Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe

Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge density wave, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to nonkagome surface layers. Here, we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifies a $2\times 2$ charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin mapping across steps of unit cell height demonstrates the existence of spin-polarized electrons with an antiferromagnetic stacking order. We further uncover the correlation between antiferromagnetism and charge order anisotropy, highlighting the unusual magnetic coupling of the charge order. Finally, we detect a pronounced edge state within the charge order energy gap, which is robust against the irregular shape fluctuations of the kagome lattice edges. We discuss our results with the theoretically considered topological features of the kagome charge order including unconventional magnetism and bulk-boundary correspondence.

Figure 1

(a) Many-body interaction (red springs) driven topology in kagome lattice (red spheres). The interaction not only opens a charge density wave gap at $E_F$, but also produces a nontrivial Berry phase (red circular arrows) that leads to orbital currents and magnetism (thick red arrows) and a topological edge state (yellow ring). The light and dark red ellipsoids represent unoccupied and occupied electronic states, respectively. (b) Crystal structure of FeGe. The low temperature magnetic structure is an approximate $A$-type antiferromagnet. (c) Topographic image of a half unit cell step consisting of Ge and FeGe layers, and the enlarged Ge layer marked with the honeycomb lattice (blue lines). (d) Topographic image of the kagome lattice layer of FeGe, and the enlarged image marked with the kagome lattice (red lines). (e) $dI/dV$ map taken at $E_F$ for the same kagome lattice region, and its Fourier transform identifying the $2\times 2$ vector peaks. (f) Energy distribution of the three pairs of $2\times 2$ vector peak intensities. Counting from the highest to the lowest intensity vector peak pairs, we define an anticlockwise chirality. (g) $dI/dV$ spectrum taken on the kagome lattice, showing an energy gap. The insets show two tunneling current maps for the same region taken below and above this energy gap. We also mark the kagome lattice as black lines. The center of this marked kagome lattice shows a reversal of intensity for these two maps, consistent with a charge order. (h) Temperature dependence of tunneling spectrum showing the disappearance of energy gap at 104 K, which is just above the charge ordering temperature. The inset shows the Fourier transform data of a $dI/dV$ map taken at $E_F$ at 104 K, showing the disappearance of $2\times 2$ vector peaks.

Figure 2

(a) Topographic image of kagome terraces with unit cell steps (upper panel) and their height profile (lower panel). A magnetic tip is used to obtain the data, and the kagome lattices are expected to couple antiferromagnetically along the $c$ axis. (b) $dI/dV$ maps taken at $E_F$ for the region in $\mathbf{a}$ with tip spin polarized in up (upper panel) and down (lower panel) directions. (c) $dI/dV$ signal at $E_F$ for kagome terraces ④ and ⑤ as a function of $c$ axis magnetic field sweeping. The lower inset shows the schetch illustrating spin configurations for the tip and sample at different magnetic fields. The upper inset shows the $dI/dV$ data for kagome terraces ④ and ⑤ with $B=+1\mathrm{T}$. (d) High-resolution $dI/dV$ magnetic contrast data for terrace ④. The data are taken at the orange box region in (b), and obtained through subtracting $+1\mathrm{T}$ map with $-1\mathrm{T}$ map data. The white lines mark the $2\times 2$ charge order. (e) Fourier transform of (d) showing $2\times 2$ vector peaks. The right panel displays the intensity of the $2\times 2$ vector peaks along the Bragg spot direction, from which we determine the clockwise chirality. (f) High-resolution $dI/dV$ magnetic contrast data for terrace ⑤. The data are taken at the red box region in (b), and obtained through subtracting $-1\mathrm{T}$ map with $+1\mathrm{T}$ map data. (g) Fourier transform of (f) showing $2\times 2$ vector peaks. The right panel displays the intensity of the $2\times 2$ vector peaks along Bragg spot direction, from which we determine anticlockwise chirality. (h) Confirmation of the chirality switch with a nonmagnetic tip at zero field. The lower layer shows kagome lattices with a unit cell step. The middle layer shows $dI/dV$ maps taken at $E_F$ for the two terraces. The upper layer shows the $2\times 2$ vector peaks obtained by Fourier transforming the respective map data, from which we determine the opposite chirality for the two terraces.

Figure 3

(a) $dI/dV$ map taken at $E_F$ (upper layer) for unit cell kagome step edges (lower layer), showing the robust edge states. (b) $dI/dV$ maps taken for the same region at energies outside (upper and lower panels) and within (middle panels) the charge order energy gap. The kagome edge state appears only at the energies within the charge order energy gap. (c) $dI/dV$ spectra taken at the kagome lattice and step edge, respectively. The step edge data show the emergence of states within the charge order energy gap. (d) Spatial decay of the edge state. The decay can be fitted with an exponential function with a characteristic decay length of 2.1 nm. (e) Topographic image of a unit cell kagome step edge (left) and its corresponding $dI/dV$ map at Fermi energy taken at 104 K, showing the disappearance of edge state above the charge ordering temperature that is around 100 K.