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## Creator

Hayate Kunitsu, Iori Ishiguro, Natsuki Mitsuishi, [Shunsuke Tsuda](https://orcid.org/0000-0001-6209-8048), [Koichiro Yaji](https://orcid.org/0000-0002-0721-1316), Zehao Wang, Pengcheng Dai, Yoichi Yamakawa, Hiroshi Kontani, Takahiro Shimojima

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© 2026 The Physical Society of Japan(J. Phys. Soc. Jpn. 95, 073703.)[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Fermi Surface of Kagome Metal CsCr                    <sub>3</sub>                    Sb                    <sub>5</sub>                    Observed by Laser Photoemission Microscopy](https://mdr.nims.go.jp/datasets/32a7497a-1596-4d9e-8351-eee4f7f34c99)

## Fulltext

1  Fermi Surface of Kagome Metal CsCr3Sb5 Observed  1 by Laser Photoemission Microscopy 2  3 Hayate Kunitsu1*, Iori Ishiguro1, Natsuki Mitsuishi1, Shunsuke Tsuda2, Koichiro Yaji2,3, 4 Zehao Wang4,5, Pengcheng Dai4,5, Yoichi Yamakawa1, Hiroshi Kontani1,  5 Takahiro Shimojima1 6  7 1 Department of Physics, Nagoya University, Furo-cho, Nagoya 464-8602, Japan 8 2 Center for Basic Research on Materials, National Institute for Materials Science, 9 Tsukuba 305-0047, Japan 10 3 Unprecedented-scale Data Analytics Center, Tohoku University, Sendai 980-8578, 11 Japan 12 4 Department of Physics and Astronomy, Rice University, Houston 77005, USA 13 5 Rice Laboratory for Emergent Magnetic Materials and Smalley-Curl Institute, Rice 14 University, Houston, Texas 77005, USA 15  16 We investigated the Fermi surface (FS) in the paramagnetic state of Kagome metal 17 CsCr3Sb5 by employing a laser photoemission microscopy. We found a circular FS 18 and two hexagonal FSs around the Brillouin zone (BZ) center. Polarization-19 dependent measurements further enable us to detect small FS pockets at the BZ 20 boundary. The orbital characters of these FSs were determined by comparing their 21 shape and orientations, as well as the band dispersions around the Fermi level, with 22 the density functional theory (DFT) calculations. We found that the size of the FS is 23 strongly modified from the DFT calculations, suggesting the orbital-dependent 24 correlation effect. These results provide an electronic basis for exploring the 25 interplay of antiferromagnetic/charge density wave order and possible 26 unconventional superconductivity in this compound. 27  28 Kagome materials exhibit novel physical properties such as spin liquids,1–4) 29 topological quantum phases5–9) and unconventional superconductivity10–13) arising from 30 an interplay between topology, electron correlation and geometrical frustration. These 31 2  phenomena arise from the characteristic electronic features of the Kagome lattice, i.e. 1 Dirac cones, van Hove singularities (vHS), and Flat bands (FBs), tuned at the Fermi level 2 (EF). AV3Sb5 family (A = K, Rb, and Cs) exhibits superconductivity in the nonmagnetic 3 Kagome lattice with weak electronic correlation. The X-ray diffraction (XRD) studies 4 reported the 2 × 2 × 2 superstructure, suggesting the charge density wave (CDW) 5 formation,14) which might be chiral and associated with the time-reversal symmetry 6 breaking.15) Previous angle-resolved photoemission spectroscopy (ARPES) reported that 7 the CDW order originates in the nesting between vHS near EF.16)  8 In contrast, recently discovered Kagome metal CsCr3Sb5 exhibits magnetism, charge 9 order, and strong correlation17). Anomalous behaviors at 55 K in transport and 10 thermodynamic properties suggested multiple orders in both charges and spins. Nuclear 11 magnetic resonance measurements reported antiferromagnetic order. The observation of 12 the 4 × 1 superlattices from the XRD measurements indicates the CDW formation with 13 the rotational symmetry breaking. Superconductivity emerges at the transition 14 temperature (Tc) of 6.4 K at 4.2 GPa. Unconventional electron pairing mechanism has 15 been considered for this compound because of the non-Fermi liquid behavior and the 16 upper critical field exceeding the Pauli limit around the maximum Tc.17) 17 Characteristic electronic structure in CsCr3Sb5 is the FB-like feature at the binding 18 energy of 80 meV observed by ARPES.18–20) The density functional theory (DFT) 19 calculations also suggested the presence of the FB at ~300 meV above EF,21) which may 20 dominate the correlated electronic properties of this compound.22,23) Furthermore, 21 theoretical studies proposed the importance of the FS nesting condition which enhances 22 the antiferromagnetic fluctuations leading to the unconventional s± or d wave 23 superconductivity.21) The FS-related itinerant magnetism was, on the other hand, 24 proposed to be important for the formation of the antiferromagnetic order in CsCr3Sb5.24) 25 While the extensive ARPES studies reported the band structure of CsCr3Sb5,18–20,25) the 26 complete determination of the FSs has not been achieved so far. It has been shown that 27 the electronic band dispersions in CsCr3Sb5 are much broader than AV3Sb5 family,19) 28 possibly due to the strong correlation effect20) and/or structural inhomogeneity.26) For 29 understanding the origin of the DW phase transitions and superconductivity in CsCr3Sb5, 30 the experimental determination of the FSs has been highly demanded. 31 3  In this study, we report the FSs in the paramagnetic state of CsCr₃Sb₅ by employing a 1 laser photoemission microscopy, with a detecting area of 10 × 30 µm2. We succeeded in 2 observing all the FSs, i.e. three concentric FSs around the Brillouin zone (BZ) center and 3 the small FS pockets at the BZ boundary, from a small area of the sample surface. We 4 further determined the orbital characters of these FSs by comparing their shapes and 5 orientations as well as the band dispersions, with the DFT calculations. The size of the 6 FS is strongly modified from the DFT calculations, suggesting the orbital-dependent 7 correlation effect. 8 The high-quality single crystals of CsCr₃Sb₅ were synthesized by self-flux method 9 as reported in elsewhere.18) The sample was mounted on the tantalum plate with silver 10 paste and cleaved in situ at room temperature under the vacuum of 1.0 × 10-10 Torr. 11 Imaging-type spin-resolved photoemission microscopy (iSPEM)27–29) with a 10.9 eV laser 12 at NIMS was employed to visualize the FS in entire first BZ. The polarization-dependent 13 measurements were performed by employing left- and right-circularly polarized (LCP 14 and RCP) lasers. 15 CsCr3Sb5 crystalizes in a hexagonal lattice with the space group P6/mmm [Figs. 1(a) 16 and 1(b)]. The DFT calculation indicates one electron band (Sb pz) and two hole bands 17 (Cr dxz and Cr dx2-y2) crossing EF around Γ(A) point [Fig. 1(c)]. These bands tend to form 18 nearly degenerated FS sheets around kz = 0 as shown in Fig. 1(d). The electron band at 19 M(L) point forms the FS pockets showing a large kz dependence in size [Fig. 1(e)]. In the 20 laser photoemission microscopy data, we use the labeling of Γ�, M�  and K� in the two-21 dimensional BZ projected onto (001) surface. 22 First, we show the FSs of CsCr3Sb5 at 70 K (paramagnetic state) in Figs. 2(a) and 23 2(b), obtained by LCP and RCP lasers, respectively. Overall FS shapes are quite similar 24 for both measurements, while the location of the high intensity exhibits a polarization 25 dependence. One can recognize the circular FS around Γ� point and high-intensity spots 26 around M�  point. In order to clarify the weak intensity laying between BZ center and 27 boundary, we performed the curvature analysis30) for the raw FS data. The disconnected 28 portions of the FSs centered at Γ�  are emphasized in Figs. 2(c) and 2(d), which are 29 consistently observed in the peak-plot analysis of the raw FS data as highlighted by the 30 gray curves in Figs. 2(e) and 2(f). Here we overlay the markers obtained from the peak 31 plot analysis for LCP and RCP data as shown in Fig. 2(g). The disconnected portions of 32 4  the FSs [gray curves in Fig. 2(g)] can be assigned to the upper (lower) part of the 1 hexagonal FS with the corners directed to M�   (K� ) point. We note that in the present 2 experimental geometry, the photoelectron distribution in the momentum space should be 3 anisotropic and some portions of the FSs cannot be detected. As summarized in Fig. 2(h), 4 the presence of the inner (α), middle (β) and outer (γ) FS sheets were confirmed around 5 Γ� point. 6 The polarization dependence of the FS is rather clear around M�  point [Fig. 2(g)]. 7 The LCP and RCP lasers seem to detect the inner or outer part of the elliptical FS pockets 8 (δ) separated by the BZ boundary [black lines in Fig. 2(g)]. In order to investigate this 9 polarization dependence, we show the line profiles of the raw FS data [Figs. 2(a) and (b)]. 10 Figure 3(a) exhibits the line profiles along Γ�-M�  obtained by the LCP and RCP lasers at 11 azimuthal angles (θ) of 60 degrees and 120 degrees. While the line profiles at θ = 60º 12 (black) are almost identical, those for θ = 120º (gray) show clear polarization dependence 13 especially in the peaks for the FSs δ and β. The inverted open triangles in Fig. 3(a) 14 highlight the difference in the peak positions for the FS δ, reflecting two Fermi 15 momentum (kF) for the left and right part of the elliptical FS pocket around M�  point. On 16 the other hand, the inverted filled triangles on the line profiles at θ = 120º suggest the 17 presence of the peak for the FS β in the LCP data which is absent in the RCP data. The 18 pair of the peaks at ±0.2 Å-1 corresponds to the FS α. Finally, the hump structure around 19 +0.55 Å-1 can be assigned to the γ FS. Then, the line profile taken by LCP at θ = 120º is 20 well reproduced by the fitting function composed of six Lorentz functions (red dotted 21 curves) with a background (black dotted line) in Fig. 3(b), demonstrating the complete 22 assignment of the FSs in CsCr₃Sb₅. 23 Figure 3(c) shows the energy-momentum dispersions obtained by the intensity 24 profiles along Γ�–K� line at θ = 150º. We found that the FS α is formed by the electron 25 band with a bottom at EB = ∼0.6 eV around Γ� point (red dotted curve). It is also indicated 26 that the FSs β and γ consist of hole-like band dispersions (orange dotted curves). 27 Here we discuss the orbital character for each FS sheet. First, the FS α (electron band 28 at Γ� point) should have Sb pz orbital component according to the DFT band calculation 29 in Fig. 1(c). Second, we assign the orbital character for each FS sheet from its shape and 30 5  orientation. We observed three FS sheets around Γ� point, i.e. circular FS α, hexagonal 1 FS β with the corners directed to K point, and hexagonal FS γ with the corners directed 2 to M point. According to the calculated FSs at kz = π [Fig. 1(e)], the shape and orientation 3 of the inner hexagonal FS composed of Cr dxz orbital (blue) is identical to those of the 4 FS γ. The middle circular FS formed by the electron band of Sb pz orbital (green) 5 corresponds to the FS α, which is consistent with the observation in Fig. 3(c). Then, the 6 outer hexagonal FS of Cr dx2-y2 orbital (orange) is assigned to the FS β. Finally, the FS δ 7 at M�  point is determined to have Cr dxz orbital character (blue).  8 The total number of the FSs in the present data is consistent with the DFT 9 calculations. We consider that the experimental kz value is closer to π rather than 0 10 according to the coincidences in the shapes of three FSs around Γ� with the calculations. 11 However, the size of the experimental FS exhibits some deviation from the calculation in 12 Fig. 1(e). The FS γ is much larger than the blue hexagonal FS (Cr dxz), while the FSs 13 α and δ are smaller than green circular FS (Sb pz) and blue pockets (Cr dxz), respectively. 14 On the other hand, the size of the FS β is almost the same as that of orange hexagonal FS 15 (Cr dx2-y2). A possible explanation for these quantitative disagreements might be the 16 orbital-selective band renormalization.31) In this scenario, the size and shape of the FS 17 should be modified by the correlation effects for Cr d and Sb p orbitals, which is most 18 prominent for the dxz orbital. For example, the correlated FS pockets at M point (dxz) are 19 smaller than those without correlations, which is consistent with the observation of small 20 FS δ. The present results suggest the importance of electronic correlations for properly 21 understanding the paramagnetic electronic states of CsCr3Sb5. A detailed comparison of 22 experimental band velocities and bandwidths with those in theoretical calculations will 23 be helpful to support the discussion on the correlation effects. As for the small size of the 24 FS δ, there is also a possibility that the kz value at M�  point somewhat deviates from Γ� 25 point (kz = π), which tends to shrink the FS pockets. Further experimental investigations 26 on the kz dependence of the FSs will be required for more rigorous discussion. 27 In conclusion, we investigated the FSs in the nonmagnetic state of CsCr3Sb5 using 28 the laser photoemission microscopy. We found three concentric FSs around Γ� point and 29 small FS pockets around M�  point. By comparing with the DFT calculations, the orbital 30 characters of these FSs were determined from their shapes and orientations, as well as the 31 6  band dispersions near the EF. The size of the FS sheets exhibits a large deviation from the 1 DFT calculations, supporting the orbital-selective band renormalization. These results 2 provide an important insight for exploring the antiferromagnetic/charge density wave 3 order and superconductivity in CsCr3Sb5.  4  5 Acknowledgement 6 The authors thank F. Arai for the technical support of iSPEM measurements. The present 7 work was partially supported by JST CREST, Japan (Grant No JPMJCR2435), the Japan 8 Society for the Promotion of Science KAKENHI (Grant Nos. 24K01352, 24K17591, 9 25K07195), and the Innovative Science and Technology Initiative for Security Grant 10 Number JPJ004596, ATLA, Japan. The single-crystal synthesis and characterization at 11 Rice were supported by the U.S. DOE, BES under Grant Nos. DESC0012311 and DE-12 SC0026179 (P.D.) 13  14  15 References 16 *kunitsu.hayate.r8@s.mail.nagoya-u.ac.jp 17 1. L. Balents, Nature 464, 199–208 (2010). 18 2. S. Yan, D.A. Huse, and S.R. White, Science 332, 1173–1176 (2011). 19 3. T.-H. Han, J.S. Helton, S. Chu, D.G. Nocera, J.A. Rodriguez-Rivera, C. Broholm, 20 and Y.S. Lee, Nature 492, 406–410 (2012). 21 4. M. Fu, T. Imai, T.-H. Han, and Y.S. Lee, Science 350, 655–658 (2015). 22 5. E. Liu, Y. Sun, N. Kumar, L. Muechler, A. Sun, L. Jiao, S.-Y. Yang, D. Liu, A. Liang, 23 Q. Xu, J. Kroder, V. Süß, H. Borrmann, C. Shekhar, Z. Wang, C. 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(d, e) The calculated Fermi surfaces of CsCr3Sb5 at kz = 0 and π, 8 respectively. Orange, blue and green curves represent the Fermi surface composed of 9 Cr dx2-y2, Cr dxz and Sb pz orbital, respectively. 10  11  12  13  14  15  16  17  18  19  20  21  22 11  Fig. 2 1  2 Fig. 2. Fermi surface of CsCr3Sb5 observed by laser photoemission microscopy.  (a, 3 b) Fermi surface mapping of CsCr3Sb5 measured with LCP and RCP laser, 4 respectively. White lines represent the Brillouin zone boundaries. The definition of 5 the azimuthal angle and scale bar corresponding to 0.5 Å-1 are shown. (c, d) Curvature 6 analysis of the data in (a) and (b), respectively. (e, f) The peak plots of the data in (a) 7 and (b), respectively. Thick gray curves indicate the portions of the Fermi surfaces β 8 and γ. (g) Superimposed peak plots in (e) and (f). (h) Summary of the Fermi surface 9 observations.  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24 12  Fig. 3 1  2 Fig. 3. (Color online) Intensity profiles of the Fermi surface mapping data. (a) 3 Intensity profiles along Γ�–M�  line at the azimuthal angles of 60° (black) and 120° 4 (gray) measured by LCP and RCP laser. The inverted open triangles highlight the 5 difference in kF for the δ band, reflecting two kF values for the left and right side of 6 the elliptical FS pocket at M�  point. The inverted filled triangles indicate the presence 7 (LCP) and absence (RCP) of the intensity for the β FS. The dotted lines represent the 8 kF for each FS. (b) Fitting analysis for the intensity profile at the azimuthal angles of 9 120° taken by LCP laser. Red curve represents the fitting function composed of six 10 Lorentz functions (red dotted curves) and a constant background (black dotted line). 11 (c) Energy-momentum dispersions obtained by the intensity profiles along Γ�–K� line 12 at θ = 150º. The red and orange dotted curves represent an electron band for the FS 13 α, and two hole bands for the FSs β and γ centered at Γ� point, respectively. The data 14 were smoothed along both the energy and momentum directions. 15  16  17