⇦Chinese Physics Letters, 2020, Vol. 37, No. 8, Article code 087102 Experimental Observation of Electronic Structures of Kagome Metal YCr$_{6}$Ge$_{6}$ Pengdong Wang (王鹏栋)1, Yihao Wang (王宜豪)2, Bo Zhang (张波)1, Yuliang Li (李昱良)1, Sheng Wang (王盛)1, Yunbo Wu (吴云波)1, Hongen Zhu (朱红恩)1, Yi Liu (刘毅)1, Guobin Zhang (张国斌)1, Dayong Liu (刘大勇)3*, Yimin Xiong (熊奕敏)2*, and Zhe Sun (孙喆)1,4,5* Affiliations 1National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China 2Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China 3Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, China 4Key Laboratory of Strongly Coupled Quantum Matter Physics, Chinese Academy of Sciences, University of Science and Technology of China, Hefei 230026, China 5CAS Center for Excellence in Superconducting Electronics (CENSE), Shanghai 200050, China Received 8 May 2020; accepted 22 June 2020; published online 28 July 2020 Supported by the National Key R&D Program of China (Grant Nos. 2017YFA0402901, 2016YFA0401004 and 2016YFA0300404), the National Natural Science Foundation of China (Grant Nos. 11674296, 11974354 and U1432138), the Key Research Program of the Chinese Academy of Sciences (Grant No. XDPB01), the Innovative Program of Development Foundation of Hefei Center for Physical Science and Technology (Grant No. 2018CXFX002), the Collaborative Innovation Program of Hefei Science Center, CAS (Grant No. 2019HSC-CIP007), and the High Magnetic Field Laboratory of Anhui Province.
*Corresponding authors. Email: zsun@ustc.edu.cn; yxiong@hmfl.ac.cn; dyliu@theory.issp.ac.cn Citation Text: Wang P D, Wang Y H, Zhang B, Li Y L and Wang S et al. 2020 Chin. Phys. Lett. 37 087102    Abstract Using angle-resolved photoemission spectroscopy, we study electronic structures of a Kagome metal YCr$_{6}$Ge$_{6}$. Band dispersions along $k_{z}$ direction are significant, suggesting a remarkable interlayer coupling between neighboring Kagome planes. Comparing ARPES data with first-principles calculations, we find a moderate electron correlation in this material, since band calculations must be compressed in the energy scale to reach an excellent agreement between experimental data and theoretical calculations. Moreover, as indicated by band calculations, there is a flat band in the vicinity of the Fermi level at the $\varGamma$–$M$–$K$ plane in the momentum space, which could be responsible for the unusual transport behavior in YCr$_{6}$Ge$_{6}$. DOI:10.1088/0256-307X/37/8/087102 PACS:71.27.+a, 73.20.-r, 73.20.At, 41.60.Ap © 2020 Chinese Physics Society Article Text A Kagome lattice is a hexagonal star-shaped geometrical frustrated system, and it may host a flat band naturally due to the destructive interference of wave functions, in which electronic excitations are localized and with large effective mass.[1–10] In an ideal Kagome lattice, a wave function is confined in the hexagon unit and not able to propagate out of the hexagon, because the weight of wave functions will be canceled out exactly outside of the hexagon even if the nearest neighbor hopping exists. Such destructive interference occurs in each hexagon unit. In real space, as the kinetic energy is completely quenched, the hopping of the electrons is suppressed and they are localized in the hexagon lattice. The energy levels of these localized electrons are degenerated, and there is no hybridization and band broadening. Such a novel electronic band is highly different from the usual Bloch electronic states in a crystalline solid, for the latter move more delocalized with various but finite effective mass as defined by the band dispersion. Owing to the exotic characteristics of a flat band, the Coulomb interaction becomes critical, making it a popular platform for investigating the novel properties in strongly correlated many-body systems, such as ferromagnetism,[11,12] superconductivity,[13–15] Wigner crystal,[16,17] quantum spin liquid,[18,19] and fractional quantum Hall effect.[20] In addition to the flat band, there are graphene-like Dirac cones in the fundamental band structure of a Kagome lattice,[21–23] due to its topological duality with the honeycomb lattice. Therefore, the Kagome lattice is a desirable platform for exploring rich physics in a hybrid system composed of the flat band with large effective mass and the Dirac cones with massless dispersions. Recently, some magnetic materials with Kagome lattices have been intensively studied, including Fe$_{3}$Sn$_{2} $,[24,25] Co$_{3}$Sn$_{2}$S$_{2}$,[26] Mn$_{3}$Sn,[27,28] and Mn$_{3}$Ge,[29] in which unusual electronic properties have been observed, such as massive Dirac fermions, magnetic Weyl fermions, and giant anomalous Nernst effect.[30–33] However, these materials also possess strong magnetic characteristics, and electronic structures are complicated compared to the primary band dispersions of a Kagome model. YCr$_{6}$Ge$_{6}$ has a configuration of Kagome lattice with weak magnetic correlations. It crystallizes in the hexagonal HfFe$_{6}$Ge$_{6}$-type crystal structure (see Fig. 1). Ignoring the Ge$_{4}$ and YGe$_{2}$ layers, one can observe two undistorted Kagome layers consisting of Cr atoms in one unit cell of YCr$_{6}$Ge$_{6}$. Therefore, it could be a candidate for studying the distinctive band structures of a Kagome metal without the complexity caused by strong magnetic correlations. Recently, Yang et al. performed the first ARPES studies of YCr$_{6}$Ge$_{6}$ with an emphasis on electronic states in the $k_{z}=0$ plane.[34] However, the knowledge of electronic structures in this material is still very limited, more investigations are demanded to reveal the detailed band structures. Using angle-resolved photoemission spectroscopy (ARPES), we studied the electronic structures of YCr$_{6}$Ge$_{6}$. Band dispersions along $k_{z}$ direction can be clearly resolved, which indicates a significant interlayer coupling between neighboring Kagome planes. By comparing with theoretical calculation, we observed a moderate electron correlation in this material, and the band width determined by ARPES is about 60% of the theoretical value. Owing to the excellent agreement between ARPES data and theoretical calculations, we estimated that there is a flat band in the vicinity of the Fermi level, which could have significant effects on the charge transport properties.
cpl-37-8-087102-fig1.png
Fig. 1. (a) The crystal structure of YCr$_{6}$Ge$_{6}$. Y, Cr, and Ge atoms are represented by green, blue and gray balls, respectively. (b) The top view of the 2D Cr Kagome layers. (c) Single crystal XRD pattern of YCr$_{6}$Ge$_{6}$. (d) Morphology and rocking curve of YCr$_{6}$Ge$_{6}$ single crystal. The full width at half maximum was 0.15$^{\circ}$, which shows the good quality of the single crystals.
Our samples were grown by the flux method using a tin flux, following the method reported by Avila et al.[35] A mixture of starting materials with a ratio of Y:Cr:Ge:Sn = $1\!:\!3\!:\!6\!:\!20$ was put into an alumina crucible and sealed in a silica tube. The materials were heated at 1000 ℃ for 3 h, then slowly cooled down to 500 ℃ at a rate of approximately 3 ℃/h, and then cooled to room temperature. Figure 1(c) shows the XRD pattern of a YCr$_{6}$Ge$_{6}$ single crystal. Only (00$L$) reflections are present, indicating the exposed surface is $ab$-plane. The full width at half maximum of the rocking curve of (004) reflection is about 0.15$^{\circ}$, as shown in Fig. 1(d), suggesting the good quality of samples. ARPES measurements were performed at ARPES beamline (BL-13U) of the National Synchrotron Radiation Laboratory, Hefei, with a Scienta Omicron DA30L analyzer. The energy and angular resolutions were better than 20 meV and 0.3$^{\circ}$, respectively. Single crystals of YCr$_{6}$Ge$_{6}$ were cleaved to achieve clean surfaces in ultrahigh vacuum better than $6\times 10^{-11}$ torr. Various photon energies were used to characterize band structures at different $k_{z}$ in momentum space. The first-principle calculations are performed by the full potential linearized augmented-plane-wave (lapw) method based on density functional theory implemented with the WIEN2K code.[36] The generalized gradient approximation (GGA) by Perdew, Burk, and Ernzerhof (PBE)[37] are adopted to include the exchange and correlation effects. The calculated band structure of YCr$_{6}$Ge$_{6}$ are obtained in comparison with ARPES experiment. The experimental lattice parameters[38] are used in the calculations. By directly measuring the dispersion of ARPES intensity along the $c$-axis direction and mapping the Fermi surface topology with various photon energies, we observed evident $k_{z}$ dispersion in YCr$_{6}$Ge$_{6}$. Figure 2(a) shows the Brillouin zone of YCr$_{6}$Ge$_{6}$. In order to straightforwardly demonstrate the dispersion of electronic spectral weight along the $c$-axis, we cleaved along the red cut of the inset in Fig. 2(b) and exposed clean surfaces parallel to the $bc$ plane. Performing ARPES measurements on this surface reveals dispersive spectral weight along the $k_{z}$ direction [as shown in Fig. 2(b)]. Though we cannot pin down the corresponding band of these electronic states, the significant dispersion along $k_{z}$ direction proves that YCr$_{6}$Ge$_{6}$ has relatively strong coupling between neighboring Kagome layers. This result is also consistent with the fact that the resistivity is small along the $c$-axis in spite of its layered structure along $ab$-plane.[39] In Figs. 2(c)–2(e), we show the Fermi surface topologies obtained by using different photon energies. One can notice that Fermi surface varies with photon energies. This behavior further indicates that the band structures of YCr$_{6}$Ge$_{6}$ have evident dispersions in the $k_{z}$ direction. As shown in Fig. 2(b), the periodicity of $k_{z}$ dispersion is 4$\pi /c$, which suggests that the fundamental band structures of the two neighboring Kagome layers in one unit cell are quite similar. Similar 4$\pi /c$ periodicities along $c$-axis have also been observed in 122-type iron-based superconducting materials, in which the two FeAs layers in one unit cell possess the same electronic structures.[40–41] In Figs. 2(f)–2(h), regardless of the changes in spectral weight caused by matrix elements and $k_{z}$ dispersions, there is a Dirac-cone feature at $K$, which is a particular characteristic in the band structure of a Kagome lattice. In order to further prove the existence of Dirac cones, we have studied the band dispersions around $K$ in momentum space. Along several cuts around $K$ [see Fig. 3(f)], we collected ARPES intensity and plot them in Figs. 3(a)–3(e). The evolution of band dispersions shows that the bottom of the $\alpha_{1}$ band and the top of the $\alpha_{2}$ band move towards each other, and then touch each other, and then separate. Such a characteristic feature is highly similar to the electronic structure of the Dirac cone in a Kagome lattice.
cpl-37-8-087102-fig2.png
Fig. 2. (a) Hexagonal Brillouin zone of YCr$_{6}$Ge$_{6}$. (b) ARPES intensity mapping in $\varGamma $–$A$–$L$–$M$ plane. The data were taken using 91 eV photons. In the inset, the red line indicates the cleavage direction, and by measuring the side surface we could obtain the dispersive features along $k_{z}$. (c)–(e) Fermi surface topologies in different photon energies (35 eV, 50 eV, and 74 eV). (f)–(h) Dirac-cone at $K(H)$ for various photon energies.
cpl-37-8-087102-fig3.png
Fig. 3. (a) ARPES intensity at the Fermi level taken using 35 eV photons. (b)–(f) The evolution of band structures around $K$, the data was taken along the cuts as indicated in (a). The black dashed lines outline the $\alpha_{1}$ and $\alpha_{2}$ bands.
Figure 4 shows the distribution of ARPES intensity along high symmetry directions. Based on the ARPES studies on YCr$_{6}$Ge$_{6}$ by Yang et al.,[34] we found that $\varGamma$ and $A$ along the $k_{z}$ direction can be reached using 55 and 80 eV photons, respectively. Therefore, we show the data taken by using these photon energies to reveal the details of electronic structures along high symmetry directions in momentum space. Our theoretical calculations are also plotted, along with experimental data for comparison. The data of 55 eV are in agreement with the theoretical calculations along ${\varGamma}$–$K$–$M$–$\varGamma$ direction roughly, and the data taken using 80 eV photons matches the theoretical calculations along $A$–$H$–$L$–$A$ direction as well. However, we note here that, in order to obtain a reasonable consistency between the theoretical calculations and experimental data, the theoretical band dispersions must be compressed in energy scale by 40%. Such a compression of band calculations indicates evident electron-correlation effects in this material.
cpl-37-8-087102-fig4.png
Fig. 4. (a) and (b) ARPES data taken in ${\varGamma}$–$K$–$M$–$\varGamma$ and $A$–$H$–$L$–$A$ plane, respectively. (c) and (d) The corresponding second-derivative images of the ARPES data presented in (a) and (b), respectively. The yellow dashed lines are theoretical calculations, though they were compressed in energy to match the ARPES data.
As demonstrated in Fig. 4, electron-correlation effects lead to the band renormalization and the enhancement of band mass. In Ref. [34], through the analysis of specific heat, the effective band mass is estimated to be enhanced by a factor of 2, which is larger than the increment obtained in the present work by ARPES results. We argue that the difference comes from the fact that the specific heat is more sensitive to the density of states near the Fermi level, which contains significant contribution from the bands with large effective mass. The ARPES data in Fig. 4 shows the band renormalization in a large energy scale, which are mainly dominated by the bands with lower effective mass. As we know, the effective mass of flat bands is significantly larger than those of other bands in Kagome metals. Therefore, the different enhancement of effective band mass extracted from specific heat data and ARPES results hints the fact of the existence of flat bands near the Fermi level. Indeed, we are able to locate the position of the flat band in our data by taking advantage of first-principles calculations, since there is an excellent agreement between our ARPES data and theoretical calculations when the electron correlations are taken into account. As shown in Fig. 4(a), there is a flat band very close to the Fermi level in band calculations along the ${\varGamma}$–$K$–$M$–$\varGamma$ direction, while such a band disappears in the $A$–$H$–$L$–$A$ direction. This result is consistent with the data reported by Yang et al.,[34] in which there is a signature of high density of states around $\varGamma$ in momentum space. In a simplified theoretical model for a Kagome lattice, the dispersions of Bloch electronic states are highly similar to that of graphene, which spread over a wide energy range with the Dirac point at $K$, while the flat band is located at the top of the dispersions of Bloch electronic states.[33,39,42] When there is an interlayer coupling between Kagome layers in one unit cell, two sets of Kagome bands exist with their separation varying along $k_{z}$.[34] In Fig. 4, however, one can notice that the realistic band dispersions are very complicated, strikingly different from the graphene-like band dispersions for a simplified band model of a Kagome lattice. Our data indicates that there are multiple orbitals and bands that contribute to the electronic states near the Fermi level, and consequently, YCr$_{6}$Ge$_{6}$ cannot be well described by an ideal Kagome model. In summary, we have measured the band structures of YCr$_{6}$Ge$_{6}$, which shows evident $k_{z}$ dispersions due to the interlayer coupling between neighboring Kagome layers. Compared with theoretical calculations, a moderate electronic correlation is observed. Our results suggest that the flat band is close to the Fermi level when the $k_{z}$ is at ${\varGamma}$–$K$–$M$–$\varGamma$ plane in momentum space, which could be responsible for the anomalous transport properties of YCr$_{6}$Ge$_{6}$. Compared to the simplified band model of a Kagome lattice, the band structures of YCr$_{6}$Ge$_{6}$ possess multiple bands, which could smear out the characteristic features of Kagome bands. 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