Tunable topological Dirac surface states and van Hove singularities in kagome metal GdV6Sn6.

Transition-metal-based kagome materials at van Hove filling are a rich frontier for the investigation of novel topological electronic states and correlated phenomena. To date, in the idealized two-dimensional kagome lattice, topologically Dirac surface states (TDSSs) have not been unambiguously observed, and the manipulation of TDSSs and van Hove singularities (VHSs) remains largely unexplored. Here, we reveal TDSSs originating from a ℤ2 bulk topology and identify multiple VHSs near the Fermi level (EF) in magnetic kagome material GdV6Sn6. Using in situ surface potassium deposition, we successfully realize manipulation of the TDSSs and VHSs. The Dirac point of the TDSSs can be tuned from above to below EF, which reverses the chirality of the spin texture at the Fermi surface. These results establish GdV6Sn6 as a fascinating platform for studying the nontrivial topology, magnetism, and correlation effects native to kagome lattices. They also suggest potential application of spintronic devices based on kagome materials.

INTRODUCTION

Realizing and tuning novel electronic states is of great interest and importance to modern condensed-matter physics and spintronics applications. The exploration of topological physics intertwined with nontrivial lattice geometries and strong electron interactions is emerging as a new frontier in condensed-matter physics (–). Transition-metal-based kagome lattices, owing to the unique lattice geometry, have attracted particular attention, as they often show correlated topological band structures, magnetism, and diverse exotic electronic instabilities, such as spin liquid states, charge density wave (CDW), and superconductivity (–). Recently, a substantial number of experimental efforts have investigated topological phenomena in transition-metal-based kagome magnets, such as Fe3Sn2 (), FeSn (), Co3Sn2S2 (, , ), and RMn6Sn6 (where R is a rare-earth element, and the kagome layers are made of manganese atoms) (, –). In particular, the topological surface states (TSSs) derived from relativistic Weyl points, namely, surface Fermi arcs, have been observed in the time-reversal symmetry-broken Weyl semimetal Co3Sn2S2 with ferromagnetism (, ). In addition, various forms of magnetism in the low-temperature electronic ground state enable the realization of quantum-limit Chern topological magnetism (). Besides these intensively studied magnetic kagome materials, the recently discovered nonmagnetic kagome metals AV3Sb5 (A = K, Rb, and Cs) were found to have a unique combination of novel correlated phenomena and nontrivial band topology (, , –). An intriguing chiral CDW instability (, ) and superconductivity (, , ) have been observed in the absence of magnetic orders, suggesting that the vanadium kagome lattice is an ideal platform for investigating correlated quantum states. Moreover, Dirac nodal lines and nodal loops have been identified in the nonmagnetic kagome metal CsV3Sb5 (). Apart from various types of topological band crossings (e.g., Dirac and Weyl fermions), ℤ2 topology in kagome materials has also been proposed by theoretical calculations (); however, identifying and confirming the corresponding topological nature of surface states have remained an outstanding challenge, because of the lack of good candidate systems. Therefore, no clear experimental evidence for the ℤ2 topological Dirac surface states (TDSSs) in kagome materials has been reported to date. For instance, the expected TSSs in CsV3Sb5 from density functional theory (DFT) calculations lie above the Fermi level (EF) and mostly overlap with the projection of bulk states (, ). Moreover, it has remained unclear how these kagome surface states could be manipulated, a key question relevant for potential applications.

GdV6Sn6 is a newly discovered kagome system that exhibits a magnetic transition at a low temperature Tm ~ 5 K (, ). In contrast to other members of the kagome magnet family, it is the Gd-triangular lattice that generates magnetism, while the kagome layer composed of V and Sn atoms is nonmagnetic (Fig. 1A). The separation of the magnetic layer and kagome layer not only permits a direct study of the electronic structure of nonmagnetic kagome layer but also introduces a magnetic tunability from the magnetic layer below Tm. Band structure calculations suggest that GdV6Sn6 is topologically nontrivial, characterized by a ℤ2 topological invariant in the paramagnetic state (). In contrast to other ℤ2 kagome metals, such as CsV3Sb5, GdV6Sn6 has a large bulk gap around Γ, allowing the TDSSs to be well separated from bulk states around the surface Brillouin zone (BZ) center ( point) (as illustrated in Fig. 1B). Therefore, GdV6Sn6 is a tantalizing system to access and tune TDSSs, which is crucial for exploring potential applications in spintronics. Moreover, multiple van Hove singularities (VHSs), originating from the vanadium d orbitals appear near the EF at the point (Fig. 1C), providing a promising playground in the search for exotic correlated states on the kagome lattice. While theory predicts the nontrivial band topology and the great potential for nesting effects around the points at van Hove filling in GdV6Sn6, the existence of the TDSSs—as well as the manipulation of the TDSSs and VHSs—in kagome metals has yet to be experimentally demonstrated.

Fig. 1.

Crystal structure, topological classification, and van Hove singularities in kagome metals GdV6Sn6.

(A) Crystal structure of GdV6Sn6 showing the unit cell (i), top view looking along the c axis and showing the V kagome plane (ii), and side view showing two possible surface terminations as indicated by wavy line (iii). (B) Sketch of topologically nontrivial states (TSSs) in GdV6Sn6. Cones and curves represent bulk states and TSSs, respectively. (C) Schematic of a VHS in a two-dimensional electron system. (D) Bulk BZ of GdV6Sn6 and the projection of the (001) surface BZ, with high-symmetry points marked. (E) DFT calculated electronic structure of GdV6Sn6. The red dashed line indicates the Fermi level suggested by the ARPES measurement. The inset shows the parity products classifying the ℤ2 invariant for each band. Bands 169 (blue) and 171 (black) are characterized by a strong topological invariant, ℤ2 = 1, while band 173 (red) is trivial with no topological invariants.

In this work, via a combination of angle-resolved photoemission spectroscopy (ARPES) and DFT calculations, we unambiguously reveal the characteristic ℤ2 TDSSs in kagome lattices and identify two types (p-type and m-type) of VHSs at the M points, in the paramagnetic phase of the magnetic kagome metal GdV6Sn6. The direct manipulation of the TDSSs and VHSs is realized by surface potassium deposition, where the Dirac point of the TDSSs shifts from above to below the EF with increasing electron doping. The direct identification of surface states, together with the spin texture inferred from spin-resolved ARPES (spin-ARPES) measurements and theoretical calculations, confirms the bulk nontrivial ℤ2 topology and shows great promise for realizing spin polarization reversal on the surface Fermi surfaces in GdV6Sn6. Our observation of tunable correlated and topological electronic states not only establishes GdV6Sn6 as a fertile system for exploring the interplay between the nontrivial band topology, magnetism, and correlation effects native to kagome lattices but also unlocks new perspectives for the realization of spintronics devices based on kagome materials.

RESULTS

GdV6Sn6 has a layered crystal structure with the space group P6/mmm and hexagonal lattice constants a = 5.5 Å and c = 9.2 Å. It consists of V3Sn kagome layers with Sn and GdSn2 layers successively distributed in alternating layers stacked along the c axis (Fig. 1A, i and ii) (). From the crystal structure, we find that chemical bonding between V3Sn and Sn layers is strong while the bonding between the V3Sn and GdSn2 layers is weaker. Therefore, cleaving the crystal along the (001) direction will result in two possible surface terminations, namely, the V kagome and Gd terminations (marked as Kagome Term. and Gd Term. in Fig. 1Aiii). Figure 1D illustrates the bulk BZ and the projected two-dimensional (001) surface BZ, with high-symmetry points indicated. The band structure of GdV6Sn6 in the paramagnetic phase from DFT calculations is displayed in Fig. 1E, where four VHS points emerge at the M in the vicinity of EF (indicated by the red arrows and labeled as VHS1 to VHS4). A closer examination of the orbitally decomposed electronic structure from DFT indicates that the states of VHS1, VHS2, and VHS3 at the M point, characterized by V d, d, and d orbitals, are solely attributed to one sublattice in the V kagome lattice and thus are of p-type (, , ). In contrast, the states of VHS4 at the M point are attributed to a mixture of two sublattices and thus are of m-type (for details, see fig. S1). Along the K-M direction, the p-type VHS1 and VHS2 bands disperse with the opposite sign compared to the VHS3 bands, which is attributed to the sign change of the hopping parameters of d and d orbitals. The continuous direct gaps between bands appearing at every k point allow one to define the ℤ2 topological invariant for the occupied bands using parity products at time-reversal invariant momenta (). Consistent with previous calculations (), a strong topological invariant ℤ2 = 1 is assigned to bands 171 (black) and 169 (blue), while the topmost band 173 (red) is topologically trivial. Owing to the band inversion around the A point for the 172 occupied bands, Dirac cone–like TSSs are expected to reside in the large local bandgap at Γ (fig. S2). Motived by these theoretical observations, we use ARPES to systematically study the topological electronic structures of single-crystal GdV6Sn6.

Because of the two possible surface terminations upon cleaving (Fig. 1Aiii), we expect to observe two different types of ARPES spectra (). By using a small beam spot and measuring the Sn 4d core level, we have resolved the two types of terminations on the cleaved sample surface and probed their electronic structures separately. Figure 2 summarizes the photoemission experiments on pristine, freshly cleaved GdV6Sn6.

Fig. 2.

Termination dependence of the electronic structure in GdV6Sn6.

(A) XPS spectrum of in situ freshly cleaved GdV6Sn6, from which we suggest that the surface termination is the kagome layer (fig. S3). a.u., arbitrary units. (B) Fermi surface mapping measured on the kagome termination. The BZ is marked with the red dashed hexagon. (C) ARPES spectrum taken along the - direction on the kagome termination, measured with 76 eV circular (C) (i) and linear vertical (LV) (ii) polarized light. The momentum path is indicated by the red solid line in (B). (D) Same as (C), but taken along the - direction, and measured with LV polarization. (E and F) Same as (C) and (D), but probed with 86-eV photons. (G and H) Same as (A) and (B), but measured on the Gd termination. The black dashed curve marks the electronic pocket. (I and J) Same as (C) and (D), but measured with C polarization on the Gd termination. (K) Band dispersion along the -- path showing the VHS1 at the point.

We first focus on the electronic structure from the kagome termination (see fig. S3 for a detailed description of the termination assignment). The corresponding x-ray photoelectron spectroscopy (XPS) spectrum on the Sn 4d core level and Fermi surface are shown in Fig. 2 (A and B), respectively (also see fig. S3). Photon energy–dependent ARPES measurements on the kagome V layer along two different high-symmetry paths, i.e., the --- (compare Fig. 2, C and E) and -- (Fig. 2, D and F) directions, exhibit distinct band dispersions at different k planes, indicating the three-dimensionality of the electronic structure in GdV6Sn6 (consistent with the calculations in Fig. 1E). Similar to other kagome lattices, the characteristic Dirac cone around the point and the VHS point near of the kagome lattice are observed on the kagome termination (fig. S4).

The ARPES spectra collected on the Gd termination, shown in Fig. 2 (G to J), are even richer than that on the kagome termination. The XPS spectrum on the Sn core level and Fermi surface from the Gd termination are plotted in Fig. 2 (G and H), respectively. The most prominent features of the Fermi surface (Fig. 2H) are the circular-shaped pocket near the BZ center ( point, highlighted by the dashed circle in Fig. 2H) and the accompanying hexagonal-shaped sheet (dashed hexagon in Fig. 2H). The band dispersion across the point (Fig. 2J) further reveals that the circular- and hexagonal-shaped Fermi surfaces are formed by two V-shaped bands (highlighted by the red box in Fig. 2J). In addition, the measured dispersions uncover an electron-like band (centered at the ) along the --- direction (Fig. 2I) and a hole-like band along the -- direction (Fig. 2J), exhibiting a saddle point at the point (Fig. 2K), i.e., indicating the presence of a VHS, as sketched in Fig. 1C. A careful comparison (fig. S5) between the experimental and calculated bands shows good overall agreement and indicates that the identified VHS corresponds to the VHS1 labeled in Fig. 1E. On the other hand, the observed double V-shaped bands around the point appear within the bulk bandgap (Fig. 1E), implying the presence of surface states on the kagome metals GdV6Sn6.

To further validate the surface nature of double V-shaped bands around the point, we have conducted photon energy–dependent ARPES measurement. Photoemission spectra recorded at various photon energies from 40 to 100 eV reveal that the V-shaped bands around do not disperse with respect to photon energy (and thus k), in contrast to the bulk states (for details, see fig. S6). The k independence of the V-shaped bands, as illustrated by two representative spectra taken with 76 and 86 eV in Fig. 3A, confirms the two-dimensional nature of the discussed surface bands. To further explore the topological nature of the surface states, we plot in Fig. 3 (B and C) the calculated bulk states projected onto the (001) surface together with the theoretical surface spectra for the Gd termination (also see fig. S7). Comparing the measurements (Fig. 3A) with the theory calculations (Fig. 3, B and C), the TSSs derived from bulk nontrivial topology are identified around the point (indicated by the black arrows in Fig. 3C). Notably, the side-by-side comparisons of the band dispersion along the - direction (Fig. 3, A and D) and the evolution of constant energy contours at different binding energies (Fig. 3, E and F) show excellent agreement. Moreover, spin-ARPES results presented in Fig. 3G provide clear spectroscopic evidence of the spin character of the V-shaped bands, suggesting that the observed surface states originate from the bulk nontrivial ℤ2 topology in kagome metals (for details, see fig. S8).

Fig. 3.

ℤ2 TSSs in GdV6Sn6.

(A) Photon energy–dependent ARPES spectra taken along the - direction, measured with 76 eV (i) and 86 eV (ii). (B and C) The (001) surface Green’s function projection of pure bulk states (BS) (B) and the states [bulk states and surface states (SS)] on Gd termination (C). (D) Zoom-in plot of the calculated TSSs with the same energy-momentum range as the experimental dispersions in (A). (E and F) Side-by-side comparison between experiments (E) and calculations (F), which exhibits excellent agreement, of three representative constant-energy contours (E = 0, 50, and 100 meV). (G) Spin-resolved momentum distribution curve, collected along the orange line in fig. S8A. The red and blue symbols in (i) are the intensity of the spin-up and spin-down states, respectively. The black curve indicates the spin polarization (ii). The spin texture of TSSs on Fermi surface are indicated by the black arrows in [F(i)] (for details, see fig. S8).

After the identification of the TSSs and VHS bands, we further demonstrate their manipulation via in situ surface potassium deposition. The accumulation of the K atoms on the sample surface can be seen by measuring the K 3p core level, which is absent on the pristine surface (blue curve in Fig. 4A), but grows in intensity with the surface deposition (purple and red curves in Fig. 4A). With increasing doping, the Dirac point of the TSSs is tuned from above to below EF and the Dirac-like dispersion is clearly observed (Figs. 4Bii and 4C, ii and iii; see fig. S9 for the momentum-dependent dispersions of the doped TDSSs). These observations can be well reproduced by our ab initio calculations (Fig. 4D) by introducing a chemical potential shift on the surface. Furthermore, the direct observations of the whole TDSSs unambiguously demonstrate the nontrivial bulk topology. In addition to the notable energy shift of the Dirac-like TSSs (Fig. 4G), a less-marked downward shift of bulk bands is revealed (as highlighted by the red dashed curves in Fig. 4, E and F). In particular, the electron-like VHS1 band around the point increases in size, and its bottom drops by about 30 meV, as evidenced by the doping-dependent energy distribution curve taken at the point (Fig. 4H; see fig. S10 for the manipulation of the VHS1 band on the kagome termination). It is obvious that the distinct doping evolution of the Dirac bands (Fig. 4, C and G) and VHS1 band (Fig. 4H) cannot be explained by a simple rigid band shift of the EF, reflecting the different chemical potential changes of the surface and bulk states with doping, as confirmed by the calculations (Fig. 4D).

Fig. 4.

Manipulation of the TSSs and VHS via in situ potassium deposition.

(A) Doping dependence of the XPS spectrum recorded on the Gd termination, showing the characteristic Sn 4d and Gd 4f peaks. Upon potassium deposition, the K 3p peak emerges (purple and red curves), which is absent on the pristine surface (blue curve). (B) Three-dimensional intensity plot of the electronic structure measured on the pristine (i) and K-dosed surfaces (ii). The orange arrow highlights the TSSs. (C and D) Doping evolution of the band structure along the - direction from experiments (C) and calculations (D). The Dirac cone of the TSSs is above the Fermi level (EF) before doping (pristine) (i) and is tuned below EF with electron doping (ii and iii). The arrows indicate the Dirac cone of the TSSs. The insets in [D(i)] and [D(iii)] show the schematic of distinct spin current of TDSSs without and with doping. (E) ARPES spectra taken along the - direction, on the pristine surface (Gd termination), measured with 76-eV LV (i) and linear horizontal (LH) (ii) polarizations. Red dashed curve highlights bulk bands. The arrow indicates the VHS1 band. (F) Same as (E), but measured on the K-dosed surface. (G) Doping evolution of the integrated energy distribution curve (EDC) taken around . The integration window of the EDC is represented by the red box in [C(i)] and [C(iii)]. Red and black arrows mark the TSSs and bulk states, respectively. (H) Doping evolution of the EDC extracted at the point, as indicated by the red line in [E(i)], measured with LV polarization.

DISCUSSION

Our ARPES measurements, combined with DFT calculations, reveal the desired ℤ2 TDSSs in a kagome metal, namely, in the magnetic kagome metal GdV6Sn6. In addition, we identify multiple VHSs at the M point and demonstrate the successful manipulations of the TDSSs and VHSs by surface doping. With increasing doping, the Dirac point of the TDSSs is tuned from above to below EF. Notably, upon sufficient doping, the lower branch of the TDSSs can merge into the bulk bands and only the upper branch crosses EF, resulting in spin chirality reversal on the Fermi surfaces in GdV6Sn6 (as illustrated in the inset of Fig. 4Diii; for details, see figs. S8 and S9). These highly tunable TDSSs show great promise for controlling spin current via local electrostatic gates (tuning the Dirac point below the EF; see the inset of Fig. 4Diii), which deserves further experimental investigation. Moreover, the revealed tunability of the VHSs holds the potential for realizing exotic correlated states on the surface of GdV6Sn6 through Fermi surface nesting and sublattice interference by nonlocal interactions (, –). On the other hand, as GdV6Sn6 tends to form magnetic ordering below the Tm, our results would stimulate future studies on the nontrivial states in magnetic phases. For instance, at low temperature, the magnetic Gd layers can become ferromagnetic by applying a weak magnetic field, which can gap out the surface Dirac cone and generate a nontrivial Chern number (see fig. S11 for the electronic structure of GdV6Sn6 in ferromagnetism). This realizes a quantum anomalous Hall state on the surface of GdV6Sn6, and the corresponding edge states and edge currents may be detected in a step edge in scanning tunneling microscopy measurements or in thin-film transport measurements.

In summary, GdV6Sn6 is a novel magnetic kagome metal whose magnetic layer and kagome layer are separated. The crucial insights into the electronic structure, revealed by our work, provide compelling evidence that GdV6Sn6 is a long-sought kagome material that hosts TDSSs originating from a ℤ2 bulk topology. The presence of topologically nontrivial surface states combined with the ability to tune magnetic interactions in the magnetic layer makes GdV6Sn6 a promising candidate for the construction of topological devices. For example, a quantum anomalous Hall state can be induced on the surface in the ferromagnetic phase. Moreover, the multiple VHSs in the vicinity of the EF with their large density of states and tunability upon doping provide an ideal platform for correlated quantum states native to kagome lattices. Our results not only establish the kagome metal GdV6Sn6 as a fascinating playground for fundamental research connecting topological physics, electronic correlation, and magnetism but also open up a new avenue for the potential application of topological devices in spintronics, for which one could exploit the reversibility of the spin texture chirality of the surface states.

MATERIALS AND METHODS

Sample growth

Single crystals of GdV6Sn6 were grown from the Sn flux with the loading composition of Gd:V:Sn = 1:6:20. The sample was heated up to 1050°C and stayed at 1050°C for 10 hours and then slowly cooled down to 650°C at the speed of 3°C/hour. The extra Sn flux was centrifuged at 650°C. The grown single crystals were carefully examined by single-crystal x-ray diffraction to obtain the accurate lattice parameters and atomic coordinates. Accordingly, GdV6Sn6 crystallizes in a layered structure with the space group P6/mmm.

ARPES measurements

The GdV6Sn6 samples were cleaved in situ with a base pressure of better than 5 × 10−11 torr. Regular angle-resolved photoemission (ARPES) measurements were performed at the ULTRA endstation of the Surface/Interface Spectroscopy beamline of the Swiss Light Source using a Scienta-Omicron DA30L analyzer. The temperature was 20 K, and total energy resolution was better than 15 meV. The Fermi level was determined by measuring a polycrystalline Au in electrical contact with the samples. The spin-ARPES experiments were conducted at the low-energy branch of the advanced photoelectric effect experiments beamline (APE-LE) of the Elettra synchrotron (Trieste, Italy), equipped with a DA30 analyzer combined with very low energy electron diffraction (VLEED) spin detectors.

DFT calculations

Band structure calculations were performed by using the method of first-principle DFT as implemented in the QUANTUM ESPRESSO code (). The cutoff energy for expanding the wave functions into a plane-wave basis was set to 60 Ry, and the adopted K-point grid is 9 × 9 × 5. The exchange correlation energy was described by the generalized gradient approximation using the Perdew-Burke-Ernzerhof (PBE) functional (). The calculations were done for nonmagnetic GdV6Sn6 with spin-orbit coupling. We used the maximally localized Wannier functions (MLWFs) to construct a tight-binding model by fitting the DFT band structure, where 118 MLWFs were included (Gd d; V d; Sn s, p;) () and then we used the surface state Green’s function method to calculate TSSs (). To simulate the doping evolution of the band structure, we model the potassium deposition by introducing a chemical potential shift only in the top surface layer. For all calculations, we used the experimentally determined crystal structure and lattice constants (a = 5.5348 Å and c = 9.1797 Å).