Structure and transport property of FeGe. Kagome metal FeGe crystallizes in the space group P6/mmm with lattice constants a = 4.99 Å and c = 4.05 Å51,52. It consists of Fe3Ge kagome layers and Ge2 honeycomb layers stacking alternatively along the c-axis as shown in Fig. 1a29–32. Its corresponding three-dimensional (3D) BZ and projected (001) surface BZ are illustrated in Fig. 1b, where the black dots represent the high-symmetry momenta. Previous results of STM, neutron scattering and magnetic susceptibility indicate a short-ranged CO in the as-grown FeGe samples31,38, which is also confirmed by our temperature-dependent magnetic susceptibility result. It only shows an anomaly in χ//a at the CO onset temperature (TCO) [Fig. 1c]. Notably, the annealed sample shows sharper transitions in both χ//a and χ//c at TCO, which is consistent with a first order transition behavior, indicative of a long-ranged CO therein.
Figure 1d shows the photoemission intensity along \(\stackrel{-}{K}\) - \(\stackrel{-}{M}\) - \(\stackrel{-}{K}\) taken from the annealed sample, where there are two VHSs assigned as VHS1 (slightly above EF) and VHS2 (∼ 15 meV below EF) existing around the \(\stackrel{-}{M}\) point, consistent with previous reports31,34. However, our detailed temperature-dependent ARPES measurements reveal only a tiny gap opening ∼ 4 meV at EF [Supplementary Fig. S1]. It should be noted that we have performed a comprehensive real-space mapping of the ARPES intensity and probed seven points on the cleaved sample, which should effectively cover the CO domains38,41. And the CO gap is also missing according to the recent Raman and infrared spectroscopy experiments53,54. Besides, in Fig. 1f, we present the JDOS based on the symmetrized Fermi surface map detected above TCO as displayed in Fig. 1e. It does not show any pronounced peaks related to the CO wave-vectors qi (i = 1, 2 and 3). This is also confirmed by our calculated zero-frequency JDOS [Fig. 1g and Supplementary Fig. S2] and consistent with the previous theoretical work36. This finding, together with the absence of obvious gap opening around the \(\stackrel{-}{M}\) point which can account for a 100 K CO phase transition, indicate that the nesting mechanism might not be the dominating driving force for the CO formation of FeGe.
Two obvious changes related to CO in band structures. To identify the states closely associated with the CO formation, we conduct a comprehensive search for the spectral changes across the CO phase transition over the whole 3D BZ of the annealed FeGe samples. The kz determination is presented in Supplementary Fig. S3. After an extensive mapping of the electronic structure over the entire BZ, two obvious spectral changes accompanied with the long-ranged CO formation are resolved: one is around the K point and the other is around the A point.
Figure 2a shows the photoemission intensity plot along Γ - K acquired at 16 K. One electron pocket around K (assigned as α) with a band bottom at ∼ 15 meV below EF can be observed. Compared to the non-CO state at 139 K, α band moves upward by ∼ 28 meV in energy position in the CO state [Fig. 2b]. The detailed enlarged spectral evolution in the region around K [marked by the black frame in Fig. 2a] with temperature crossing TCO is shown in Fig. 2c. A constant sinking of the α band in energy position with increased temperature can be observed. And the α band is temperature-independent in the non-CO state, as demonstrated in Fig. S4. Notably, the surface aging effect is negligible, since the last data taken at 14 K is similar to that of 16 K taken in the beginning. Moreover, the integrated momentum distribution curves (MDCs) around EF [Fig. 2d], together with the integrated energy distribution curves (EDCs) around K [Fig. 2e] further highlight such a continuous spectral change. This behavior is summarized schematically in Fig. 2f, which can be deduced from the dispersion extracted based on the second-derivative of the photoemission intensity, and the Fermi surface maps around K as well [Supplementary Fig. S5].
A more dramatic spectral change across the CO phase transition is discovered in the kz = π plane. As shown in Fig. 3a, there exists a tiny electron-like band (assigned as β) centered at the A point, which barely crosses EF in the CO state at 16 K. In contrast, the bottom of β shifts downward in energy position (∼ 25 meV) in the non-CO state at 118 K [Fig. 3b]. The detailed temperature-dependent evolution of the β band is shown in Fig. 3c. It should be noted that, since the intensity of the β band is rather weak, all spectra here have been subtracted by a smoothed background EDC to highlight their characteristics [Supplementary Fig. S6]. One can clearly identify a sudden change of the β band when crossing TCO, which is further proved by the corresponding MDCs at EF [Fig. 3d], EDCs around A [Fig. 3e], and second-derivative data and Fermi surface maps around A [Supplementary Fig. S6]. Besides, the temperature-independent behavior of the β band in the non-CO state is presented in Fig. S7. Accordingly, we summarize a schematic of temperature-dependent evolution of β in Fig. 3f.
Comparison of ARPES and DFT results. To understand the origin of the observed band structure evolution across TCO, we turn to our recent DFT calculations33,39, which predict a large dimerization of a quarter of Ge1-sites along the c-axis in a 2 × 2 × 2 superstructure. Figures <link rid="fig4">4</link>a and 4(b) show the 2 × 2 × 2 CO superstructure relaxed by DFT. The large partial Ge1-dimerization induces CO in the kagome and honeycomb layers accompanied with small distortions of Fe-sites along the c-axis and a Kekulé-type distortion of Ge2-sites. Here, we calculate and compare the band structures between the non-CO and CO states to extract the low-lying electronic structure changes across the phase transition, which are shown in Figs. 4c and 4d, respectively. The band structures have been unfolded into a 1 × 1 × 1 nonmagnetic BZ. Obvious differences can be found around the K and A points near EF. Figure 4e highlights the band structure around the K point, where the electron pocket with Fe-3d character shifts upward in the CO state, accompanied by a small hybridization gap opening due to the band folding effect. This change is attributed to the small distortions of Fe-sites. The more dramatic change is at the A point, where the electron pocket with Ge-4p character shifts upward a lot in the CO state, as highlighted in Fig. 4f. This change is attributed to the large Ge1-dimerization. One could notice that the details of the energy bands between the experiment and calculation are not consistent well, especially that the energy scale differs a lot, this might be due to the complicated correlation effect and antiferromagnetic reconstruction the 3D electronic bands in FeGe.