Discovery and construction of surface kagome electronic states induced by p-d electronic hybridization in Co3Sn2S2

Kagome-lattice materials possess attractive properties for quantum computing applications, but their synthesis remains challenging. Herein, based on the compelling identification of the two cleavable surfaces of Co3Sn2S2, we show surface kagome electronic states (SKESs) on a Sn-terminated triangular Co3Sn2S2 surface. Such SKESs are imprinted by vertical p-d electronic hybridization between the surface Sn (subsurface S) atoms and the buried Co kagome-lattice network in the Co3Sn layer under the surface. Owing to the subsequent lateral hybridization of the Sn and S atoms in a corner-sharing manner, the kagome symmetry and topological electronic properties of the Co3Sn layer is proximate to the Sn surface. The SKESs and both hybridizations were verified via qPlus non-contact atomic force microscopy (nc-AFM) and density functional theory calculations. The construction of SKESs with tunable properties can be achieved by the atomic substitution of surface Sn (subsurface S) with other group III-V elements (Se or Te), which was demonstrated theoretically. This work exhibits the powerful capacity of nc-AFM in characterizing localized topological states and reveals the strategy for synthesis of large-area transition-metal-based kagome-lattice materials using conventional surface deposition techniques.

Abstract: Kagome-lattice materials possess attractive properties for quantum computing applications, but their synthesis remains challenging.Herein, we show surface kagome electronic states (SKESs) on a Sn-terminated triangular Co3Sn2S2 surface, which are imprinted by vertical pd electronic hybridization between the surface Sn (subsurface S) atoms and the buried Co kagome lattice network in the Co3Sn layer under the surface.Owing to the subsequent lateral hybridization of the Sn and S atoms in a corner-sharing manner, the kagome symmetry and topological electronic properties of the Co3Sn layer is proximate to the Sn surface.The SKESs and both hybridizations were verified via qPlus non-contact atomic force microscopy (nc-AFM) and density functional theory calculations.The construction of SKESs with tunable properties can be achieved by the atomic substitution of surface Sn (subsurface S) with other group III-V elements (Se or Te), which was demonstrated theoretically.This work exhibits the powerful capacity of nc-AFM in characterizing localized topological states and reveals the strategy for synthesis of large-area transition-metal-based kagome lattice materials using conventional surface deposition techniques.
Transition metal (TM)-based kagome materials provide an attractive platform for investigating correlated topological properties [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and developing kagome lattice applications 16 .However, the number of already synthesized kagome materials is limited, thus the construction of tailored kagome electronic bandstructures remains challenging 12 .Kagome physics is generally twodimensional (2D) but kagome electronic states (KESs) are usually induced by kagome planes embedded in the bulk material.These planes of most known TM-based kagome materials are buried under cleavable surfaces of these crystals 14,17 because the kagome planes usually exhibit higher surface energies than their vicinal planes do 10 , which is a roadblock for direct observation and manipulation of KESs in these materials.This issue, however, can be addressed if we are able to build KESs on a surface of a relatively low surface energy (termed surface kagome electronic states, SKESs).Building the SKESs enables directly real-space observation and manipulation of rich kagome physics in the atomic limit by surface characterization techniques, such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM).As a consequence, feasible tunability of the SKESs could also be achieved by tip manipulation or molecular beam epitaxy.
Introduction of a capping layer composed of nonmetal atoms over a kagome plane often lowers the surface energy of the kagome plane 10 .A SKES is thus built if the capping layer could inherit the underlying kagome symmetry electronically.This strategy is, however, unsuitable for chargetransfer (CT) insulators, e.g.copper oxides, in which the TM d bands and p bands of surface adatoms are separated and independent (Fig. 1a) 18,19 .Fortunately, most TM-based kagome materials are CT metals, where the p bands of non-metal atoms overlap and hybridize with the TM d bands near the Fermi level (Fig. 1b) 9,12,14 .This type of hybridization can potentially electronically imprint the kagome symmetry of a less stable kagome plane onto a more stable but hexagonal or triangular surface plane, as schematically shown in Fig. 1c.Co3Sn2S2, a kagome magnetic Weyl semimetal, is a good candidate to verify whether SKESs could be induced on a non-kagome-latticed surface of a kagome materials.Two major types of its surfaces (Type-I and Type-II) show triangular lattices in scanning tunneling microscopy (STM) images 10,17,[20][21][22][23] but exhibit kagome-related electronic properties 17,23 .The triangular lattices observed in STM images and a comparison of theoretical surface energies indicate that these two surfaces are, most likely, not Co3Sn-terminated ones, but are covered by S or/and Sn atoms.In line with the strategy proposed in Fig. 1c, we infer that surface Sn and subsurface S atoms, which forms a corrugated honeycomb lattice on the Sn-terminated surface, could electronically imprint the kagome symmetry of the Co3Sn layer forming a SKES (the left part in Fig. 1c).On the Sterminated surface, surface S atoms might have chance to inherit the triangular symmetry of the Co3 trimer underneath (the right part in Fig. 1c).This state could be regarded as an incomplete SKES, in which negligible electron hopping exists in one of the two kagome triangles, as termed incomplete-SKES (i-SKES).
Herein, we experimentally and theoretically verified our inference for building SKESs on Co3Sn2S2 surfaces and theoretically tested to tune the SKES by substitute transition metal atoms for surface Sn and S atoms.SKESs (i-SKESs) were observed in non-contact atomic force microscopy (nc-AFM) images on the Type-II (-I) surface.Force spectra and associated density functional theory (DFT) calculations were used to confirm the assignment of type-II (-I) surface to the Sn-(S-) terminated surface.The nc-AFM images were interpreted with the help of DFT calculations, which reveal that the strong p-d hybridization of the p orbitals of surface Sn or subsurface S with the d orbitals of the Co3 kagome network underneath occurs near the Fermi level.
The hybridization leads to an SKES (i-SKES) imprinted on the Sn-terminated Type-II (Sterminated Type-I) surface.We also theoretically generalized this SKES construction strategy by substituting the surface Sn (S) atoms with group III-A, IV-A, or V-A element (Se or Te) atoms.

SKES on Type-II surface of Co3Sn2S2
The bulk crystal of Co3Sn2S2 belongs to space group 3 ̅ , comprising a triangular lattice with constants a = 5.37 Å and c = 13.15Å 11 .As shown in Fig. 2a and Extended Data Fig. 1, Co3Sn2S2 has a layered structure composed of a kagome Co3Sn plane (red atoms) sandwiched between two triangular S planes (yellow atoms), which are then further encapsulated by two separate triangular Sn planes (blue atoms).Unlike STM images, which provide information on delocalized states, qPlus nc-AFM images could reveal the spatial gradients of short-range repulsive interactions resulting from localized electronic states at the single-chemical-bond level [24][25][26][27][28][29][30][31][32][33] .Consequently, it can trace electronic orbitals and/or interactions with unprecedented resolution 24,34 .Therefore, we performed nc-AFM imaging and short-range force spectroscopy on cleaved Co3Sn2S2 surfaces.
The AFM was equipped with a qPlus sensor, and a CO-functionalized tip was used for imaging (Fig. 2b).
There are two commonly obtained cleaved Co3Sn2S2 surfaces: one consisting of a few vacancies (Type-I) and the other containing many adatoms (Type-II).By local contact potential difference (LCPD) measurement, the Type-I surface, with a much higher work function, is demonstrated most likely to be the S surface 23 .However, the Co3Sn and Sn surfaces have comparable surface work functions and cannot be convincingly distinguished by LCPD, thus leaving the Type-II surface identification a remaining issue.Figure 2c shows an STM image of the S (Type-I) surface, which features a triangular lattice with a few S vacancies.In the nc-AFM image (Fig. 2d), the surface S atoms appeared as bright spots with slightly anisotropy (region αI), maintaining their triangular pattern.A further zoomed-in image shown in Fig. 2e shows three linelike features, equivalently distributed in terms of the rotational angle, extending from each S atom.
These "lines" converge to rather blurry regions (the βI region) in the image, while the remaining dark region is denoted as γI, implying the formation of i-SKES.The Type-II surface, which displays a triangular lattice network decorated with a few adatoms in the STM image (Fig. 2f), shows bright dots assembling in the same triangular lattice in the nc-AFM images acquired at relatively large tip-sample distances (Extended Data Fig. 2a).In a zoomed-in nc-AFM image, we found the dots are circular in shape (region αII marked in Extended Data Fig. 2b), which outline a blurry triangular (βII), and an indistinctly hexagonal region (γII).As the tip approaches the sample surface (Extended Data Fig. 2c and Extended Data Fig. 2d), the circular shape of the dots evolves into explicitly triangular shape in the αII region and the blurry triangles become sharper in region βII.They eventually connect to form a 2D pattern showing a breathing kagome pattern (Fig. 2g).In a zoomed-in image (Fig. 2h), the αII region appear as bright triangles with each side 2.77 Å in length, while the βII region appear bigger but as slightly blurry triangles with each side 3.02 Å in length, which is 9% longer than that of the αII region.The kagome-latticed Type-II surface appears to resemble the structure of the Co3Sn layer, which is, however, less stable compared to the Sn layer under exposure to the surface 10 .If the kagomeappeared pattern was, as we inferred in Fig. 1c, imprinted electronically from the Co3Sn layer, the Type-II surface would be the energetically preferred Sn-terminated surface.Force spectra measurements and DFT calculations were thus called to solve this surface identification issue.

Identification of Type-II surface
We first measured vertical short-range force spectra on the less controversy S (Type-I) surface to verify the reliability of our experiment and theory comparison.As shown in Fig. 3a, the force spectra at the αI, βI, and γI regions all hit the attractive-repulsive tuning point below 3Å, with the respective height of the turning point at the αI (γI) regions 0.9 Å higher (0.6 Å lower) than that at the βI region.In Fig. 3b, we tentatively assessed those three regions to the top-layer S (black dashed circle), the Co3 trimer (red dashed triangle) and the Sn atom (blue dashed triangle) in the Co3Sn layer, respectively.Given that, our DFT calculations well reproduced those experimental force curves in Fig. 3c, which were plotted using the same color code and exhibit comparable respective heights of the turning positions, i.e., 0.9 Å versus 1.0 Å (0.6 Å versus 0.6 Å) for the αI (γI) region, compellingly supporting those tentative assignments.More importantly, these experiment-theory coincidences, in turn, confirm the assessment of the Type-I surface to the S surface and validate our force-spectra-comparison method of identifying surface terminations of Co3Sn2S2.pm and 50 pm for that shown in (d).Both experimental vertical short-range force curves were deconvoluted from associated frequency-shift curves using the Sader-Jarvis method 35 .
Figure 3d plots the experimental force spectra on the Type-II surface, in the same color and spatial schemes used on the Type-I surface.As the tip approaching the surface, the αII region (black) appears the least attractive among all the three regions and first reaches the turning point at 1.92 Å, while that value is 1.60 Å and 1.31 Å for regions βII, and γII, respectively, in which region γII shows a larger attractive force.We modeled the acquiring process of those force curves on both the Co3Sn and Sn surfaces using DFT calculations.The surface Sn atoms show appreciable surface relaxations on the Co3Sn surface and are 0.42 Å lifted from the Co3Sn plane (the cross section in Extended Data Fig. 3a).Consequently, the force spectrum on the Sn atom (blue curve in Extended Data Fig. 3b) first reaches its minimum and shows strong repulsion at shorter distances.The two triangular regions, i.e., the surface Co3 trimer sit on a Sn atom and a S atom underneath (Co3/Sn and Co3/S) are less repulsive in comparison with the surface Sn (hexagonal) region, apparently inconsistent with the experimental spectra on the Type-II surface where the two triangular regions exhibit stronger repulsion.This contradiction does not support the assessment of the Co3Sn surface to the Type-II surface.
The Sn surface contains triangularly distributed Sn atoms (blue balls in Fig. 3e) in the topmost layer while the same lattice of S atoms (yellow balls), with a lateral shift of (1/3, 1/3) unit cell, is placed in a layer just 0.56 Å below.Each Sn or S atom sits over a Co3 trimer, which could be regarded as a region of triangular symmetry, while the Sn atom in the Co3Sn layer appears a hexagonal symmetry.Thus, we could tentatively assign the Sn and S triangles to triangular regions αII (black) and βII (red), respectively, and the Sn@Co3Sn hexagon to hexagonal region γII (blue).
Associated theoretical force spectra (Fig. 3f) show consistent results with the experimental ones in terms of the order of repulsion among those three regions.This verifies our assignment that region αII (βII and γII) represents the Sn (S and Sn@Co3Sn) site, as denoted by the superimposed atomic structure in Fig. 2h.Thereby, based on site-dependent force spectra measurements and corresponding DFT calculations, we identified that Type-II surface, which hosts SKES, is the Sn surface of Co3Sn2S2.

p-d hybridization between surface atoms and the kagome plane
To elucidate the origin of the kagome-shaped feature on the Sn surface revealed in the nc-AFM images in Figs.2g and 2h, the projected local density of states (PLDOS) for the Sn-terminated Co3Sn2S2 surface is plotted in Fig. 4a.It shows a group of electronic states around the Fermi level (EF), which is nearly isolated from other states and ranges from -0.38 to 0.50 eV, as highlighted by the parallel black dashed lines.These states do not consist of the s-orbital component of the surface Sn or S atoms (see Extended Data Fig. 5 for details).We replotted PLDOSs of the p orbitals of surface Sn and subsurface S atoms and the d orbitals of the Co3 trimers underneath between -0.38 and 0.50 eV in Fig. 4b, which indicate strong electronic hybridization between the surface Sn (S) p orbitals, denoted in blue (green), and the d states of the underlying Co3 trimers (in orange).
The positions of the four pronounced hybridization peaks are highlighted using four dashed lines.
The p-d hybridized states effectively impose the triangular-shaped electron density of the triangular Co3 trimers on those of the surface Sn and S atoms.Figure 4c depicts the square of the wavefunction norms (|ψ| 2 ) of the occupied hybridized states, showing a triangular-shaped contour at each Sn or S site.Six of these triangles surround a hexagonal area around the Sn@Co3Sn site, where the contour density is the lowest, forming a kagome lattice network on the surface.The plot of the |ψ| 2 contour also reveals the lateral interconnections of the triangularly shaped density contours, indicating their lateral electronic hybridization in real space.The PLDOS confirms this lateral hybridization between Sn and S, which forms electronic states at -0.25 and 0.37 eV (red dashed lines in Fig. 4b).Therefore, through vertical p-d hybridization and subsequent lateral p-p hybridization, the kagome symmetry of the Co3Sn plane underneath was electronically imprinted on the Sn-terminated surface, and an SKES was successfully demonstrated.
The hybridization of Sn and S with the Co kagome lattice network also transferred the nontrivial properties of the kagome electronic states onto the Sn surface.A scanning tunneling spectral (STS) measurement of the Sn surface (Extended Data Fig. 6a) exhibits a sharp peak at approximately -10 meV (Pk), as indicated by the red arrow.This sharp feature fits well with the two flat bands near EF of the Sn surface (Extended Data Fig. 6b), which are SKESs that are laterally hybridized between Sn-Co3 and S-Co3 states.The position of Pk shifts toward EF under an applied magnetic field perpendicular to the surface with both up-and down-field orientations (Extended Data Fig. 6c).Such an unconventional splitting trend indicates negative flat band magnetism, further confirming the topological origin of the lateral hybridization SKESs.
DFT calculation results for the S surface are displayed in Fig. 4d-4f for comparison with those of the Sn surface.The associated PLDOS spectra were plotted in Fig. 4d.It exhibits a group of isolated states between 0.12 and 1.16 eV, where only the p orbitals of S (both at surface and in bulk) and d orbitals of Co are involved.In this energy window, a zoomed-in PLDOS plot of the surface S and subsurface Co3Sn layers, also indicates vertical hybridization between the surface S p states and the underlayer Co d states, denoted by the dashed lines in Fig. 4e.These vertical p-d hybridizations impose triangular-shaped Co3 electronic states on the surface S atoms, as revealed by the |ψ| 2 contour in Fig. 4f.These hybridized states on S atoms could, as we illustrated in Fig. 1d and Fig. 2e, be regarded as an i-SKES because there are no electronic states on top of the other sublattice over the Co kagome network (marked by red solid line triangles in Fig. 4f).As a result, the flat bands observed around EF on the Sn surface were absent on the S surface, even in a wider energy window 10,23 .(a-c), for the S surface.Boundaries of the isolated p-d hybridized states is at 0.12 and 1.16 eV, as marked by the two black dashed lines in (d).(e) Zoomed-in PLDOS plotted from 0.12 to 1.16 eV.(f) Isosurface contour of |ψ| 2 integrated from 0.12 to 1.16 eV.The black solid lines mark the hybridized states on S atoms; while the red solid lines mark the missing sublattice of the i-SKES.

Strategy for constructing a family of SKESs
We have experimentally and theoretically demonstrated the feasibility of SKES construction.
The construction strategy requires that (i) the surface and subsurface (if any) atoms fit in a honeycomb lattice, (ii) their in-plane states vertically hybridize with both of the corner-sharing triangular-shaped sublattices of the kagome lattice underneath, and (iii) their hybridized states then subsequently hybridize laterally with each other to form an SKES, as illustrated in Fig. 5a.In Co3Sn2S2, the Sn terminated surface approximately meets all these requirements, in which the surface Sn atoms are located on one sublattice, and subsurface S atoms, only 0.56 Å below the surface, reside on the other sublattice.The S-terminated surface does not meet requirement (i), but the additional deposition of hetero-or homo-atoms onto the other sublattice (sublattice plane a, SLa, see Fig. 5b) fills the incomplete part of the i-SKES, enabling the construction of SKESs on the S surface with tunable properties.Furthermore, we could obtain more diverse types of SKESs by substituting the S atoms with Se or Te (sublattice plane b, SLb, see Fig. 5b) during bulk crystal growth.
DFT calculations were performed to examine the geometric and electronic structures of the surfaces with modified SLa and SLb planes.Diverse surface electronic hybridizations and SKESs were verified.Similar vertical p-d electronic hybridizations are preserved when SLa = Ge, Sn, or Pb and SLb = S or Se.A typical |ψ| 2 contour of the isolated states near EF for SLa = Sn and SLb = Se was shown in Fig. 5c, revealing kagome features that are comparable to those of the Snterminated Co3Sn2S2 surface.The PLDOS (Extended Data Fig. 7a) indicate that the hybridization states comprising Sn and Se p orbitals and d orbitals of Co are restricted within the energy range of -0.5 to 0.5 eV.They are isolated from other electronic states and can therefore be considered pure p-d hybridized SKES near EF.We also constructed a more typical breathing SKES by more significantly unbalancing the hybridized states distributed on the SLa and SLb sites, as achieved by substituting the SLa site with heavier elements, like Sb and Bi (Fig. 5d and Extended Data Fig. 7b).For SLa = Al, Ga, In, or Si or SLb = Te, their s orbitals, in addition to the p-d hybridization, are involved in vertical hybridization with Co around EF (Fig. 5e and Extended Data Fig. 7c).The involvement of the s orbital results in the |ψ| 2 contour of the hybridized states appearing spherical in shape, which significantly weakens the kagome feature on the surface.The energetically isolated hybridized states are mixed with other states for surfaces where SLa = P or As, in which the surface kagome feature is eliminated (Extended Data Fig. 7d).These results reveal that the S surface of Co3Sn2S2 can be used as a template for constructing various SKESs with tailored properties.

Conclusions
In summary, we have demonstrated a strategy for constructing energetically stable SKESs that involves electronically imprinting the kagome lattice symmetry of an undersurface layer through vertical p-d and lateral p-p electronic hybridizations.The strategy was verified using the Sn surface of Co3Sn2S2, which is a prototypical kagome magnetic Weyl semimetal.By combining chemicalbond-resolved nc-AFM images, vertical short-range force spectra, and DFT calculations, we explicitly found SKESs on the Sn surface of Co3Sn2S2.Our DFT calculations revealed that these states originate from the strong vertical electronic hybridization between triangularly arranged surface Sn or subsurface S atoms and the Co3 trimers of the Co3Sn kagome lattice underneath, accompanied by lateral hybridizations of the surface Sn and subsurface S states.STS measurements verified the appearance of kagome symmetry-featured topological properties on the Sn surface.To generalize this strategy, DFT calculations explored the surface electronic structure variations for atomic substitutions of surface Sn (subsurface S) with III-A, V-A, and IV-A (Se or Te) elements on the Sn surface.We also theoretically demonstrated the feasibility of constructing surface kagome structures by depositing group III-A or IV-A elements on the S surface.The demonstration of nc-AFM for investigating localized electronic surface states aside, our strategy for building SKES enriches the design routes to construct semi-metallic 2D kagome materials with topologically non-trivial properties.

Single crystal growth of Co3Sn2S2
A Sn/Pb mixed flux was used to grow single crystals of Co3Sn2S2.First, the starting materials were mixed at a molar ratio of Co:S:Sn:Pb = 12:8:35:45 (Co (99.95% Alfa), Sn (99.999%Alfa), S (99.999% Alfa), and Pb (99.999%Alfa)).The mixture was placed in an Al2O3 crucible sealed in a quartz tube that was slowly heated to 673 K for 6 h and then maintained for 6 h to avoid heavy loss of sulfur.Thereafter, the quartz tube was heated to 1323 K for 6 h and maintained for 6 h before slowly cooling to 973 K over 70 h.At 973 K, rapid decanting and subsequent spinning in a centrifuge were performed to remove flux.Finally, hexagonal-plate single crystals with diameters of 2-5 mm were obtained.Energy-dispersive X-ray spectroscopy and X-ray diffraction were used to determine the compositions and phase structures of the crystals.

QPlus nc-AFM measurements
Non-contact AFM measurements were performed on a combined nc-AFM/STM system (Createc) at 4.7 Kwith a base pressure lower than 2 × 10 -10 mbar.All measurements were performed using a commercial qPlus tuning fork sensor in the frequency modulation mode with a Pt/Ir tip at 4.5 K.The resonance frequency of the AFM tuning fork was 27.9 kHz, and the stiffness was approximately 1800 N/m.The Co3Sn2S2 samples were cleaved at <10 K in an ultrahigh vacuum chamber and transferred to the nc-AFM/STM head within 10 s. nc-AFM images and shortrange force spectra were recorded using CO-functionalized tips.The oscillation amplitudes used in all measurements are stated in the corresponding figure captions.

DFT calculations
DFT calculations were performed using the generalized gradient approximation for the exchange-correlation potential, the projector augmented wave method 36 and a plane-wave basis set as implemented in the Vienna ab-initio simulation package 37,38 .The energy cutoff for the plane-wave basis was set to 400 eV for structural relaxations and 500 eV for the energy and electronic structure calculations.Two k-meshes of 7×7×1 and 11×11×1 were adopted for the structural relaxations and total energy (electronic structure) calculations, respectively.The mesh density of the k points was fixed when performing the related calculations with primitive cells.In geometric structure relaxation, van der Waals (vdW) interactions were considered at the vdW-DF level with the optB86b functional as the exchange functional (optB86b-vdW) 39,40 .Symmetrical slab models were employed, and the surface atoms were fully relaxed until the residual force per atom was less than 0.005 eV• Å -1 .To avoid image interactions between adjacent unit cells, a vacuum layer of more than 20 Å thick was added to the slab cell perpendicular to the surface.The optimized lattice constants of bulk Co3Sn2S2 are 5. II regions, respectively.The surface Sn atom represents the αII region (green triangle) in the SPM images.Its higher vertical position and the largest localized electron density leads to the strongest repulsion in the frequency shift image, exhibit no dissipation in the damping image and significant tunneling current in the STM image.As for the embedded Sn (the γII region), it is highly metallic according to the cross-sectional ELF plot; this allows to dynamically form chemical binds between the embedded Sn and the O atom of the CO tip during scanning.As a result, significant damping signal (white hexagons in d) in a nearly hexagonal shape was recorded around the embedded Sn atoms while appreciable tunneling current was obtained in the associated STM image (white hexagons in e).The surface S atom (orange triangles, representing region βII) sits at a position in between those two types of Sn atoms in terms of the vertical position, strength of Pauli repulsion and electronic conductance, so that it yields moderate Pauli repulsion, showing blurry triangles in the frequency shift image and nearly insulating feature in the STM image.Such assessment of Sn (surface), S and Sn (embedded) sites to regions αII, βII, and γII is also consistent with the experimental measurement of force curves.

Fig. 1 |
Fig. 1 | Schematic of vertically hybridized electronic states in charge-transfer kagome metal Co3Sn2S2.Schematic of the energy bands near Fermi level in (a) charge-transfer insulator and (b) charge-transfer metal, showing the difference in their p-d orbital overlap on the cleaved surfaces.(c) Schematic of surface kagome electronic state (SKES, the left part) and incomplete surface kagome electronic state (i-SKES, the right part) formation through vertical p-d hybridization in a charge-transfer kagome metal.

Fig. 2 |
Fig. 2 | Surface kagome electronic structure of the Sn surface in Co3Sn2S2.(a) Side view of the atomic model of the vertically stacked Sn-S-Co3Sn-S-Sn layers in Co3Sn2S2.(c) STM image of the S surface of Co3Sn2S2.(b) Schematic of the nc-AFM measurements using a qPlus sensor with a CO-functionalized tip in the frequency modulation mode.(d) Chemical-bond-resolved nc-AFM image of the S surface taken in the blue square in (c).(e) Zoomed-in image from (d) to show the incomplete kagome lattice.Three distinct regions within a unit cell with bright, blurry, and dark contrast, which are marked by black solid line triangles, red solid line triangles, and blue dashed line hexagon, are labeled as αI, βI, and γI regions.The atomic structure of S surface with the underlying Co3Sn plane is superimposed.(f) STM image of the Sn surface of Co3Sn2S2.(g) Chemical-bond-resolved nc-AFM image of the Sn surface taken in the area marked by a blue square in (f).(h) Zoomed-in image from (g), showing the kagome lattice.Three distinct regions within a unit cell with bright, blurry, and dark contrast, which are marked by black solid line triangles, red solid line triangles, and blue dashed line hexagon, are labeled as αII, βII, and γII regions.The atomic structure superimposed is the Sn surface with the underlying S and Co3Sn plane.Scanning parameters: (c) and (f), Vs = -400 mV, It = 100 pA; (d) and (e), amplitude = 100 pm, scanning height = 180 pm lower from a tunneling junction of Vs = -4 mV, It = 10 pA; (g) and

Fig. 3 |
Fig. 3 | Identification of the Sn surface by short-range force spectra.(a) Experimental vertical short-range force spectra measured at the center of the αI (black), βI (red), and γI (blue) regions.(b) and (c) DFT optimized surface structure and vertical short-range force spectra on the S surface.(d) Experimental vertical short-range force spectra measured at the center of the αII (black), βII (red), and γII (blue) regions.(e) and (f) DFT optimized surface structure and vertical short-range force spectra on the Sn surface.Spectra displayed in (a) were obtained with an amplitude of 25 Fig. 4 | Vertical p-d hybridizations at the Sn and S surfaces in Co3Sn2S2.(a) PLDOS of the Sn surface.Two black dashed lines at -0.38 and 0.50 eV indicate the boundaries of a group of isolated p-d hybridized states.(b) PLDOS of the top three atomic layers of the Sn surface, from -0.38 to 0.50 eV.Blue and red dashed lines denote the vertically p-d hybridized states between the surface (subsurface) Sn (S) atoms and the Co3 trimers underneath, while the red dashed lines also indicate in-plane (laterally) p-p hybridized states between surface Sn and subsurface S atoms.(c) Isosurface contour of |ψ| 2 , integrated from -0.38 eV to the EF, on the Sn surface superposed with the atomic structure of the top three atomic layers of the surface in the right part.Red solid lines highlight the kagome lattice.(d-f) Duplicate PLDOS and |ψ| 2 isosurface contour plots, in the same schemes used in (a-c), for the S surface.Boundaries of the isolated p-d hybridized states is at 0.12

Fig. 5 |
Fig. 5 | Theoretical strategy for artificially constructing a family of surface kagome electronic states.(a) Schematic of the vertical p-d hybridization between the Co3 trimer and the surface atoms.Blue and yellow triangles indicate the hybridized triangular-shaped electronic state on the two sublattices of the kagome symmetry, respectively.(b) Schematic of the surface planes located on top of sublattice a (blue, SLa plane) and sublattice b (yellow, SLb plane) of the kagome plane (red).(c-e) Plots of |ψ| 2 isosurface contours of hybridized states.(c) Contour of a p-d hybridized SKES for SLa = Sn and SLb = Se.Deposition of Ge and Pb on the S surface also generate the same type of SKESs.(d) Contour of a p-d hybridized asymmetric SKES for SLa = Sb and SLb = S, where the S and Sb sites show substantially different intensities.Deposition of Bi on the S surface also generate the same type of SKESs.(e) Contour for SLa = Al and SLb = S, where 37 and 13.15 Å along the a and c directions, respectively.A tip-sample model was established for the force spectral calculations.In particular, the AFM tip was modeled using a five-layer thick Pt(111) cluster, the bottom of which adsorbs a CO molecule, and a (4 × 4) Co3Sn2S2 slab was employed to model the sample surface.Our tip model exhibited a significant p-wave feature, which contributes to the high resolution in images Extended Data Fig. 1 | Atomic structure of Co3Sn2S2.Extended Data Fig. 2 | nc-AFM images at different scanning heights on Type-II surface.(a) Constant-height nc-AFM image scanned at the tunneling height of V s = -4 mV, I t =10 pA.(b) Enlarged from the red square in (a) to show the α II , β II , and γ II regions within a supercell.(c) and (d) Constant-height nc-AFM images at different scanning heights on the Type-II surface.The x and y directions have drifted a little during the scanning time.The number below each image is the scanning height the lowered from a tunneling junction height of V s = -4 mV, I t =10 pA.Scanning amplitude = 50 pm.Extended Data Fig. 3 | DFT calculated vertical short-range force spectrum on optimized Co3Sn surface.(a) DFT optimized surface structures of the Co3Sn surface.(b) DFT calculated vertical short-range force spectra on the three typical regions marked by the blue hexagon, black and red triangles in (a), plotted with the same color code.Extended Data Fig. 4 | Localized electronic states of the surface Sn atoms through p-d hybridization on Sn surface.(a) and (b) Top and side view of electron localized function (ELF).Both the surface Sn and subsurface S sites are surrounded by significantly localized electron densities that are crucial for repulsive interactions in nc-AFM imaging.The density above the surface Sn atom is even more localized than that of the S atom, indicating the surface Sn atom behaving like an atom of a non-metallic element, which is in opposite to its usually metallic behavior as those bulk Sn atoms show.(c)-(e) Frequency-shift, damping, and current channels of an nc-AFM image.The green and orange triangles and the white hexagon represent the α

Extended Data Fig. 5 |
DFT calculated PLDOS of S orbitals in Sn terminated Co3Sn2S2.Between the energy range of 0.38-0.50eV, only the p orbitals participate in the hybridization, both for the surface and bulk S atoms.Extended Data Fig. 6 | Physical properties of the SKES on Sn surface of Co3Sn2S2.(a) STS on Sn surface.The red arrow marks the flat-band related electronic state residing at -10 mV.(Vs= -400 mV, It = 100 pA, Vmod = 0.5 mV).(b) DFT calculated electronic band structure with the SOC included where the flat-band is highlighted in red.(c) Energy shift of the flat-band peak position as a function of vertical magnetic field, showing the feature of negative orbital magnetism.Extended Data Fig. 7 | SKES constructed with different elements in SLa and SLb on Co3Sn2S2.(a) p-d hybridized surface structure by depositing Pb or Ge elements on S surface or substitute the subsurface S atoms with Se atoms on Sn surface.(b) Asymmetric p-d hybridized surface structure by depositing Sb or Bi elements on S surface.(c) s-d and p-d hybridized surface structure by depositing Al, Ga, In or Si elements on S surface, or substitute the subsurface S atoms with Te atoms on Sn surface.(d) Mixed hybridized surface structure by depositing As or P elements on S surface.