Distance-Dependent Evolution of Electronic States in Kagome-Honeycomb Lateral Heterostructures in FeSn

In this work, we demonstrate the formation and electronic influence of lateral heterointerfaces in FeSn containing Kagome and honeycomb layers. Lateral heterostructures offer spatially resolved property control, enabling the integration of dissimilar materials and promoting phenomena not typically observed in vertical heterostructures. Using the molecular beam epitaxy technique, we achieve a controllable synthesis of lateral heterostructures in the Kagome metal FeSn. With scanning tunneling microscopy/spectroscopy in conjunction with first-principles calculations, we provide a comprehensive understanding of the bonding motif connecting the Fe3Sn-terminated Kagome and Sn2-terminated honeycomb surfaces. More importantly, we reveal a distance-dependent evolution of the electronic states in the vicinity of the heterointerfaces. This evolution is significantly influenced by the orbital character of the flat bands. Our findings suggest an approach to modulate the electronic properties of the Kagome lattice, which should be beneficial for the development of future quantum devices.

An in-depth understanding of exotic quantum phases in condensed matter systems is highly imperative for the development and designs of future quantum devices relying on strong electronic correlations.Among various condensed matter systems, Kagome lattices have been quickly emerging as one of the most important platforms for studying correlated and topological electronic states. 1 In the Kagome lattice, atoms are arranged into a two-dimensional network comprising hexagons interspersed with triangles. 24] Till date, the Kagome lattice has been realized in a wide range of materials, including layered materials, [4][5][6][7][8][9][10] non-van der Waals materials, 3,11 and organometallic frameworks, [12][13][14][15][16][17][18] which are expected to lead to the realization of correlated topological phases, 10,[19][20] , excitonic Bose-Einstein condensation, [21][22] spin liquid, [23][24] unconventional charge density waves, 5, 25-28 magnetically intertwined superconductivity, 1,[29][30] and spintronic devices. 31ong the various types of Kagome lattice materials, the Kagome metal FeSn has attracted tremendous attention.3][34][35] Recent studies have revealed the presence of Dirac fermions and flat bands in bulk FeSn crystals using angleresolved photoemission spectroscopy and de Haas-van Alphen quantum oscillations. 35eoretical studies have uncovered intricate details on the behavior of flat bands in Kagome metals. 36In particular, it has been shown that topological flat bands arise predominantly from the dz2 orbital, which is consistent with the symmetries of the Kagome lattice, including its three-fold rotational symmetry.Strong crystal field splitting is essential to clearly distinguish these bands; in its absence, inter-orbital interactions can disrupt the stability of the flat band formation.Such findings contradict the widespread belief in the ubiquity of ideal flat bands in Kagome metals, since multiple d-orbitals with incompatible symmetries and/or insufficient crystal field splitting could prevent their manifestation. 36Nevertheless, the potential for strong electron correlation effects remains due to the high localization of the d-bands.Complementary to the bulk studies, epitaxial FeSn films grown on a substrate, SrTiO3 (STO) (111), were shown to exhibit surface flat bands that can potentially be integrated into heterostructures for various device applications. 37Previous investigations have primarily focused on vertical heterointerfaces along the stacking direction.A critical gap remains in the control of the lateral heterointerfaces formed between the Fe3Sn Kagome and Sn2 honeycomb layers and the thorough understanding of their influences on the electronic structures of the Kagome lattice.
The study of the lateral heterointerfaces has proven challenging due to the absence of exposed Fe3Sn-and Sn2-terminated surfaces on the same plane in FeSn single crystals, which has limited the current understanding.
In this study, we report the formation and profound electronic implications of lateral heterostructures of Fe3Sn/Sn2 in FeSn thin films.The films are grown epitaxially on STO (111) using molecular beam epitaxy and investigated via the combination of scanning tunneling microscopy/spectroscopy (STM/STS) and density functional theory (DFT) calculations which provide a comprehensive approach to understanding.The epitaxial growth of FeSn films on STO allows a thorough examination of the lateral Fe3Sn/Sn2 heterointerfaces, which is not possible in bulk FeSn single crystals.Our STS results reveal three distinct density of states peaks on the Fe3Sn-terminated surface.Those located at about -0.2 eV and 0.1 eV can be assigned to the surface flat bands of the Kagome lattice with 3d orbital character, as confirmed by the DFT calculations, whereas the peak at -0.05 eV may originate from the parabolic band by gaping out of a dispersive band of FeSn.In addition, we determine the bonding motif between the Fe3Sn-and Sn2-terminated surfaces at the lateral heterointerfaces.More notably, we discover an unusual long-range effect of the lateral heterointerface, where the surface flat bands are suppressed near the interface but recovered at a distance that depends on the orbital character of the state, as confirmed by STS line spectroscopy and DFT calculations.Our findings elucidate the impact of lateral heterointerfaces on the electronic behavior of the Kagome lattice, potentially providing a tool for engineering the electronic properties of FeSn to facilitate the development of future electronic and spintronic devices.

Results and discussions
It was previously reported that the Kagome metal FeSn is a bulk antiferromagnet with Neel temperature TN of 370 K 38 .FeSn consists of an alternating stack of two-dimensional Fe3Sn Kagome layers and Sn2 honeycomb layers, as illustrated in Figure 1a, along the c-axis.0] By tuning the growth parameters in the molecular beam epitaxy process, we are able to grow epitaxial films of FeSn on STO (111) with island sizes ranging from 20 nm to 70 nm.The growth of FeSn on STO (111) follows the Volmer-Weber mode, which is characterized by the formation of isolated three-dimensional flat-top islands, as shown in Figure 1b (see Figure S1 and S2 in SI for details).This result is in agreement with a recent study of the growth of FeSn films on STO (111) using the MBE technique. 41It should be noted that the distance between the two adjacent Kagome layers in the FeSn single crystal is measured to be ~ 4.4 Å.However, as shown in the STM image and the corresponding line profile in Figure 1c-d, the distance between the Kagome topmost layer and the Sn2 underneath layer is about 2.9 Å, while that between the Sn2 layer and the second Kagome layer is approximately 1.5 Å. and b show atomic resolution STM images of the Kagome-and Sn2-terminated surfaces of the FeSn film grown on STO (111), respectively.The Sn2-terminated surface shows a honeycomb pattern with three bright and three dark protrusions (illustrated by the green spheres of different shades in the schematics superimposed in Figure 2d), representing a buckled honeycomb lattice of Sn.In contrast, the Fe3Sn Kagome-terminated surface exhibits hexagonally close-packed bright protrusions, 32 where the Kagome unit can be viewed as a Starof-David pattern with a Sn atom located at the center, 32,43 as illustrated in Figure 2c.To examine the electronic structures of the Kagome-and Sn2-terminated surfaces, we perform the differential conductance spectra shown in Figures 2e and f, respectively.Three pronounced peaks are observed in the dI/dV spectrum of the Fe3Sn Kagome surface: the two broad peaks are located at about -0.2 eV and 0.1 eV, while the narrow peak is located at ~ -0.05 eV.In contrast, no distinct features are found in the dI/dV spectrum of the Sn2 layer.In addition, our dI/dV maps taken simultaneously with the STM images show the characteristic Kagome pattern on the Fe3Sn layers in the bias range from -0.05 eV to -0.2 eV (Figure S3 in SI).

Figures 2a
To gain a better understanding of the origin of the peaks in the dI/dV spectrum of the Kagome surface, we perform DFT calculations on a 6-layer FeSn slab terminated by the Kagome layer, as shown in Figure 2g.The analysis of the orbital characters of the DOS and the band structures (see Figure 2h) allow us to identify the characteristics of the high intensity peaks in the experimental dI/dV spectrum: the surface flat band of the Kagome lattice results in a broad peak near -0.2 eV, due to the contributions from both dz2 and (dxz + dyz) orbitals of Fe atoms.
The peak at 0.1 eV is attributed to the (dxz + dyz) orbital character, which contributes to the surface flat band of the Kagome lattice along the M-K line.[45] The bulk flat band is located at around 0.6 eV with the major contribution from the dxz/dyz and dxy/dx2-y2 orbitals.Further details on the orbital characters of the electronic states of the Fe3Sn Kagome layer can be found in Figure S4, SI.The observation that bands having significant dz2 contributions are wide flat band within the Brillouin zone, contrasting with those from other d orbitals which form narrower flat bands, aligns closely with the latest theoretical findings. 36These findings emphasize the significance of d-orbital symmetry (from orbital rotation) and crystal field splitting in the formation of flat bands in Kagome lattices.As for the peak located at -0.05 eV, it could result from a gap out by the hybridization between the nonorthogonal dxz/dyz orbital of the Kagome surface and the bulk state (see Figure S5 and the associated discussion in SI). Interestingly, we observe lateral heterointerfaces formed between the Fe3Sn Kagome and Sn2terminated surfaces (Figure 3a). Figure 3b shows a high-resolution STM image taken at the lateral heterointerface.The Kagome and honeycomb layers are identified on the lower left and upper right corners, respectively, using the characteristics of the two surfaces discussed in  We further perform DFT calculations to gain insights into the chemical configuration of the bonding at the Kagome-honeycomb interface.Figure 3c shows the calculated molecular model of the boundary, which is energetically more favorable than the various other bonding possibilities, as illustrated in Figure S7, SI.Apparently, it fits very well with the pentagonheptagon configuration determined from the STM images, which is responsible for the formation of the Kagome-honeycomb interface found in this work.From high-resolution STM images, we occasionally observe another type of bonding motif at the interface as depicted in  To be quantitative on the distance-dependence of the peak evolution from the heterointerface boundary, we plot the areas of the three distinct peaks, as shown in Figure 4d-f, respectively, for the entire 28 STS line spectra and obtain the fitting curves.Detailed information of the analysis, as well as the fitting parameters, can be found in Figures S10 and S11 in SI.Our results unambiguously reveal long-range heterointerface effects on the electronic structures of the Fe3Sn lattice.The overall trends of the distance-dependent evolution are similar between the electronic states at ~ -0.05 eV and 0.1 eV, but different to that at ~ -0.2 eV, as evidenced by the different functions used in the fittings.The "coupling" length to the heterointerface is ~ 1.3 nm for the peak at -0.2 eV, while for the peaks located at -0.05 eV and 0.1 eV, this length is about 2.8 nm and 2.2 nm, respectively.Note that STM images display the convolution of geometric and electronic structures.The suppression of the electronic states near the lateral heterointerface could lead to perturbations to the morphology, e.g., the dark regions next to the boundary on the Kagome layer (Figures 3b and 4b).
To elucidate the long-range effects of the lateral heterointerface, we perform DFT calculations.
Our model system, consisting of a lateral heterointerface connecting Fe3Sn and Sn2 terminated surfaces (Figure 3c), is 6 layers thick (Figure 4g).Only a peak at ~ -0.2 eV is visible close to the lateral heterointerface, and its intensity increases as further away from the boundary.
Conversely, the peak at 0.1 eV, another surface flat band feature as discussed earlier, is not visible near the boundary, appearing slightly away.This result agrees well with the distance dependence of the peak evolution observed in the experiments, which can be attributed to the orbital character of the electronic states.The peak at 0.1 eV contains the major contributions from the (dxz + dyz) orbitals.As these states with the xy-plane component interact with the p orbitals of the Sn2-terminated surface at the same energy, its intensity near the lateral heterointerface disappears.In contrast, the peak at -0.2 eV is contributed by the dz2 and (dxz + dyz) orbitals together.The number of the p orbital states on the Sn2-terminated surface at the same energy level is very small compared to the number of the states at 0.1 eV, therefore the interaction with the dz2 and (dxz + dyz) of Fe3Sn is rather weak, resulting in only a reduction instead of complete suppression of the peak at -0.2 eV near the lateral heterointerface.This observation clearly illustrates the orbital selectivity of the flat band in the lateral heterostructures.Lastly, the peak at -0.05 eV observed in the experiment is absent in the DFT results.As shown in Figure 4d-f, the three Fe3Sn states have different "coupling" lengths with the heterointerface.This length is longest at ~ 3 nm for the peak at -0.05 eV.Unfortunately, the lateral distance between the bulk and the heterointerface is less than 3 nm in our atomic model due to the limitation of the number of atoms in the DFT.Therefore, the peak at -0.05 eV, with the most extended interaction length with the heterointerface observed in the experiment, is not captured in DFT.
In addition, we have also identified Fe3Sn-Fe3Sn and Sn2-Sn2 homo-interfaces formed between two different Fe3Sn or Sn2 domains.Detailed information can be found in Figures S13 and S14 in SI.These boundaries have no pronounced influence on the electronic structures of the adjacent domains, different from the heterointerfaces.We attribute it to the formation of a 'defect'-like boundary with phase slips at the homo-interface as compared to the strong covalent bonding that leads to the influence of the Sn2 electronic states on that of Fe3Sn at the 'sharp' heterointerface.

Experimental method
The substrate preparation and sample growth were performed in a standard molecular beam epitaxy (MBE) chamber with a base pressure of 6×10 -10 mbar.After treatment, samples were directly transferred in-situ into an Omicron low temperature scanning tunneling microscope (STM) operated at the liquid nitrogen temperature (~77.5K) with based pressure of 1.8×10 -11 mbar for characterization.Before deposition, the Nb-doped (0.5% by weight) SrTiO3(111) was cleaned using acetone and isopropyl alcohol, then immediately transferred to the MBE chamber.The substrate was slowly heated up and kept at 400 o C for 60 mins to ensure a complete degassing.The substrate was then annealed at approximately 1150 o C using direct current heating for 60 mins and then gradually cooled down to obtain a proper smooth and clean surface for the growth.FeSn was deposited onto the substrate in the MBE chamber by co-deposition of pure Sn and Fe using two different electron beam evaporators with flux current of 200 nA and 0.4 nA, respectively.The substrate was maintained at around 530 o C during the growth using resistive heating facilities.The temperature of the substrate was monitored by a thermocouple mounted at the heating stage in the MBE chamber.STS spectra were obtained using a lock-in amplifier with the modulation signal set at 26 meV in amplitude and 1.1 kHz in frequency.The STM tip was calibrated by measuring reference spectra on the silver substrate to avoid tip artifacts.

Theoretical approaches
We performed ab initio calculations based on density functional theory (DFT) [48][49] as implemented in the Vienna Ab Initio Simulation Package (VASP) [50][51] with projector augmented wave potentials [52][53] and spin polarization.The Perdew-Burke-Ernzerhof (PBE) form 54 was employed for the exchange-correlation functional with the generalized gradient approximation (GGA).The energy cutoff was set to 500 eV for all calculations.The Brillouin zone was sampled with a 25×25×1 G-centered k-grid.Atomic relaxations were performed until the Helmann-Feynman force acting on each atom became smaller than 0.01 eV/Å.FeSn adopts the P6/mmm space group, with the unit cell containing two Kagome layers composed of Fe atoms.These layers are enclosed by the Sn layer along the out-of-plane direction.The lattice parameters of bulk FeSn are found to be a = b = 5.285 Å and c = 4.444 Å.These values are in agreement with experimental measurements of a = b = 5.298 Å and c = 4.448 Å. 55

Figure 1 .
Figure 1.(a) In-plane schematics of the Fe3Sn Kagome-and Sn2 honeycomb-terminated surfaces in FeSn.(b) Overview STM image (Vs = 4 V, It = 5 pA) showing the morphology of top-flat islands of FeSn epitaxially grown on STO (111) that follows the Volmer-Weber growth mode.(c) Close-up STM image (Vs = 3 V, It = 5 pA) illustrating the stacking of different layers in an isolated FeSn island.(d) Height profile taken along the blue line in (c), highlighting the unequal distances between the layers.The cartoon in (d) illustrates the alternating stacking of Fe3Sn Kagome and Sn2 layers along the c-axis of the FeSn island.

Figure 2 .
Figure 2. (a) A close-up STM image (Vs = -0.05V, It = 600 pA) showing hexagonally close-packed bright protrusions of the Fe3Sn-terminated Kagome surface.(b) A close-up STM image (Vs = -0.05V, It = 500 pA) showing the buckled honeycomb pattern of the Sn2-terminated surface.(c-d) Zoomed-in STM images (Vs = -0.05V, It = 600 pA; Vs = -0.05V, It = 500 pA) with the schematics overlaid to highlight the Star-of-David pattern of the Kagome surface and the buckled honeycomb pattern with three bright and three dark protrusions of the Sn2terminated surface, respectively.Blue dots represent Fe atom, and green dots for Sn.(e) and (f) dI/dV spectra (setpoint: Vs = 0.3 V, It = 260 pA) taken on the Kagome and Sn2 layers, respectively.Three pronounced peaks are observed on the Kagome layer, as marked by the arrows in (e), while no significant peak is observed on the Sn2 layer.(g) Top and side views of the model structure of a 6-layer (6-Fe3Sn and 6-Sn2) slab, and (h) Orbital projected band structure and density of states (DOS) calculated by DFT.The highlighted gray regions represent the energies at which the peaks occur, corresponding to the arrows in (e).

Figure 2a- d .
Figure 2a-d.These two layers are on the same surface plane, as confirmed by the height profile analysis (Figure S6, SI), which could arise from the formation of stacking faults in the epitaxial film.The arrangement of individual Fe and Sn atoms at the interface is illustrated on the STM image.The honeycomb surface displays a zigzag edge, while the Kagome surface features a straight edge.The two different lattices are covalently linked by Fe-Sn bonds in the pentagonheptagon pairs (5-7 rings) that consist of Fe and Sn atoms, which is considered the motif driving the formation of the heterointerface.

Figure 3 .
Figure 3. (a) STM image (Vs = 3 V, It = 5 pA) illustrating the in-plane boundary formed between the Fe3Sn Kagome and Sn2 honeycomb layers, as marked by the dashed blue line.(b) High-resolution STM image (Vs = 3 V, It = 5 pA) showing the atomic arrangement at the heterointerface boundary.The molecular models are overlaid on the STM image to illustrate how the Kagome and honeycomb layers are covalently linked together at the interface.(c) DFT model with the most energetically favorable bonding motif at the interface, which is consistent with that determined from the STM image in (b).

Figure S8 ,
Figure S8, SI.The presence of this configuration may be related to some intermediate states during the formation of the interface.

Figure 4 .
Figure 4. (a) Overview STM image (Vs = 3 V, It = 5 pA) illustrating the heterointerface boundary where the line STS spectra are taken.(b) Zoomed-in STM image (Vs = -0.05V, It = 600 pA) into the Kagome surface area next to the heterointerface boundary.(c) The line STS spectra (setpoint: Vs = 0.4 V, It = 340 pA) are taken along the white trace from the heterointerface into the Kagome surface area shown in (b).(d), (e), and (f) Areas of the peaks located at ~ -0.2 eV, -0.05 eV, and 0.1 eV vs. distance from the heterointerface boundary extracted from the STS line spectra.Solid orange curves are the fittings.(g) Partial orbital projected density of states (PDOS) for In this work, we investigate the effects of the Kagome-honeycomb lateral heterointerface on the flat bands and electronic structures of the Fe3Sn Kagome layer via the combination of STM/STS experiments and DFT calculations.Lateral heterointerfaces are established in the FeSn thin films epitaxially grown on the STO (111) substrate by MBE.Our STS data show the distinct peaks on the Kagome surface, whose origin and orbital characters are thoroughly explained by the DFT calculations.We further demonstrate that the Kagome-honeycomb lateral heterointerface has profound and long-range impacts on the electronic structures of the Kagome layer.Particularly, the two surface flat bands of the Kagome layer with the different orbital characters respond differently to the Kagome-honeycomb interface.This study and the orbital selectivity mechanism give rise to the potential for engineering the electronic properties of Kagome metal FeSn to facilitate the development of future quantum devices.