# Ubiquitous Flat Bands in a Cr-based Kagome Superconductor

Yucheng Guo  Department of Physics and Astronomy, Rice University, Houston,
77005 Texas, USA  Advanced Light Source, Lawrence Berkeley National
Laboratory, Berkeley, 94720 California, USA  Zehao Wang  Department of Physics
and Astronomy, Rice University, Houston, 77005 Texas, USA  Fang Xie
Department of Physics and Astronomy, Rice University, Houston, 77005 Texas,
USA  Yuefei Huang  Department of Materials Science and NanoEngineering, Rice
University, Houston, Texas 77005, USA  Bin Gao  Department of Physics and
Astronomy, Rice University, Houston, 77005 Texas, USA  Ji Seop Oh  Department
of Physics and Astronomy, Rice University, Houston, 77005 Texas, USA
Department of Physics, University of California, Berkeley, 94720 California,
USA  Han Wu  Department of Physics and Astronomy, Rice University, Houston,
77005 Texas, USA  Zhaoyu Liu  Department of Physics, University of Washington,
98105 Washington, USA  Zheng Ren  Department of Physics and Astronomy, Rice
University, Houston, 77005 Texas, USA  Yuan Fang  Department of Physics and
Astronomy, Rice University, Houston, 77005 Texas, USA  Ananya Biswas
Department of Physics and Astronomy, Rice University, Houston, 77005 Texas,
USA  Yichen Zhang  Department of Physics and Astronomy, Rice University,
Houston, 77005 Texas, USA  Ziqin Yue  Department of Physics and Astronomy,
Rice University, Houston, 77005 Texas, USA  Applied Physics Graduate Program,
Smalley-Curl Institute, Rice University, Houston, 77005 Texas, USA  Cheng Hu
Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, 94720
California, USA  Chris Jozwiak  Advanced Light Source, Lawrence Berkeley
National Laboratory, Berkeley, 94720 California, USA  Aaron Bostwick  Advanced
Light Source, Lawrence Berkeley National Laboratory, Berkeley, 94720
California, USA  Eli Rotenberg  Advanced Light Source, Lawrence Berkeley
National Laboratory, Berkeley, 94720 California, USA  Makoto Hashimoto
Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator
Laboratory, Menlo Park, 94025 California, USA  Donghui Lu  Stanford
Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo
Park, 94025 California, USA  Junichiro Kono  Department of Physics and
Astronomy, Rice University, Houston, 77005 Texas, USA  Department of
Electrical and Computer Engineering, Rice University, Houston, 77005 Texas,
USA  Smalley-Curl Institute, Rice University, Houston, 77005 Texas, USA
Department of Materials Science and NanoEngineering, Rice University, Houston,
77005 Texas, USA  Jiun-Haw Chu  Department of Physics, University of
Washington, 98105 Washington, USA  Boris I. Yakobson  Department of Materials
Science and NanoEngineering, Rice University, Houston, Texas 77005, USA
Robert J. Birgeneau  Department of Physics, University of California,
Berkeley, 94720 California, USA  Qimiao Si<EMAIL_ADDRESS>Department of
Physics and Astronomy, Rice University, Houston, 77005 Texas, USA  Pengcheng
Dai<EMAIL_ADDRESS>Department of Physics and Astronomy, Rice University,
Houston, 77005 Texas, USA  Ming Yi<EMAIL_ADDRESS>Department of Physics and
Astronomy, Rice University, Houston, 77005 Texas, USA

###### Abstract

In the quest for novel quantum states driven by topology and correlation,
kagome lattice materials have garnered significant interest due to their
distinctive electronic band structures, featuring flat bands (FBs) arising
from the quantum destructive interference of the electronic wave function. The
tuning of the FBs to the chemical potential would lead to the possibility of
liberating electronic instabilities that lead to emergent electronic orders.
Despite extensive studies, direct evidence of FBs tuned to the chemical
potential and their participation in emergent electronic orders have been
lacking in bulk quantum materials. Here using a combination of Angle-Resolved
Photoemission Spectroscopy (ARPES) and Density Functional Theory (DFT), we
reveal that the low-energy electronic structure of the recently discovered Cr-
based kagome metal superconductor CsCr3Sb5 is dominated by a pervasive FB in
close proximity to, and below the Fermi level. A comparative analysis with
orbital-projected DFT and polarization dependence measurement uncovers that an
orbital-selective renormalization mechanism is needed to reconcile the
discrepancy with the DFT calculations, which predict the FB to appear 200 meV
above the Fermi level. Furthermore, we observe the FB to shift away from the
Fermi level by 20 meV in the low-temperature density wave-ordered phase,
highlighting the role of the FB in the emergent electronic order. Our results
reveal CsCr3Sb5 to stand out as a promising platform for further exploration
into the effects of FBs near the Fermi level on kagome lattices, and their
role in emergent orders in bulk quantum materials.

##  I Main

In the intricate tapestry of quantum materials, electron correlations play a
pivotal role in determining the material properties where either the onsite
Coulomb repulsion is pronounced or electron kinetic energy is significantly
reduced. These conditions underpin the emergence of exotic quantum states such
as magnetism, unconventional superconductivity, and charge orders, observed in
systems including moiré lattices, heavy fermion compounds, cuprates, and iron-
based superconductors [1, 2, 3, 4, 5, 6, 7]. Recently, geometrically
frustrated lattices such as the kagome and pyrochlore systems have shown
promise due to the emergence of topological FBs from quantum interference of
the electronic wavefunctions, which impart non-local topological features to
the systems [8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. The FBs, when tuned to
near the chemical potential, can provide a large amount of degenerate
electronic states across the Brillouin zone that are available to respond to
interactions, hence leading to electronic instabilities and potential emergent
electronic orders. Therefore, the goal of engineering these lattices to align
a topological FB to the Fermi level ($E_{F}$) has always been an important
aspect of kagome metal research [1]. Despite numerous reports on positioning
other topological features like the Van Hove singularities (VHSs) [18, 19, 13,
20, 21, 22, 14, 23] and Dirac points at the Fermi level [12, 24, 25, 26, 10,
27, 28], stabilizing a kagome lattice to bring these FBs into close proximity
to the $E_{F}$ continues to be challenging, especially in a system with
electronic orders.

Within the landscape of kagome lattice materials, extensive studies on the
binary systems including CoSn [9, 24], FeSn [12, 10, 25], and FeGe [29, 11,
14], the 135 systems AV3Sb5 [30, 31, 32, 33, 34, 20, 35, 36, 17] and ATi3Bi5
(A=K, Rb, Cs) [23, 37], and the 166 systems RMn6Sn6 and RV6Sn6 (R=Tb, Y, Yb,
Gd, Er, Dy, Ho, Sc…) [38, 27, 26, 18, 21, 39, 40, 41, 42], have revealed
emergent orders, from quantum magnetism and unconventional superconductivity
to nematicity and charge orders. These phases are often discussed in
connection to characteristic features in the electronic structure such as the
VHSs or Dirac fermions, attributed to the inherent topology of the kagome
lattice. However, the anticipated quantum states induced by the kagome FBs
remain elusive, despite significant theoretical predictions [43, 44, 45, 46,
47, 48, 49, 50]. A noteworthy development in this context is the discovery of
Ni3In, which is reported to host a partial FB at the $E_{F}$ by DFT
predictions and simultaneously exhibit non-Fermi liquid transport behaviors
[51]. This finding bolsters the hypothesis that a FB at the $E_{F}$ extending
throughout the momentum space could be a promising avenue to realize exotic
quantum orders in bulk quantum materials.

The chromium-based kagome metal CsCr3Sb5 has recently been discovered and
identified as a promising candidate [52]. Notably, this material exhibits
phase transitions characterized by the appearance of superlattice peaks
observed by x-ray diffraction below 54K, suggested to be a unidirectional
density wave order. First principle calculations reveal multiple competing
spin density wave phases, suggesting strong magnetic fluctuations and
frustration [53, 54]. Under the application of hydrostatic pressure, this
order is suppressed, and a superconducting dome appears with a $T_{c}$ peaking
at 6.4 K. 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 other symmetry-breaking
electronic orders [7, 55]. By combining polarization-dependent ARPES
measurements and DFT calculations, we provide a systematic study of the
electronic structure of this new kagome system. Our measurements reveal that
the measured Fermi surface and VHSs match reasonably well with DFT predictions
[52, 53]. However, we identify the presence of FBs at $E_{F}$ extending
through a large range of the Brillouin zone, with a mixture of multiple
orbital characters. Its location in energy is much closer to $E_{F}$ compared
to that from the DFT calculations, suggesting the presence of electron
correlation effects. Moreover, as the temperature is lowered across the
density wave order transition temperature, this FB exhibits a downward shift
of approximately 20 meV away from the $E_{F}$, suggesting its potentially
important role in the emergence of the density wave order. Consequently, our
measurements reveal CsCr3Sb5 as an important kagome platform where flat bands
are tuned to the vicinity of the Fermi level and, as a result, participate in
the electronic orders that appear in proximity to superconductivity.

Figure 1:  Overall electronic structure of kagome metal CsCr3Sb5. (a) The
crystal structure for CsCr3Sb5. The red solid lines denote the 2D Cr kagome
lattice. (b) DFT-calculated band structure of CsCr3Sb5. (c) DFT-calculated
band structure of CsV3Sb5. In (b) and (c), 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. (d) Comparison of the DOS of CsCr3Sb5 (cyan) and
CsV3Sb5 (orange) whose FB energy positions are indicated by the red arrows,
respectively. (e) 3D BZ of CsCr3Sb5. $k_{z}$ = 0 plane is marked by the red
hexagon while $k_{z}$ = $\pi$/c plane is marked by the blue hexagon. (f) Fermi
surface of CsCr3Sb5 measured with 102eV photons on the left and DFT
calculation on the right. Red solid lines mark the 2D projected BZ. Blue
arrows denote the light polarization. (g) Same as (f) but at EB = 0.5eV. The
black dashed circles mark the position of the VHS at the M point.

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 $a=5.445\,\AA$ and $c=9.250\,\AA$, where the Cr atoms
form a kagome lattice (Fig. 1a). The corresponding 3D BZ is plotted in Fig.
1b. 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 considerably more electron filling than
CsV3Sb5. This is reflected in the calculated band structure and density of
states (DOS) (Fig. 1b-d), 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 FB in CsCr3Sb5 is much
closer to $E_{F}$, positioned approximately 200 meV above the $E_{F}$, in
contrast to around 1 eV for CsV3Sb5. Also, the VHSs lie well below $E_{F}$ for
CsCr3Sb5, while CsV3Sb5 hosts multiple VHSs near $E_{F}$. The difference in
the predicted FB position is also pronounced in the DOS calculations,
highlighted by red arrows in Fig. 1d. To visualize the electronic structure of
CsCr3Sb5, we present ARPES results measured at 10K on a kagome termination
dominant surface (see core level measurement in the Supplementary Information
and Fig. S1). From a detailed photon-energy dependence measurement, we can
determine the inner potential of CsCr3Sb5 to be 19 eV (see Supplementary
Information and Fig. S4). The Fermi surface map corresponding to the kz = 0
plane is shown in comparison to that calculated from DFT (Fig. 1f).
Noticeably, the Fermi surfaces contain a large pocket around the $\Gamma$
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 $E_{F}$, 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. 1g).

Figure 2:  Orbital-dependent electron correlation effects. (a) The definition
and illustration of the orbitals in CsCr3Sb5. (b)-(g) orbital projected DFT
for Cr (b) ${d_{xz}}$ , (c) ${d_{yz}}$, (d) ${d_{xy}}$, (e)
${d_{x^{2}-y^{2}}}$, (f) ${d_{z^{2}}}$ orbitals and Sb1 (g) ${p_{z}}$ orbital.
(h) Orbital selective rules for photoemission matrix elements for the orbitals
defined in (a) and the measurement directions are drawn. Red lines indicate
the direction of the analyzer slit. Black hexagons indicate the BZs.
Horizontal (vertical) blue arrows mark the LH (LV) light polarization. (i)-(l)
band dispersion taken with 114eV (i) LV and (k) 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 ${d_{yz}}$ character band position while the white dashed arrow denotes
its position in the observation, suggesting a possible orbital-selective band
renormalization for ${d_{yz}}$ orbitals.

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-3$d$ orbitals
and Sb-5$p$ orbitals illustrated in Fig. 2a. We adopt the site-dependent local
coordinates as the basis shown by the colored arrows to fully respect the
lattice symmetry (see Supplementary Information). Orbital-projected DFT
calculations of the band structure along the high symmetry directions are
presented in Fig. 2b-g. The topological flat bands associated with the kagome
lattice are predominantly of ${d_{xz}}$ and ${d_{yz}}$ orbital character,
immediately above $E_{F}$. In an ARPES measurement, the even/odd parity of
these orbitals with respect to the high symmetry directions in relation to the
light polarization determines whether the spectra of these orbitals are
observable or suppressed via the photoemission matrix elements. For the
orbitals as defined on the kagome lattice in Fig. 2a, we tabulate the
observable orbitals under all the possible high symmetry directions and light
polarizations in Fig. 2 (see Supplementary Information and Fig. S2). LH (LV)
is linear horizontal (linear vertical) polarization. Figure 2i-l presents the
band dispersions corresponding to $k_{z}$ = $\pi$/c (taken with 114eV photons)
along two high symmetry directions in the BZ under two polarization
directions. The calculations projected into orbitals that are visible under
each measurement geometry accordingly are directly overlapped onto the
measured dispersions (see Supplementary Information Fig S5 for the band
dispersion without DFT overlapped). 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 selective
rules in Fig. 2h suggest these features can be attributed to ${d_{yz}}$ or
${d_{xy}}$ orbital characters. 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 ${d_{yz}}$ character band marked by the solid
white arrow, the agreement can be better established (see Supplementary
Information Fig. S3). Another possibility that we cannot rule out is that the
flat portion of ${d_{xy}}$ character near -2 eV being strongly renormalized.
In either scenario, orbital-dependent correlation effects would need to be
invoked in CsCr3Sb5, reminiscent of that found in the multi-orbital system of
the iron-based superconductors [56, 57, 58, 59].

Figure 3:  FBs observed at $E_{F}$. (a) DFT calculated orbital projected
partial DOS. (b)-(d) Band dispersions measured with 100 eV photons along
$\bar{\Gamma}$-$\bar{M}$ with stacked EDCs plotted accordingly. Lines of the
same colors denote high symmetry point positions. The measurement geometry and
polarization are as marked. (e)-(g) Same measurement but taken along
$\bar{\Gamma}$-$\bar{K}$-$\bar{M}$. The red triangles on the EDCs mark the
FB’s energy position at $\Gamma$.

Having discussed the overall electronic structure, we next focus on the FB
near $E_{F}$ (Fig. 3). First, from the orbital-projected band structure
calculated by DFT, we see that the kagome topological flat band appears at
0.25eV above $E_{F}$, and is mostly composed of ${d_{xz}}$ and ${d_{yz}}$
characters (Fig. 2b-c). Their location in energy is indicated by peaks in the
orbital-projected DOS as marked by the red arrow in Fig. 3a. In Fig. 3b-g, we
present the zoom-in views of band dispersions measured under different
experimental geometries together with the energy distribution curves (EDC)
along each momentum path. Specifically, Fig. 3b-d shows dispersions measured
along $\bar{\Gamma}-\bar{M}$ while Fig. 3e-g shows dispersions along
$\bar{\Gamma}$-$\bar{K}$-$\bar{M}$. Figure 3b,c,e,f were measured under
polarizations that have both an in-plane component and an out-of-plane
component. Figure 3d,g were measured under in-plane polarizations only.
According to the orbital selection rules in Fig. 2h, the selected orbitals for
each panel are summarized as the following: Fig. 3b (${d_{xz}}$, ${d_{xy}}$,
${d_{z^{2}}}$), Fig. 3c (${d_{yz}}$, ${d_{x^{2}-y^{2}}}$, ${d_{z^{2}}}$), Fig.
3d (${d_{xz}}$, ${d_{xy}}$), Fig. 3e (${d_{yz}}$, ${d_{xy}}$, ${d_{z^{2}}}$),
Fig. 3f (${d_{xz}}$, ${d_{x^{2}-y^{2}}}$, ${d_{z^{2}}}$), Fig. 3g (${d_{xz}}$,
${d_{x^{2}-y^{2}}}$). We note that for all of the setups, a flat band feature
close to $E_{F}$ can be observed. This can be seen in the ubiquitous peak in
the EDCs within 100 meV of $E_{F}$, 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 pocket near $E_{F}$ (Fig. 2). 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
$E_{F}$. Hence, the peak that we observe in all the EDCs at $\Gamma$ between
the electron band bottom and $E_{F}$ must be the kagome FB brought down from
above $E_{F}$. Furthermore, considering that the FB is observable under all of
the polarization geometries, including those that only allow either even or
odd parity orbitals to be observed, this suggests that both ${d_{xz}}$ and
${d_{yz}}$ orbitals are participating in forming the observed FB.
Specifically, in Fig. 3d and e, the observed FB can be exclusively assigned to
having ${d_{xz}}$ and ${d_{yz}}$ orbital content, respectively, as ${d_{xy}}$
orbitals can not be observable at the first BZ center subjecting to
photoemission matrix elements [60].

An additional confirmation for the observation of the FB below $E_{F}$ can be
noted from a zoom-in view of the region near $\Gamma$. The prominent feature
seen near the $\Gamma$ point is an electron band of dominantly ${p_{z}}$
character. This band is also seen in CsV3Sb5, albeit with a shallower band
bottom due to the smaller electron filling [61]. However, we notice that
distinct from the CsV3Sb5 case, there is a kink feature on the electron
dispersion near -70 meV, as marked by a white arrow in Fig 4 from the MDC-
fitted band position. From the DFT calculations, it is clear that this
electron band hybridizes with the kagome flat band where they cross. (see
Supplementary Information and Fig. S7) Since the energy position of this kink
feature matches with the observed peak in the EDCs, this is an indication of
the hybridization of the FB with the electron dispersion, and 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. We can
quantitatively extract the location of the FB by fitting the EDC, which gives
a location of -76 meV as measured at 10 K (Fig. 4b-c).

Figure 4:  Temperature dependence of the FB across $T^{\prime}$ (a) Band
dispersion taken with 114 eV LH polarization and horizontal slit direction at
10 K (left) and 140 K (right). White (10K) and red (140K) dots denote the
fitted MDC positions (see supplementary material) for the electron pocket at
$\Gamma$. The arrows mark a kink in the dispersion indicating hybridization
with the FB. (b) EDC1 measured at the denoted position in (a) at 10K, 140K,
and then thermally cycled back to 10K. (c) Fitting details for the 10K and
140K EDC1 where a Lorentz peak (orange) and a constant background (gray) are
convoluted with FD function and a fixed Gaussian peak with 40 meV Full Weight
Half Maximum (FWHM mimicking 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 Lorentz 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
convoluted with a Gaussian peak with 40 meV FWHM. The dotted line marks the
transition $T^{\prime}$ previously reported [52].

Next, we examine the temperature dependence of the FB across $T^{\prime}$
(Fig. 4). Firstly, we present the comparison of band dispersion along
$\bar{\Gamma}$-$\bar{M}$ taken with LV polarization and horizontal slit at 10K
and 140K (Fig. 4a). This experimental setup selects FB of ${d_{yz}}$ orbital
according to Fig. 2h. The FBs are visible at both temperatures, marked by a
white and red arrow respectively from the kink in the fitted dispersion. From
the spectral image, the FB location appears to be closer to $E_{F}$ 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 $E_{F}$ 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 LH polarization and
horizontal slit at 10K (T $<$ $T^{\prime}$) and 140K (T $>$ $T^{\prime}$)
shows that FB of ${d_{xz}}$ orbital also shift towards $E_{F}$ (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 Fig. S6.

##  II Discussions

From our systematic polarization dependence measurements, we clearly resolve
the presence of the kagome flat bands near $E_{F}$ in CsCr3Sb5. In comparison
to the isostructural CsV3Sb5, the Cr system is effectively electron-doped to
an extend that at the DFT level, the kagome flat bands are brought much closer
to $E_{F}$. However, as we have observed, additional electron correlation
effects are at play that further renormalize the orbitals associated with the
kagome flat bands such that the flat bands are brought closer to $E_{F}$ [62,
63]. 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 $E_{F}$ [16].

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 2x2. Both
these systems exhibit the VHSs at the M points of the BZ in the proximity of
$E_{F}$. 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 the occurrence of the 2x2 charge order in these
systems. Second, we consider kagome metals where the flat bands are in the
vicinity of the Fermi level. There are also two regimes where materials have
been studied. Ni3In represents a regime where the flat band is in proximity to
$E_{F}$ 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 point,
albeit on the non-ordered strongly fluctuating side of the phase diagram [51].
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 temperature [12, 11, 26, 64]. 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$\sim$2 eV [11]. However, a recent work on FeSn thin film 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 nature [65], which
is likely common for these Fe- and Mn-based system with exceptionally high
ordering temperatures.

CsCr3Sb5 is clearly not in this regime. 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 doping [66, 67]. Yet, the flat band in
CsCr3Sb5 is clearly participating in the low temperature order, evident in its
shift away from $E_{F}$. 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 side, 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 $E_{F}$ in CsCr3Sb5 give rise to
antiferromagnetic fluctuations, suggesting the important role that these FBs
play in this emergent order [54]. 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 $E_{F}$, and the moderate orbital dependent correlation
effects suggest that CsCr3Sb5 opens up access to a previously unexplored
regime in the overarching phase diagram of kagome metals that offers important
insights into novel phases associated with the topological flat band physics.

##  III Acknowledgments

This research used resources of the Advanced Light Source, which is a DOE
Office of Science User Facility under contract no. DE-AC02-05CH11231. Use of
the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator
Laboratory, is supported by the U.S. Department of Energy, Office of Science,
Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. The
single-crystal synthesis work at Rice was supported by the U.S. DOE, BES under
Grant No. DE-SC0012311 (P.D.) and the Robert A. Welch foundation grant number
C-1839 (P.D.). The ARPES work at Rice University was supported by the U.S. DOE
grant No. DE-SC0021421, the Gordon and Betty Moore Foundation’s EPiQS
Initiative through grant No. GBMF9470 and the Robert A. Welch Foundation Grant
No. C-2175 (M.Y.). Y.G. was supported in part by an ALS Doctoral Fellowship in
Residence. Y.Z. is partially supported by the Air Force Office of Scientific
Research (AFOSR) Grant No. FA9550-21-1-0343. The theory work at Rice is
supported by the AFOSR Grant No. FA9550-21-1-0356 (F.X.), by the NSF Grant No.
DMR-2220603 (Y.F.), and by the Robert A. Welch Foundation Grant No. C-1411
(Q.S.), and by the Vannevar Bush Faculty Fellowship ONR-VB N00014-23-1-2870
(Q.S.). Computational modeling was supported by the Office of Naval Research
Grant N00014-22-1-2753 (Y.H. and B.I.Y.). The transport and thermodynamic
measurements at UW were supported by the Air Force Office of Scientific
Research (AFOSR) under Award No. FA2386-21-1-4060 and the David Lucile Packard
Foundation (J.H.C). M.H. and D.L. acknowledge the support of the U.S.
Department of Energy, Office of Science, Office of Basic Energy Sciences,
Division of Material Sciences and Engineering, under contract DE-
AC02-76SF00515.

##  IV Author contributions

PD initiated this project. MY, PD and QS oversaw the project. YG, JSO, ZR, YZ,
ZY, and CH carried out the ARPES measurements with the help of ER, AB, CJ, MH,
and DL. The ARPES data were analyzed by YG and HW with the help of MY. Single
crystals were synthesized by ZW and BG under the guidance of PD. $U$(1)
auxiliary-spin calculations were carried out by FX, YF, and QS. Density-
functional theory calculations and tight-binding model fitting were carried
out by YH under the guidance of BY. Transport measurements were carried out by
ZL and JC. YG and MY wrote the paper with input from all co-authors.

##  V Competing interests

The authors declare no competing interests.

##  VI Methods

###  VI.1 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 $O_{2}$. 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 ℃ within 12 h, kept for 50 h, cooled
to 580-600 ℃ at a rate of 1.5-3 ℃/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
$mm^{2}$.

###  VI.2 ARPES measurements

ARPES experiments were performed at the MAESTRO beamline of the Advanced Light
Source and beamlines 5-2 of the Stanford Synchrotron Radiation Lightsource.
The MAESTRO beamline is equipped with a Scienta electron analyzer with home-
designed deflector mode, with measurements taken under a beamspot of 10 x
10${\mu}m^{2}$. SSRL beamline 5-2 is equipped with a DA30 electron analyzer,
and a beamspot of 50 x 10${\mu}m^{2}$ was used. The angular resolution was set
to 0.1∘. The total energy resolution was set to 20 meV or better. All the
samples were cleaved in-situ at 10 K and all the measurements were conducted
in ultra-high vacuum with a base pressure lower than 5 $\times$ 10-11 Torr.

###  VI.3 DFT calculations

All DFT calculations were performed with Vienna ab initio simulation package
(VASP) code [68, 69], with Perdew-Burke-Ernzerhof exchange-correlation
functional [70]. The energy cutoff of plane wave basis is 450 eV, and 3D
Brillouin zone is sampled with k-point mesh of $11\times 11\times 5$. 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 Wannier90 package [71].

##  VII Data Availability

All data needed to evaluate the conclusions are present in the paper and
supplementary materials. Additional data are available from the corresponding
author on reasonable request.

##  VIII Code Availability

The band structure calculations used in this study are available from the
corresponding authors upon reasonable request.

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