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Anomalous quasiparticles in the zone center electron pocket of the kagom\'e ferromagnet Fe3Sn2

One material containing kagome bilayers and featuring both exceptional magnetism and electron transport is the ferromagnetic metal Fe3Sn2. Notwithstanding the widespread interest in Fe3Sn2, crystal twinning, difficulties in distinguishing surface from bulk states, and a large unit cell have until now prevented the synchrotron-based spectroscopic observation of sharply resolved quasiparticles near the Fermi surface which could be responsible for the anomalous properties appearing at low temperatures for the material. Here we report microfocused laser-based angle-resolved photoemission spectroscopy (micro-ARPES), which offers the first look at such quasiparticles. The high spatial resolution allows individual crystal twin domains to be examined in isolation, resulting in the discovery of three-fold symmetric electron pockets at the Brillouin zone (BZ) center, not predicted by early tight-binding descriptions but in agreement with density functional theory (DFT) calculations, which also feature Weyl nodes. The quasiparticles in these pockets have remarkably long mean free paths, and their Fermi surface area is consistent with reported quantum oscillations. At the same time, though, the best-defined Fermi surface is reduced at low temperature, and the quasiparticles generally are marginal in the sense that their wavelength uncertainty is of order the deviation of the quasiparticle wavelength from the Fermi vector. We attribute these manifestations of strong electron-electron interactions to a flat band predicted by our DFT to lie just above the dispersive bands seen in this experiment. Thus, beyond demonstrating the impact of twin averaging for ARPES measurements of band structures, our experiments reveal many-body physics unaccounted for by current theories of metallic kagome ferromagnets.

noteworthy is the prediction from 2011 based on a tight binding model that a kagomé material which is both ferromagnetic and metallic could display interesting collective phenomena such as the fractional quantum Hall effect in the absence of an external magnetic field 3 .
Rhombohedral (space group R-3m, SG-166) Fe3Sn2 is precisely such a substance 17 . Its building blocks are bilayers of distorted, three-fold (not six-fold) symmetric kagomé layers of Fe atoms alternating with single layers of stanene, as shown in Fig. 1a. Of long-standing interest have been the ferromagnetic properties, including a high Curie temperature of 640 K 1 and a spin reorientation transition near 120 K, which was recently confirmed to be of first order 5,6 . The latter follows from a crossing of different free energies associated with subtly different band structures and resulting Fermi surfaces for the different moment directions 4,6 (see figure SI8 in supplementary information (SI)). The electronic band structure itself has been directly investigated by photoemission 4,[18][19][20] , scanning tunneling microscopy 21 , and bulk transport Haas-van Alphen measurements 7,18 . In contrast, density functional theory (DFT) for the bulk material yields neither obvious flat bands nor Dirac nodes (see figure SI10) but does reveal Weyl points near the Fermi surface 4 . Nonetheless, it accounts for the seeming appearance of Dirac nodes in ARPES in terms of superposed bulk and surface bands 4,20 . The ARPES data collected so far do not display sharply resolved Weyl nodes. However, there is another feature that unambiguously distinguishes the tight-binding calculations from DFT predictions, namely, only DFT predicts electron pockets surrounding the zone centers (see figure 1c and figure SI7 -SI9 4 ). Furthermore, as shown in figure 1c, the pockets are highly sensitive to electron correlation effects as parametrized by the effective Coulomb interaction U in DFT + U calculations, and so could be exploited for measurement of U. We have therefore set out to search for and characterize these pockets experimentally.
Here, we report the first detailed experimental study of the distinct electron pockets, present in lower resolution and more surface-sensitive measurements at the Brillouin zone (BZ) center of Fe3Sn2 4 , by employing state-of-the-art micro-focused laser ARPES (µ-ARPES) to overcome the presence of crystallographic twinning. Our results are consistent with the same density functional calculations which suggest that the Dirac-like cones reported in conventional synchrotron-based ARPES 4,18 derive from a coincidence between minima and maxima of surface and bulk bands 4,20 , respectively. At the lowest temperature (6 K), there are very sharp quasiparticles which define small Fermi surfaces around the Brillouin zone centre, and their inverse lifetimes show the rapid linear increase with binding energy characteristic of strongly interacting fermions. On warming, the most sharply resolved band crossing the Fermi surface effectively dissolves, possibly due to hybridization and subsequent localization involving a flat band placed by DFT just above the chemical potential.

Motivation for spatially resolved ARPES experiments
ARPES is the natural technique for determining the electronic band structure and has been applied on numerous occasions to Fe3Sn2 4,[18][19][20] . However, there are four potential difficulties in assessing ARPES data, beyond the usual challenge of distinguishing surface from bulk contributions. A first challenge relates to the large number of atoms per unit cell (18 Fe and 12 Sn), leading to closely spaced bands which, due to magnetic order, will also be spin-split. A second difficulty is the possibility of crystal twinning originating during the crystal growth and which corresponds to rotation by = × 60°, = ±(1,3,5) (figure 1a). A third problem is the possibility of different surface terminations, which would yield different ARPES results. A fourth aspect is the presence of ferromagnetism where, due to spin-orbit coupling, different magnetic domains are associated with different electronic structures 4 .
The first problem can only be remedied by ultra-high-resolution spectroscopy, while the remaining three are all linked to different types of multidomain structures over which ordinary ARPES measurements perform averages. For instance, in the case of crystal twinning, the complication is caused by the "breathing" kagomé motif of Fe3Sn2 consisting of two different corner-triangle sizes denoted by triangles with different colors in figure 1a, resulting in a threefold rotation symmetry, rather than six-fold, in the absence of magnetic order 4 . The twinning will be clearly observed when the isoenergy surfaces are away from the high symmetry = (0, ) planes as shown by the results of the DFT calculations in figure 1b (U = 1.3 eV); U = 1.3 eV is chosen (figure 1c) as it can reproduce the electron pockets found by ARPES near the Γ point, which will be discussed in detail later. However, the ARPES results reported thus far are predominantly six-fold symmetric 4,[18][19][20] , which can only be attained at exactly the high symmetry = (0, ) planes for a single domain phase. Tanaka et al. 20 interpreted their ARPES results as being three-fold symmetric for ≠ (0, ), but the data quality is not sufficient to reach that conclusion unambiguously.
Here, we address the question of discriminating domains with different crystallographic twins, surface termination, and magnetic orientation, by using three forms of photoemission microscopy to characterize Fe3Sn2, namely, spatially-resolved X-ray photoelectron spectroscopy (XPS), X-ray absorption spectroscopy (XAS), and X-ray magnetic circular dichroism (XMCD), which are used to distinguish physical domains related to surface termination and magnetism, respectively, and show that in fact they are uncorrelated.
Separately, by using -focused laser ARPES, we probe at very high energy and momentum resolution the band structure close to the Brillouin zone center Γ. In addition to discovering electron pockets, we also observe directly that there are different electronic domains in Fe3Sn2 rotated around the c-axis by = × 60°, = ±(1,3,5). By varying the temperature and by comparing the evolving magnetic domain pattern, we conclude that the observed differences in band structure are solely due to twinning and not due to different magnetic states. Direct comparison of the laser -ARPES data with synchrotron ARPES data that averages over much larger areas (presented in the SI) shows that the data from synchrotron ARPES corresponds to the average over crystallographic twins and therefore cannot be interpreted without help from either calculations or a spatially resolved technique like -ARPES.

Spatially-resolved XMCD, XAS, and XPS
We first consider the magnetic domain configuration and different surface terminations, which typical ARPES averages over, by using x-ray photoemission electron microscopy (XPEEM) to obtain spatially resolved XAS and XPS maps of the sample. In our case, the XAS is monitored using photoelectrons with kinetic energy below ~ 1 -2 eV (low energy secondary electron, 'bulk' sensitive to a depth of a few nm from the surface) while the XPS photoelectrons have a kinetic energy of 96 eV (surface sensitive); the sample was cleaved in vacuum and investigated at 80 K, the base temperature of the cryostat. Figure 2a shows the XMCD map, which is

Laser -ARPES
We performed laser -ARPES (detailed setup described in SI) to probe the electronic structure at high energy and spatial resolution to determine inhomogeneities in the electronic structure linked to magnetic, chemical, and crystallographic domains. The 6.01 eV photon energy limits the Brillouin zone probed to near the  point, which nonetheless is of great interest because it enables detailed imaging of the electron pocket seen previously at low resolution with a large beam 4 , and predicted by DFT 4,19,20 but not by other band theories 18 . Figure  as can be seen from the energy-momentum cut image (figure 3a(iii) and (iv)). We also notice a very weak broad band lying at higher binding energy labeled as , which has asymmetric intensity similar to that of the and bands, indicating that it is three-fold symmetric as well.
The two distinct areas rotated by 180° with respect to each other, i.e., twinned domains, can be mapped in real-space by tracing the intensity differences between the left versus right side of the band in the ARPES cut [figure 3a(iii) and (iv), where data for LH and LV polarizations are summed]. Figure 3c is the resulting domain image, where for band intensity larger on the left side, we label the sample position in red, otherwise we color it green. In the gradation from green to red, white indicates no intensity difference. In the upper panel of figure 3c, we see that there is a relatively abrupt transition from the "red" to "green" regions, indicating that the twinned domain is rotated discontinuously. A rough measurement of the domain wall angle gives a value of 60°, in agreement with the twin rotation for the crystal structure.
The bulk electronic properties of Fe3Sn2 undergo pronounced evolution on cooling below 80 K, where the spin reorientation to the low temperature phase is complete 5 . Particularly dramatic are the modulation of the carrier density depending on the magnetization direction below 80 K 24 and the temperature dependence of the anisotropic magnetoresistance and planar Hall effect 23 , which features a threefold (not sixfold) antisymmetric term as a function of in-plane field direction. To determine whether any of the ARPES features which we see at low temperature could be related to these transport phenomena, we have collected -ARPES data at 80 K, which is at the boundary of these characteristic temperatures but still in the regime where the magnetism is dominated by domains with moments along the kagomé planes 6 , although with smaller domains compared to 6 K. The lower panel of Figure 3c shows the intensity asymmetry image for 80 K, which is not appreciably different from the 6 K image above it. This is not surprising since based on magnetometry 6 , magnetoresistance 5 , and magnetic domain imaging 6 , the magnetization is in the kagome plane for temperatures below 80 K. The major effect of warming in this case is a broadening of the spectra, and in particular the loss of the very sharp bands as seen in figure 4a, which we discuss in greater detail below. In the SI, we show that the earlier synchrotron ARPES data are consistent with an average over the twin domain data obtained from laser µ-ARPES. We attribute the three-fold pattern itself to originate from probing off high-symmetry plane, yet still close to = 0 plane (see SI for further explanation), confirming the bulk nature of the spectral data; high symmetry probing at = 0 plane or = plane will generate a six-fold pattern regardless of the "breathing" pattern of the kagomé.

Comparison to DFT calculations
We now take advantage of the high real and reciprocal space resolution of our single domain

Sharp but marginal quasiparticles at low temperatures
Key parameters of quasiparticles which include their Fermi surface areas, mass, and scattering rates, are calculated from our experimental data. We display the representative dispersion cuts for the individual linear photon polarizations in figure 4a(i) and (iii) for horizontal (LH) polarization at 6 and 70 K, respectively, and in figure 4a(ii) and (iv) for vertical (LV) polarization at 6 and 70 K, respectively. LH displays mostly the band, indicating it is an even orbital with respect to the incident plane of the experiment, while the , , and bands are odd parity orbitals. In Table I  The area of the electron pockets is calculated by tracing the visible peaks of the corresponding band at the Fermi level and assuming a circular extrapolation to make closed contours. More details on the EDC of the bands from to band minimum can be found in figure SI5.
For the band, λ =155 ± 5 Å at 6 K, a remarkably long mean free path for a topological (bulk) metal and comparable to that for the much simpler surface Dirac quasiparticles for the n-type Bi2Te3 topological insulator (~190 Å) 27 ; for , λ is reduced by a factor of two to ∼ 85 Å but is still long by the same standards. These values are consistent with the residual ( = 2 K) and a carrier density of 1.8 × 10 28 −3 from transport data 5,24 for samples similar to ours, grown by the same method by the same group. In particular, applying the Drude formula 0 = 2 for conductivity, we obtain a scattering time It is also interesting to ask whether there is bulk evidence for small Fermi surfaces similar to those which we have discovered. The answer is yes: the calculated de Haas van Alphen (dHvA) frequency 254 T of the band, whose Fermi surface is centered on Γ , is in reasonable agreement with that measured for reference 7 (~200 T) and attributed to the "Dirac ring" vanishes, which is consistent with the Δ measured for the band at 70 K, and also the fact that at 6 K, the band becomes invisible for binding energies above a similar energy.
The conclusion is that / scaling is roughly obeyed in the sense that marginal quasiparticles for both the and the bands are distinguishable or not near the Fermi surface to an extent consistent with Eq(1). However, the value for '/ is unusually large, and the energymomentum diagram is very peculiar in that the much broader band seems much more associated with the minimum near Γ than the short, 20 meV stretch of band visible near the Fermi surface, which simply looks like a sharp copy of the band displaced upwards by the same 20 meV towards . These observations, not easily accounted for by DFT, together suggest a many-body origin for the band. A possible scenario is that there is strong hybridization between flat and band states near the bare Fermi surface which results in interaction-induced (Mott-like) localization that reduces the free carrier density; for the electron pockets seen here would then be correspondingly reduced by  , and the resulting ( ) band will be raised towards by Δ = ℏ  . There will of course still be broad spectral weight from the unrenormalized ( ) bands at the original , and for binding energies in excess of Δ , the localized electrons rejoin the Fermi sea and the spectral weight will reside primarily near the band as might be calculated using DFT. Warming would similarly act to delocalize the carriers, and thus cause the loss of the "band".

Conclusions
We have discovered electron pockets labeled as , , and centered at the   This shows that the magnetic domain has no correlation to the surface termination. Panel d.
shows that the intensity difference found in panel c. is step-like with intensity ratio of 1.8 ± 0.6.

A. Sample growth and structural characterization
Fe3Sn2 crystalizes in a rhombohedral structure with space group 3 ̅ , with crystal axis , = 5.34 Å, = 19.80 Å, and = 120°. Fe3Sn2 single crystals were grown by a vapor transport method. Stoichiometric iron powder (Alfa Aesar, ＞99.9%) and tin powder (Alfa Aesar, ＞ 99.9%) were placed into an evacuated quartz tube. Then the tube was annealed at 800℃ for 7 days before quenching in icy water. The crystal structure of the polycrystalline Fe3Sn2 precursor is confirmed by the x-ray diffraction (XRD) data shown in Fig. SI1a. The obtained polycrystalline Fe3Sn2 precursor was thoroughly ground and sealed with I2 (~ 4 mg/cm 3 ) in a quartz tube 1 cm in diameter and 16 cm in length. Fe3Sn2 single crystals were obtained under a temperature gradient of 650 ℃ (source) to 720 ℃ (sink) for two weeks.
The cleaved surface for laser ARPES is confirmed to be (001), the ab plane, from low energy electron diffraction (LEED) measurements on a freshly cleaved surface, as shown in Fig. SI1b. The typical cleaved surface is displayed in figure SI1.c indicating a flat surface suitable for ARPES measurements.

B. Magnetic domain and surface termination probed by X-ray photoemission electron microscopy (XPEEM)
The surface termination of the Fe3Sn2 samples is probed by mapping the Sn 3d3/2 and Fe 2p3/2 local photoemitted electron intensities using the spectroscopic capabilities of the SPELEEM III instrument (Elmitec GmbH) at the Surface/Interface Microscopy (SIM) beamline of the Swiss Light Source. The photon excitation energy was varied such that the kinetic energy of the detected electrons was fixed at 96.8 eV in order to achieve a high surface sensitivity (~2 Å according to the universal curve 1 ). The photoemission peaks are determined by recording XPEEM image sequences with x rays, linearly polarized in the plane of the sample, with varying photon energy. The samples are cleaved in situ prior to the XPEEM measurements at 80 K, base temperature of the cryostat. A typical result is shown in Fig. SI2a, displaying a clear cleaved surface and an area with glue residue and a crack. The XPS intensity distributions for the Sn 3d3/2 and Fe 2p3/2 peaks are shown in Fig. SI2b, c, respectively. Electrons emitted from the Sn 3d3/2 orbitals have two distinct intensities on the spatially resolved map in Fig. SI2b, revealing a large region of higher intensity together with smaller islands of lower intensity. The iron emission map shown in Fig. SI2c is more homogeneous and has a much lower signal to noise ratio, expected from the lower non-resonant x-ray absorption of Sn, Z = 50, when compared to Fe, Z = 26, which prevents the observation of the smaller islands as in panel (b). The XPS spectra displayed in panel (c) are obtained by integrating over an area larger than that for the Sn XPS peak shown in panel (b). We assign the bright area in Fig. SI2b as stanineterminated and the darker area as kagomé-terminated. However, we cannot determine the exact kagomé termination, i.e., whether it is one or two Fe layers (Fig. SI2d.i or ii) within the intensity resolution of our measurements. The cleaved surface discussed here is different from the photoemission experiment presented in figure 2 of the main manuscript. A comparison between these two sets of data shows that the area attributed to kagomé-terminated can vary in size and is not limited to only small areas as shown in Fig. 2b.
The magnetic domain configuration was determined using the x-ray magnetic circular dichroic (XMCD) effect. XPEEM images were recorded by exciting the sample with circularly polarized x-rays with the photon energy tuned to the Fe L3 edge and measuring the intensity of the low energy secondary electrons (with a probing depth of about 3-5 nm). Magnetic contrast maps were finally obtained by pixelwise division of two XPEEM images recorded with opposite x-ray helicities.

Intensity ratio of XPS signal
The PEEM micrographs showing different terminations in Fe3Sn2 can be numerically analysed as following: 1. We assume that the photon penetration depth is much longer than the escape depth of the most energetic photo-electron, i.e., an electron at the Fermi level. Thus, we ignore the exponential decay component of the photon intensity.
2. Assumption 1 leads to an expression of photo-electron intensity from a given atom called , on layer called , with distance from the surface as where is the escape depth of the electron, is the proportionality constant that contains the photon cross section of atom at layer of type , and is the atom density at layer of type . 3. Generalizing (2), we can express the total intensity from atoms a from all layers of type b as a summation where we assume the proportionality constant to be the same for all similar layers at different depths.
With these three points we can start to write down the expression of XPS intensity from both Sn and Fe in total. First, we notice that there are three possible terminations and call them double kagome termination ( ), single kagome termination ( ), and stanene termination ( ) as shown in figure SI2d.

Double kagome termination ( )case
The total Sn and Fe intensity from this termination can be expressed as where Sn, is the proportionality constant for Sn atoms in the stanene layer, Sn, is the Sn density in the stanene layers, Sn, , Fe, are the proportionality constants for Sn, Fe atom in the kagome layer, respectively, Sn, , Fe, are the Sn, Fe densities at the kagome layer, respectively, ℎ is the distance of Fe layers between two adjacent kagome layers (the kagome bilayer), ℎ is the distance of Fe layers in the kagome layer to the nearest stanene layer, is the distance of Sn atom layers between two adjacent kagome layers (the kagome bilayer), is the distance of Sn atom layers from a kagome layer to the nearest stanene layer. According to this model, we should be able to see the Fe peak contrast between different terminations. However, our data display a rather homogenous signal whose origin is already explained in the previous section.
Meanwhile, for Sn intensity, we can posit that Sn, ≈ 2 Sn,k on account of the twice higher density of Sn in the stanene rather than in the kagome layer. And finally, it is also reasonable to assume Comparing with the experimental result of ℎ / = 1.84 ± 0.57 from figure 2 in the main text, while we cannot tell if the darker region is coming from the single or the bi-layer kagome, we can safely infer that the bright regions have stanene termination.

C. Micro-focused Laser Angle Resolved Photoemission Spectroscopy (µ-ARPES)
For the µ-ARPES measurements, we use a 6.01 eV 4 th -harmonic generation continuous laser from LEOS as photon source, a custom-built micro-focusing lens to focus the beam spot diameter to ~3 m, and an MB-Scientific analyzer equipped with a deflection angle mode to map the dispersion relation while keeping the area of interest intact (i.e., not changing due to sample rotation). Typical energy and angular resolution were 3 meV / 0.2°. The pressure during the measurement is kept at < 10 −10 mbar. The sample is mounted on a conventional 6-axes ARPES manipulator described in Ref. 2 and sample position is scanned with an xyz stage of 100 nm resolution and < 1 μm bidirectional reproducibility. A more detailed explanation can be found in Ref. 3 . During the measurement, the temperature is first lowered to 6 K, where the sample is cleaved in situ, and the sample drift at subsequent higher temperatures is tracked by using the edges of the sample as reference. The samples are pre-aligned to the high symmetry cut with low energy electron diffraction (LEED) after cleaving.
The perpendicular momentum of the electrons measured by ARPES can be obtained from the expression where * is the effective mass of the electron, = ℎ − − | | is the kinetic energy of the electron, ℎ is the photon energy, | | is the binding energy of the electron, is the work function of the detector, is the inner potential of the material, and is the analyzer slit angle (more details can be found in these references 4,5 ). The laser photon energy used, 6.01 eV, corresponds to a perpendicular momentum close to the center of the Brillouin zone ≈ × 2 , 6.01 ≈ 5.93 ≈ 6, as shown in Fig. SI3, whose inner potential used is taken from Ref. 6 . The synchrotron photon energy used is 48 eV, which also lies roughly in the same position at the center of the Brillouin zone, 48 ≈ 11.98 ≈ 12. From Fig. SI3 we can see that those two photon energies differ by two Brillouin zones.
We can also estimate the uncertainty in determination ( ) from the escape depth of the electron. In this case, we can focus on the electron close to the Fermi energy ( ≈ 1.64 eV), which has an escape depth around ≈ 60 Å according to the universal curve 1 , giving us These values give us an estimation of ranging ≈ (0.02 − 0.08) Γ agreeing (by the order) with the estimation from the universal curve.

Synchrotron vs Laser ARPES
Twinned domains exist in Fe3Sn2 and will both contribute to the ARPES data if the beam spot is bigger than the size of the domains. For example, we show in Fig. SI4a an example of ARPES data measured with 48 eV photon energy, temperature 17 K, and a spot size of ~35 collected at the SIS beamline, Swiss Light Source, equipped with Scienta R4000 hemispherical analyser. The overall feature shows a 6-fold pattern with no indication of a 3fold pattern. A closer look around the center also shows a rather blurred circular shape, which can be attributed to a combination of all twinned domains that it may cover. This central feature can in fact be reconstructed from the laser ARPES results by combining data from both twinned domains and different polarizations (LH+LV) to give us the picture shown in Fig. SI4b. Indeed, we reproduce the synchrotron ARPES data but with higher momentum resolution.

Fitting momentum distribution curve (MDC)
The momentum distribution curves (MDC) are fitted to obtain the half peak width (Δk) which can be related to the averaged scattering length of the quasiparticle as λ = 1 Δk . We obtain this peak by fitting the MDC peak with a Voigt lineshape, i.e., a Lorentzian convolved with a Gaussian, where the Gaussian simulates the instrument response. For momentum scans (MDC), the latter combines angular and energy resolutions to yield a full-width-at-half-maximum (FWHM) In this case we set ≈ 0.001 Å −1 and ≈ 3 meV and as listed in table I in the main manuscript. We can therefore see that typically the broadening in the MDC is due to the broadening in the energy distribution curve (EDC) because < ( ) −1 . Figure SI5(c) shows the sharp quasiparticle peak of at the Fermi level, fitted with a Voigt function to represent the detector response. We obtain the resolution corrected Lorentzian FWHM of 2.5 meV.

D. Density Functional Theory Calculations
Electronic structure calculations are performed within density functional theory (DFT) using the projector augmented wave method (PAW) 7 as implemented in the Viena ab initio simulation package (VASP) 8,9 . The exchange-correlation potential is described using the Perdew-Burke-Ernzerhof (PBE) 10 functional within the generalized-gradient approximation (GGA). Plane waves are used as a basis set with a kinetic energy cutoff of 450 eV. To sample the Brillouin zone, we employ a 24 × 24 × 24 Monkhorst-Pack grid. The spin-orbit coupling (SOC) is included in our calculations as described in Ref. 11 . We take into account the p and d semi-core states for the Fe and Sn PAW datasets used, respectively, and the simplified on-site Hubbard U correction 12 is added for the Fe d orbitals. We determined a Hubbard U value of 1.3 eV to reproduce the ARPES band structure around the Γ point at the Fermi level. Band structures calculated using several different U values with magnetic moments pointing in the kagomé plane are shown in Fig. SI7 (notation and labeling of Brillouin zone points are shown in Fig. SI6). In Fig. SI8, the band structure evolution as a function of magnetic moment direction ( ∥ , = 70°, and ∥ ) is also plotted with selected U values displayed (0, 0.5 and 1.3 eV). Fig. SI9 simulates the band at ARPES energy window by plotting bands in the range of = 0 − 0.05 ΓZ.

"Dirac points" in DFT calculations at various U values
We attempted to reproduce the "Dirac points" predicted in the tight-binding model by changing the U value in the DFT calculations as shown in Fig. SI10. Our results show that the "Dirac points" are not reproduced for U values between 0 and 1.3 eV. One may see that the closest resemblance of the band dispersion to the linear crossing is achieved at a U value of 0.5 eV or above, where the gap is narrow but never fully closes.