Introduction

Quantum materials with a large density of states, such as associated with flat bands (FBs), can display exotic quantum states. The FBs, when tuned to near the chemical potential, can provide a large amount of degenerate electronic states across the Brillouin zone (BZ) that are available to respond to interactions, hence leading to electronic instabilities and potential emergent electronic orders, such as magnetic order, charge-density-wave, and unconventional superconductivity1,2,3,4,5,6,7. While FBs near the Fermi level can be achieved through moire superlattices of magic-angle twisted bilayer graphene8,9,10, geometrically frustrated lattices such as the kagome and pyrochlore systems can also exhibit FBs from quantum interference of the electronic wavefunctions11,12,13,14,15. However, stabilizing a kagome lattice to bring these FBs into close proximity to the EF has been challenging, and establishing a relationship between FBs and the electronic/magnetic order has been particularly difficult.

For example, extensive experimental studies on the kagome lattice materials, including the binary 11 systems ((Fe,Co)Sn16,17,18,19,20 and FeGe21,22,23), the 135 systems (AV3Sb524,25,26,27,28,29,30,31 and ATi3Bi5 (A = K, Rb, Cs)32,33,34,35), and the 166 systems (RMn6Sn6 and RV6Sn6 (R = rare earth)36,37,38,39,40,41,42,43,44), have revealed emergent orders, from quantum magnetism and unconventional superconductivity to nematicity and charge orders. However, these phases are often discussed in connection to characteristic features in the electronic structure, such as the Van Hove Singularities (VHSs) or Dirac fermions, attributed to the inherent topology of the kagome lattice, and not to the kagome FBs45,46,47,48,49,50,51,52. A noteworthy development in this context is the discovery of Ni3In, which is reported to host a partial FB at the EF by density functional theory (DFT) predictions and simultaneously exhibit non-Fermi liquid transport behaviors53. This finding bolsters the hypothesis that a FB at the EF extending throughout the momentum space could be a promising avenue to realize exotic quantum orders in bulk quantum materials. Theoretically, models of d-electron systems on kagome and related lattices have been mapped to a Kondo lattice description through the notion of compact molecular orbitals, through which a phase diagram with emergent flat bands and strange metallicity has been identified54,55,56.

The chromium-based kagome metal CsCr3Sb5 has recently been discovered and identified as a promising candidate57. Notably, this material exhibits phase transitions characterized by the appearance of superlattice peaks observed by X-ray diffraction (XRD) below TCDW = 54 K, suggested to be a unidirectional charge density wave (CDW) order. Magnetic susceptibility and nuclear magnetic resonance measurements indicate the simultaneous onset of a magnetic order57. First principle calculations reveal multiple competing density wave phases58,59. Under the application of hydrostatic pressure, the two orders are separated in temperature and suppressed, and a superconducting dome appears with a Tc peaking at 6.4 K57. Although the phase diagram is reminiscent of that of other known unconventional superconducting families such as the iron-based superconductors and cuprates, where superconductivity competes with static magnetic order6,60, there has not yet been an understanding of the nature of the competing order, nor evidence of FBs and their association with magnetism across the 54 K phase transition.

By combining polarization-dependent angle-resolved photoemission spectroscopy (ARPES) measurements and DFT calculations, we unveil the presence of FBs near EF extending through a large portion of the BZ. As the temperature is lowered across TCDW, this FB exhibits a downward shift of approximately 20 meV away from the EF. From resonant inelastic X-ray scattering (RIXS) experiments, we find clear non-dispersive magnetic excitations above the density wave transition temperature near the BZ center. The overall energy spread as well as the center energy position of the magnetic excitations show an increase below TCDW, consistent with the observed shift in FBs from the ARPES measurements. Therefore, our combined ARPES and RIXS measurements signal that the low-temperature order contains a component that is magnetic in origin and that the associated excitations include electron-hole excitations of FBs, implying that FBs in the vicinity of the Fermi level play a role in the magnetic excitations in proximity to unconventional superconductivity6,61,62,63.

Results

CsCr3Sb5 crystallizes in a layered hexagonal lattice consisting of alternatingly stacked Cr-Sb sheets and Cs layers (space group P6/mmm No. 191) with lattice parameters a = 5.4956(1) Å and c = 9.2602(2) Å at 293 K, where the Cr atoms form a kagome lattice (Fig. 1A)57. The characterization of CsCr3Sb5 can be found in Supplementary Fig. S1. The corresponding 3D BZ is plotted in Fig. 1B. Figure 1C shows a map of the reciprocal space in the (H, K, 0) plane where superlattice peaks associated with the density wave order below TCDW are marked. Our X-ray diffraction maps at 110 K (Fig. 1D) and 35 K (Fig. 1F) confirm the appearance of the superlattice peaks at (1/4, 0, 0) and (0, 1/4, 0) in the (H, K, 0) plane below TCDW57, as can be directly observed along the line cuts (Fig. 1E, G). We summarize our key findings in Fig. 1H, I. From ARPES measurements, we find FBs just  ~ 60 meV below the Fermi level that exhibit a  ~ 20 meV downward shift below TCDW (Fig. 1H). Our RIXS measurements conclusively identify magnetic excitations near the BZ center with a spectral width of  ~ 100 meV. These excitations broaden and shift in energy below TCDW (Fig. 1I), corresponding to a broadening of the magnetic electron-hole excitations due to the temperature-dependent shift of the FBs away from the Fermi level. In the following, we present our detailed ARPES and RIXS experimental results.

Fig. 1: Crystal structure, X-ray diffraction, Schematic of ARPES and RIXS results.
figure 1

A Unit cell of CsCr3Sb5. The Cr forms a kagome lattice. B, C Reciprocal space of CsCr3Sb5. CDW observed by XRD are shown as red arrows or red points. The green arrow marks the q of temperature-dependent RIXS, where q∥ is the projection of q onto the sample surface. D, F XRD in the (H, K, 0) plane at 110 K and 35 K. E, G Corresponding cuts of (F) and (G), respectively. H Cartoon illustration of the ARPES observed shift of the kagome flat band away from EF below TCDW. I Cartoon illustration of the observed shift of the magnetic excitations observed by RIXS across TCDW. The light orange and light blue shaded areas indicate the spectral weight that is coupled to particle-hole excitations across EF illustrated in (H).

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As CsCr3Sb5 is isostructural to the well-studied CsV3Sb5, we first compare the DFT calculated band structure of the two systems. As Cr has one additional valence electron, CsCr3Sb5 has more electron filling than CsV3Sb5. This is reflected in the calculated band structure (Fig. 2A, B), where the main features in the two systems are qualitatively similar except an overall raised chemical potential in CsCr3Sb5 compared to that of CsV3Sb5. In particular, the kagome FBs in CsCr3Sb5 are much closer to EF, positioned approximately 200 meV above the EF, in contrast to around 1 eV for CsV3Sb5. Also, the VHSs lie well below EF for CsCr3Sb5, while CsV3Sb5 hosts multiple VHSs near EF. The difference in the predicted FB position is also pronounced in the density of states (DOS) calculations, highlighted by red arrows in Fig. 2C. To visualize the electronic structure of CsCr3Sb5, we present ARPES results measured at 10 K on a kagome termination dominant surface (see core level measurement in the SM and Supplementary Fig. S2). The Fermi surface map corresponding to the kz = 0 plane is shown in comparison to that calculated from DFT (Fig. 2D). Noticeably, the Fermi surfaces contain a large pocket around the Γ point and small pockets around the M points, in good alignment with the DFT calculations for the phase without the density wave order. To note, no remarkable band folding was observed on the Fermi surface. Meanwhile, the VHSs at the M points are observed at 0.5 eV below EF, evident in the characteristic triangular pockets around the K points with their corners touching at the M points, giving a good overall agreement with the DFT calculations (Fig. 2E).

Fig. 2: Electronic structure of CsCr3Sb5.
figure 2

A DFT-calculated band structure of CsCr3Sb5. B DFT-calculated band structure of CsV3Sb5. In (A) and (B), red arrows mark the energy position of the flat bands (FB) while red circles mark the positions of the VHSs in both CsCr3Sb5 and CsV3Sb5. C Comparison of the DOS of CsCr3Sb5 (cyan) and CsV3Sb5 (orange), whose FB energy positions are indicated by the red arrows, respectively. D Fermi surface of CsCr3Sb5 measured with 102 eV photons on the left and DFT calculation on the right. Red solid lines mark the 2D projected BZ. Blue arrows denote the light polarization. E Same as (D) but at EB = 0.5 eV. The black dashed circles mark the position of the VHS at the M point. F The definition and illustration of the orbitals in CsCr3Sb5. G–J band dispersion taken with 114 eV (G)(H) LV and (I)(J) LH polarization along the \(\bar{\Gamma }\)-\(\bar{K}\)-\(\bar{M}\)-\(\bar{K}\) and \(\bar{\Gamma }\)-\(\bar{M}\)-\(\bar{\Gamma }\) directions. The DFT calculations projected onto the orbitals observable in each measurement geometry, according to the selection rules, are overlapped on the band dispersions for comparison. Blue arrows denote the polarization direction. The white solid arrow denotes the dyz character band position, while the white dashed arrow denotes its position in the observation, suggesting a possible orbital-selective band renormalization for dyz orbitals. K Band dispersions measured with 100 eV photons (kz = 0) along \(\bar{\Gamma }\)-\(\bar{M}\). The measurement geometry and polarization are as marked. L EDCs stacking in band dispersions taken with LH polarization at in (K). M Same as (L) but taken with LV polarization. Lines of the same colors in (K–M) denote high symmetry point positions.

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To further visualize the electronic structure of CsCr3Sb5 and understand its orbital textures, we present a detailed comparison between band dispersions along high symmetry directions and the orbital-projected DFT in Fig. 2. The low-energy electronic states are mostly populated by the five Cr-3d orbitals and Sb-5p orbitals illustrated in Fig. 2F. We adopt the site-dependent local coordinates as the basis shown by the colored arrows to fully respect the lattice symmetry (see SM Supplementary Fig. S3). Orbital-projected DFT calculations of the band structure along the high symmetry directions suggest that the topological flat bands associated with the kagome lattice are predominantly of dxz and dyz orbital character, immediately above EF (see SM Supplementary Fig. S3). Experimentally, we can utilize the polarization-dependent photoemission matrix elements to gain information on the dominant orbital character of the observed dispersions. Based on a detailed analysis of such matrix elements for all of our measurement geometries (see SM Supplementary Fig. S3), we can overlay the orbital-projected calculated bands from symmetry-allowed orbitals along two high symmetry directions in the BZ under two polarization directions (Fig. 2), while raw data without DFT is provided in the SM Supplementary Fig. S6). While most features exhibit reasonable overall agreements, we notice that there is a portion of a flat dispersion between \(\bar{K}\)-\(\bar{M}\) near  −1 eV (dotted white arrow in Fig. 2I) connected to an electron band towards \(\bar{\Gamma }\). The orbital selection rules suggest these features can be attributed to dyz or dxy orbital characters (see SM Supplementary Fig. S3). However, no bands in the DFT calculations match this flat portion. To capture this feature, we note that if a renormalization factor of 1.4 is applied to the dyz character band marked by the solid white arrow, the agreement can be better established (see SM Supplementary Fig. S4). Another possibility that we cannot rule out is that the flat portion of dxy character near  −2 eV being strongly renormalized. In either scenario, orbital-dependent correlation effects would need to be invoked in CsCr3Sb5, which is not uncommonly found in multi-orbital systems, including the iron-based superconductors64,65,66,67, a recently reported Mn-based kagome system68, as well as Ca1−xSrxRuO469.

Having discussed the overall electronic structure, we next focus on the FB near EF. First, from the orbital-projected band structure calculated by DFT, we see that the kagome topological flat band appears at 0.25 eV above EF. In Fig. 2K-M, we present the measured band dispersions within 1 eV of EF along Γ-M measured under different polarizations together with the energy distribution curves (EDC). Interestingly, for both polarizations, a flat band feature close to EF can be observed. This can be seen in the ubiquitous peak in the EDCs within 100 meV of EF, and is especially clear at the \(\bar{\Gamma }\) point marked by the red arrows, where according to the DFT calculations, should only have an electron band near EF (Fig. 2A). The location of the electron band bottom can be seen in the EDCs at \(\bar{\Gamma }\) in the form of a hump near −0.7 eV. The only feature above the electron band in the DFT calculation is the kagome flat band, situated slightly above EF. Hence, if we assume that the DFT results are reasonably accurate, the peak we observe in all the EDCs at Γ, located between the electron band bottom and EF, must be the kagome flat band that has been brought down from above EF.

Furthermore, considering that the FB is observable under all of the polarization geometries (see SM and Supplementary Fig. S9 for the complete set of measurements), including those that only allow either even or odd parity orbitals to be observed, this suggests that both dxz and dyz orbitals are participating in forming the observed FB. An additional confirmation for the observation of the FB below EF can be noted from the electron band at Γ. This Sb pz-dominated band is also seen in CsV3Sb5, albeit with a shallower band bottom due to the smaller electron filling70. However, distinct from the CsV3Sb5 case, we observe a bending of the electron dispersion near −70 meV in CsCr3Sb5 (Fig. 2K). From the DFT calculations, it is clear that this electron band hybridizes with the kagome flat band where they cross (see SM and Supplementary Fig. S9). Since the energy position of this slope change matches with the observed peak in the EDCs, this is an indication of the hybridization of the FB with the electron dispersion. We note that while electron-boson coupling generically could also result in dispersion kinks, in such situations, a broadening of the imaginary part of the self-energy beyond the mode energy must also accompany the modification of the real part of the self-energy. Since we do not observe such broadening, we can definitively exclude electron-boson coupling as a potential cause of such dispersion bending (see Supplementary information S9 for detailed analysis). The observed hybridization of the flat band with the electron band further confirms that the FB we observe is intrinsic, not due to disorder-induced localized states that do not interact with the intrinsic band structure. The observation of this hybridization kink also confirms that the peak we observe in the EDC is not due to spectral weight leaking from an FB located above EF, but rather an FB that is located below EF.

Having identified the kagome flat bands, we next present our RIXS results to reveal the low-energy excitations. While ARPES measures the single-particle spectral function in momentum space (k), RIXS measures two-particle excitations in momentum transfer q = Δk, such as magnetic excitations, phonons, crystal-field excitations and plasmons71. The nature of the excitations can be determined by polarization analysis. Specifically, magnetic excitations can be conclusively determined when the scattered photons have rotated polarization from the incident beam72. Such excitations have been observed in cuprates via cross polarization RIXS measurements73,74,75,76. Figure 3A illustrates the scattering geometry of our RIXS experiments. To conclusively determine spin excitations of the system and exclude other excitations, we used π-polarized light with 90° scattering angle between the incident and scattered X-rays of wave vectors kin and kout, respectively. As the dominant low-energy electronic states of CsCr3Sb5 are derived from Cr 3d orbitals, we carried out Cr L3-edge RIXS to unravel its low-energy excitations. Figure 3B plots the X-ray absorption spectra across the Cr L3-edge and shows X-ray energies at which RIXS measurements were taken. Figure 3C plots the RIXS spectra of CsCr3Sb5 taken at these different incident photon energies. The 90°-scattering geometry with π-polarized X-rays ensures the measurement of spin excitations. A clear spectral feature of spin excitation appears around 70 meV as a shoulder of elastic scattering. This energy is smaller than the spin excitation energy scales of the iron61 and copper-oxide superconductors62,77.

Fig. 3: RIXS measurements.
figure 3

A Illustration of RIXS scattering geometry. The scattering plane was perpendicular to the ab plane of CsCr3Sb5. The incident and scattered wave vectors of X-rays, i.e., kin and kout, are orthogonal. The polarization of incident X-rays was in the scattering plane, i.e., π-polarized, resulting in RIXS with a cross-polarization geometry. The polarization of scattered X-rays was unresolved. The projection of wavevector change q onto the ab plane is denoted as q∥. B Cr L3-edge X-ray absorption spectrum (XAS) of CsCr3Sb5 recorded at 300 K. Colored vertical bars indicate the X-ray energies used in RIXS measurements. C Incident-energy-dependent RIXS with q∥ along the ΓM direction at 25 K. Spectra in color were recorded with π-polarized X-rays at selected energies. The RIXS spectrum with σ polarization, i.e., X-ray polarization perpendicular to the scattering plane, shows the instrumental energy resolution of RIXS. D Demonstration of curve fitting for RIXS data analysis. In addition to a linear background, a measured RIXS spectrum was fitted to a spectral profile consisting of three components: one elastic and two electronic excitations. See SM for fitting details. E First Brillouin zone in the a*b* plane of reciprocal space. The red arrow indicates q∥ of momentum-dependent RIXS measurements. F Momentum-dependent RIXS with q∥ along ΓK at 25 K. The energy of incident photons was set to 575.2 eV to optimize the shoulder feature. The dashed lines plot the elastic components; the colored shades indicate spectral profiles arising from spin excitations. G Dispersion of fitted E0 of two spin excitations as a function of in-plane momentum q∥.

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To quantitatively determine the energy scale of the spin excitations in CsCr3Sb5, we used a general damped harmonic oscillator model to generate the spectral profile of the spin excitations78,79

$$S({q}_{| | },E)=A\,\frac{{E}_{0}}{1-{{{\rm{e}}}}^{-\beta E}}\frac{2\,\gamma \,E}{{\left({E}^{2}-{E}_{0}^{2}\right)}^{2}+{(\gamma E)}^{2}},$$
(1)

where E0 is the undamped energy, γ the damping factor, \(\beta=\frac{1}{{k}_{{{\rm{B}}}}T}\) (kB is the Boltzmann constant) and A is a constant. The elastic peak was modeled using a Voigt function, with its spectral width determined by the instrumental resolution. The contribution from the fluorescence tail was described with a polynomial function. Since the spectral profile around zero energy was wider than the instrumental resolution, a low-energy component of spin excitation was required to fit the data. Therefore, the measured RIXS spectrum was fitted to a spectral profile comprising three components: one elastic peak, two electronic excitations and one polynomial background, as shown in Fig. 3D. We note that we cannot describe the finite energy electronic excitations with a single peak because the overall fit would then require elastic scattering much larger than the instrumental resolution (see Supplementary Information S10).

We also measured momentum-dependent RIXS with q∥ along Γ − K (Fig. 3E) to further verify that the observed electronic excitations arise from transitions involving FBs. Figure 3F summarizes the q∥ dependence of the magnetic excitations within the available momentum transfer range along the [H, H, 0] direction. The fitted undamped energy E0 of the two spin components in our RIXS data shows no dispersion for all q∥ within the available range, as plotted in Fig. 3G. This is consistent with the FB results concluded from ARPES measurements.

Finally, we present the temperature dependence of the FBs and spin excitations across TCDW. In Fig. 4A we compare the band dispersion along \(\bar{\Gamma }\)-\(\bar{M}\) taken with linear vertical (LV) polarization at 10 K (left) and 140 K (right). This experimental setup selects the FB of dyz orbital (See SM Supplementary Fig. S7). The FBs are visible at both temperatures, as seen in the spectral image, the peak in the EDC, as well as from the bend in the fitted electron dispersion (marked by a white and red arrow, respectively). From the spectral image, the FB location appears to be closer to EF at 140 K compared to 10 K. This can be seen better from the direct comparison of the EDC taken at the location marked by the black arrow: the peak is shifted towards EF at 140 K by about 20 meV, and is recovered after thermally cycling back to 10 K. The direction of the shift is opposite to that expected purely from the thermal broadening effect of the Fermi-Dirac distribution and hence indicates a real shift of the FB. Similarly, the comparison of band dispersion along \(\bar{\Gamma }\)-\(\bar{M}\) taken with linear horizontal (LH) polarization and horizontal slit at 10 K (T  <  TCDW) and 140 K (T  >  TCDW) shows that FB of dxz orbital also shift towards EF (Fig. 4E). We provide the continuous temperature evolution of this shift and the fitting result in Fig. 4F with the detailed temperature evolution presented in Fig. 4E. Additional temperature dependence measurements and data analysis are given in the Supplementary Information and Supplementary Fig. S6.

Fig. 4: Temperature-dependent results of ARPES and RIXS.
figure 4

A Band dispersion taken with 114 eV LH polarization and horizontal slit direction at 10 K (left) and 140 K (right). White (10 K) and red (140 K) dots denote the fitted MDC positions (see SM) for the electron pocket at Γ. The arrows mark a kink in the dispersion, indicating hybridization with the FB. B EDC1 measured at the denoted position in (A) at 10 K, 140 K, and then thermally cycled back to 10 K. C Fitting details for the 10 K and 140 K EDC1 where a Lorentzian peak (orange) and a constant background (gray) are multiplied by the Fermi-Dirac (FD) function convolved with a fixed Gaussian peak of 40 meV Full-Width-Half-Maximum (FWHM mimicking the experimental resolution). Blue/red dots are the raw data points, the same as (B). Vertical dashed lines mark the fitting range. The dashed arrows denote the fitted Lorentzian peak positions. D Same as (A) but measured with LV polarization. E EDC2 as marked in (D) measured from 10 K to 90 K. (F) Fitted FB positions from EDCs after dividing the FD function convolved with a Gaussian peak with 40 meV FWHM. The dotted line marks the transition TCDW previously reported57. G Temperature-dependent RIXS. Open circles depict raw RIXS data measured with π-polarized incident X-rays at an energy of 572.5 eV and temperatures of 25, 70, and 150 K; solid lines plot the fitted elastic components. The shaded areas denote RIXS features arising from spin excitations. H RIXS spectra at 25 K (blue) and 70 K (red) after removing the elastic component. The bottom panel compares their fitted components of spin excitations. I, J Evolution of fitted parameters E0 and γ for temperatures changed across TCDW. The vertical dashed line indicates the CDW transition temperature TCDW.

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We also conducted temperature-dependent RIXS measurements at temperatures across TCDW. Figure 4G presents the measured RIXS spectra within an energy range of 0.3 eV. All spectra were analyzed using the same curve-fitting scheme as shown in Fig. 3D. To highlight the spectral changes, Fig. 4H compares RIXS spectra above and below TCDW after removing elastic scattering, revealing a subtle yet distinct broadening and shift towards higher energy as the temperature is cooled across TCDW. For quantitative analysis, Fig. 4I, J show the evolution of the fitted bare energy E0 and damping factor γ of both spin excitations, which align with ARPES results shown in Fig. 4F. The observed excitations are coupled to the electron-hole excitations across the Fermi level. As such, the broadening and shifting of the spin excitations likely reflect the shifting of the FBs away from EF, both below and above EF.

Discussions

First, from our systematic polarization dependence ARPES measurements, we clearly resolve the presence of the kagome flat bands near EF in CsCr3Sb5. In comparison to the isostructural CsV3Sb5, the Cr system is effectively electron-doped to an extent that, at the DFT level, the kagome flat bands are brought much closer to EF. However, our observations indicate that bare DFT does not accurately reproduce the flat bands below EF. When the necessary correlation corrections are applied, the discrepancies in the flat band position can be reconciled at a qualitative level, although improved sample quality and refined theoretical approaches are encouraged to further resolve this matter80,81. This is reminiscent of the flat band observed in the 3D pyrochlore material CuV2S4, where the destructive interference and orbital-selective correlation effects work in tandem to pin the flat bands to EF82. It is also in line with the theoretical notion of emergent flat bands, the anticipated quantum phase transitions and strange metallicity54,55,56 and, by extension, unconventional superconductivity.

Second, since the temperature-dependent shift of the FBs away from the Fermi level observed by ARPES across TCDW is largely consistent with the increase in both the spin excitation energy and bandwidth observed by RIXS near the Γ point, our results taken together provide compelling evidence that spin excitations probed by RIXS are coupled to the quasiparticle excitations of the FBs near the Fermi level. From previous X-ray diffraction experiments, it is clear that a structural phase transition occurs below TCDW in CsCr3Sb557. Our RIXS results indicate that this transition is also associated with changes in spin excitations. Hence, this transition is likely a composite order that involves both structural and magnetic degrees of freedom, potentially analogous to the structural and spin density wave order in the iron-pnictide superconductors61, which calls for future neutron scattering experiments to elucidate.

Third, we discuss the potential mechanism for the involvement of the kagome FBs in the formation of this electronic order. Since the chemical potential of CsCr3Sb5 happens to be near the kagome FBs, it is conceivable that their presence drives an electronic order that pushes the FBs away from the Fermi level, as we have observed. With hydrostatic pressure, this electronic order is suppressed, which would leave residual density of states from the FBs near EF to experience the quantum fluctuations expected near a quantum critical point and potentially enable superconductivity. Moreover, unlike the pinning of the large DOS to the M points of the BZ for the VHSs in a kagome metal, the kagome FB provides a high density of states across a much larger portion of the BZ. Therefore, they could be susceptible to multiple types of electronic instabilities of similar energy scales and different q’s, which may be a cause for the involvement of both the lattice and spin degrees of freedom. It remains interesting to theoretically map out the competing orders promoted by the FBs that develop near-EF region in CsCr3Sb5.

Finally, it is interesting to compare CsCr3Sb5 to the other known kagome metal systems that have been extensively studied. First, AV3Sb5 and FeGe are both kagome metals that exhibit charge orders with an in-plane periodicity of 2 × 2. Both these systems exhibit the VHSs at the M points of the BZ in the proximity of EF. While nesting is unlikely to be the dominant driving mechanism for the charge order as theoretically predicted, it may still be a necessary but insufficient condition for selecting the q for the 2 × 2 charge order in these systems. In particular, AV3Sb5 has no magnetism from 3d electrons but has coexisting superconductivity and charge order, while FeGe has a strong coupling of a charge density wave and magnetic order but no superconductivity83,84. CsCr3Sb5 appears to be special as suppression of the density wave by hydrostatic pressure drives strange metallicity and induces superconductivity57.

For kagome metals where the flat bands are in the vicinity of the Fermi level, there are two regimes where materials have been studied. Ni3In represents a regime where the flat band is in proximity to EF yet not readily observed by photoemission. In this regime, no electronic orders are formed yet, but the system exhibits non-Fermi liquid transport behavior, indicating proximity to a potential quantum critical point53. Arguably in the opposite limit is the category of compounds that exhibit strong ordered magnetism. Kagome magnets, including FeSn, FeGe, and the Mn- and Fe-based 166 systems all exhibit magnetism with ordering temperatures well above room temperature16,21,37,85,86. The electronic structure of these compounds, when calculated for the paramagnetic state, all show kagome flat bands that live in the vicinity of the Fermi level, which in the magnetically ordered state split via the exchange splitting, often with an energy scale of 1 ~ 2 eV21. However, recent work on FeSn thin film that measures its electronic structure through its magnetic ordering temperature reveals that the exchange splitting of the bands remains largely intact above the magnetic ordering temperature, demonstrating that the origin of the magnetism in this system is local in nature87, which is likely common for these Fe- and Mn-based system with exceptionally high ordering temperatures.

CsCr3Sb5 is clearly different. Cr-based systems are typically magnetic, but more itinerant than Fe- and Mn-based systems. The similarity of the measured dispersions in the low-temperature density wave ordered phase to the DFT calculated band structure of the non-ordered phase indicates that the modification of the electronic structure through this order is subtle. This is not uncommon for systems with electronically driven orders with a similar ordering temperature, such as some of the underdoped iron-based superconductors where band folding due to the spin density wave is often hard to observe when close to the optimal doping88,89. Yet, the flat band in CsCr3Sb5 is clearly participating in the low-temperature order, evident in its shift away from EF and its coupling with spin excitations. Hence, CsCr3Sb5 appears to exist in a regime that is also close to the potential quantum critical point of the phase diagram but on the ordered side54,55,56, a place that is between the strong magnetically ordered kagome metals and Ni3In. Recent theoretical studies have revealed that the flat bands in close proximity to EF in CsCr3Sb5 give rise to antiferromagnetic spin fluctuations, suggesting the important role that these FBs play in this emergent order59. Interestingly, under the tuning knob of hydrostatic pressure, the competing phase in CsCr3Sb5 is suppressed and superconductivity emerges. This drastic response to pressure, together with the observed FB near EF, and its potential association with spin excitations, suggests that CsCr3Sb5 opens up access to a previously experimentally unexplored regime in the overarching phase diagram of kagome metals that offers intriguing insights into novel phases associated with the topological flat band physics.

Methods

Crystal growth and characterization

The CsCr3Sb5 single crystals were grown using the self-flux method. Cs (Solid, Alfa 99.8%), Cr (Powder, Alfa 99.95%), and Sb (Powder, Alfa 99.5%) in a molar ratio of 12:3:30 were mixed. The mixture was loaded into an alumina crucible, and sealed in a Ta/Nb tube by arc welding under an argon atmosphere with one atmospheric pressure. The tube was sealed in an evacuated quartz tube to protect Ta/Nb from O2. The Ta/Nb tube was used to prevent the reaction between Cs vapor and the quartz tube, but Cs can still react slightly with Ta/Nb. The sample was heated to 850–905 °C within 12 h, kept for 50 h, cooled to 580–600 °C at a rate of 1.5–3 °C /h, and cooled to room temperature naturally. Thin crystalline flakes can be found in the melts, and the crystals are stable to water and the air. The sample size for this experiment is about 1 × 1 mm2.

ARPES measurements

ARPES experiments were performed at the MAESTRO beamline of the Advanced Light Source and beamline 5-2 of the Stanford Synchrotron Radiation Lightsource. The MAESTRO beamline is equipped with a Scienta electron analyzer in a home-designed deflector mode and uses a beamspot of 10 × 10 μm2. SSRL beamline 5-2 employs a DA30 electron analyzer with a 10 × 30 μm2 beamspot. The angular resolution was set to 0.1° and the total energy resolution to ≤ 20 meV. All samples were cleaved in situ at 10 K, and measurements were conducted in ultra-high vacuum (base pressure  < 5 × 10−11 Torr). In figures, the error bars denote the standard errors 1σ in the fitted parameters, calculated as the square root of the diagonal elements of the covariance matrix returned by the least-squares fitting procedure.

RIXS measurements

We conducted Cr L3-edge RIXS measurements using the AGM-AGS spectrometer at beamline 41A90 of the Taiwan Photon Source, National Synchrotron Radiation Research Center, Taiwan. The total RIXS energy resolution was 26 meV, determined by the spectral full width at half maximum of the elastic scattering with σ polarization. The angle between the incident and scattered X-rays was fixed at 90° for both incident-energy-dependent and temperature-dependent RIXS measurements, with unresolved polarization of scattered X-rays. Prior to XAS and RIXS measurements, crystallographic axes were aligned using hard X-ray diffraction with a specially designed tilting adjustment holder. Subsequently, samples were cleaved in air to expose a (001) surface. X-ray absorption spectra were acquired using a photodiode in fluorescence yield mode. The error bars of fitting constants represent the 1σ standard errors on the fit parameters.

DFT calculations

All DFT calculations were performed with the Vienna ab initio simulation package (VASP) code91,92, with Perdew-Burke-Ernzerhof exchange-correlation functional93. The energy cutoff of the plane wave basis is 450 eV, and the 3D Brillouin zone is sampled with a k-point mesh of 11 × 11 × 5. All atoms are relaxed until residual force is under 0.01 eV/Å. A tight-binding model of 31 orbitals is fitted from DFT results with Wannier functions, as implemented in the Wannier90 package94.

XRD measurements

The structure information of the crystal was investigated at ORNL using a Rigaku XtaLAB PRO diffractometer equipped with a HyPix-6000HE detector on single crystals with a dimension of 0.1 × 0.1 × 0.01 mm3. A molybdenum anode was used to generate x-rays with wavelength λ = 0.7107 Å. The samples were cooled by a Helium gas flow provided by an Oxford N-Helix cryosystem.

SEM and EDS measurements

The chemical composition is measured in the FEI Quanta 400 is a high-resolution field emission scanning electron microscope. It is equipped with SE, backscatter, and EDS detectors, and can operate in high vac, low vac, and Wet modes. It is also equipped with a cooling stage.