integrated and plotted in k,l.

Figure 2 |
Figure2| Characterization of the van Hove singularities in ScV6Sn6.a-c, Experimentally identified vHS dispersions in ScV6Sn6 using ARPES.The cut 1-4 in a-c plot the ARPES spectra measured perpendicular to the K-M-K direction, with the cut 1 crossing the K point and the cut 4 crossing the M point (see panel j for the exact momentum positions of cut 1-4).We identified three coexisting vHS in ScV6Sn6 as marked with black, orange, and cyan guidelines in a-c, respectively.d-e, Corresponding DFT band structures of ScV6Sn6 for comparison with the ARPES spectra in ac.The fat bands in d-f represent the spectral weight of the dxy, dxz, and dz2 local orbitals, respectively.g-i, Schematics of the saddle point dispersions or vHSs.The concavity of vHS is identical for dxy and dxz vHS, while it becomes opposite for the dz2 vHS.j, Schematics of the pristine (grey hexagons) and the √3×√3 folded (cyan hexagons) in-plane Brillouin zones of the ScV6Sn6.Dashed and solid orange arrows represent the reciprocal lattice vectors.k-n, Temperature dependence of the vHSs across the charge order transition.The cyan and black dashed lines are guide for the eye for the dz2 and dxy vHS dispersions near the Fermi level, respectively.All data were collected with 129 eV photons, measuring the kz » 0 high-symmetry plane of the three-dimensional Brillouin zone.

Figure 3 |
Figure 3 | Fermi surface reconstruction and charge order gap opening across the √×√ transition.a,b, The Fermi surface of ScV6Sn6 in the normal and charge-ordered state, respectively.The data were obtained using 115 eV photons corresponding to the kz » p high-symmetry plane.The cyan and orange solid lines in a-f are guide for the eye highlighting the band dispersion around the Γ % point.c,d, Stack of the constant energy contours of ScV6Sn6 in the normal and chargeordered state, respectively.e,f, Normal and charge-ordered state dispersion of ScV6Sn6 measured along the Γ % -M ' high symmetry direction marked in a,b.The cyan and orange arrows highlight the back bending of the dispersion due to the charge order gap opening at the Fermi level.The right panels in e,f display the energy distribution curves measured at the √3×√3 charge order Brillouin zone boundary, i.e. at the two thirds of Γ % -M ' momentum.The spectral weight shift and charge order gap opening is evident from the energy distribution curves as marked with the black arrow in f. g,h, DFT band structure of ScV6Sn6 in the normal and charge-ordered state, respectively.The band structure in the charge-ordered state is unfolded to the pristine Brillouin zone to facilitate comparison.The black arrow in h indicates the charge order gap observed in the experiment.

Figure 4 |
Figure 4 | Element-and site-resolved DFT band structure and DFPT phonon modes of ScV6Sn6.a-c, kz-integrated DFT band structure and its projection to the V and Sn(1) orbitals, respectively.The insets display the corresponding Fermi surfaces.d, The phonon dispersion of ScV6Sn6 obtained from the DFPT calculation.e, The phonon partial density of states of ScV6Sn6 projected to the Sc, V, Sn(1), Sn(2), and Sn(3) sites of the unit cell (see Fig. 1c).f,g, The DFPT phonon dispersion and phonon partial density of states of CsV3Sb5, respectively, for comparison with the ScV6Sn6 in d,e.

Figure 5 |
Figure 5 | Phase diagram of charge order in Sc(V1-xCrx)6Sn6 series.a, Evolution of the normalized resistivity T/T300K as a function of Cr-doping in x = 0, 0.01, 0.02, 0.03, and 0.06 samples.b, Doping-temperature phase diagram of the charge order in ScV6Sn6.