Introduction

The lattice geometry and crystalline symmetry are key factors determining the electronic properties of a crystal. One of the most prominent examples is the kagome lattice, a two-dimensional (2D) corner-sharing triangular network, which recently emerges as a rich frontier for exploring topological and correlated electronic phenomena1,2,3,4,5,6,7,8,9,10,11. Owing to its unique lattice geometry, the kagome lattice naturally incorporates linear band crossings hosting Dirac fermions4,5 as well as destructive interference-derived flat bands in its electronic structure. During the past decade, the topological aspects of kagome lattice have been intensively studied in transition-metal kagome magnets11,12,13,14,15,16,17,18; various topologically nontrivial electronic ground states associated with different forms of magnetism have been realized, such as (massive) Dirac fermions and flat bands in ferromagnetic Fe3Sn212,13 and antiferromagnetic FeSn14, Chern-gapped Dirac fermions in ferromagnetic TbMn6Sn615, Weyl fermions in the ferromagnet Co3Sn2S216,17 and the noncollinear antiferromagnet Mn3Sn18, and so on.

More interestingly, in the absence of magnetism, electron correlations could also provoke the emergence of unusual electronic states in kagome lattices7,8,9,10. A notable example is the recently discovered topological kagome metals AV3Sb5 (A = K, Rb, Cs)19,20. This family of materials not only carries a nontrivial Z2 topological index with band inversion20, but also hosts cascade of symmetry-breaking electronic orders including (potentially chiral) charge density wave (CDW)21, nematic/sematic order22 and superconductivity20. Subsequent studies have revealed involved intertwining between these electronic orders that gives rise to numerous exotic phenomena23, including intrinsic anomalous Hall effect24,25, unusual competition between CDW and superconductivity26,27, pair density wave order28, and possible Majorana zero modes inside the superconducting vortex core29. It has been suggested that AV3Sb5 resembles the high-Tc superconductors in view of the enriched low-temperature (T) orderings23. Whilst the ongoing investigations provide glimpse to the rich interplay between topology and correlations in kagome lattice, the experimental realization has been still limited, in great part owing to the rarity of kagome materials. Here, we report a new class of vanadium compounds which contains kagome bilayers in their crystal structures. The two members in this class, namely AV6Sb6 (A = K, Rb, Cs) and V6Sb4, host different types of Dirac nodal lines in their band structures. Moreover, superconductivity is realized in the former under pressure. These results identify the bilayer vanadium-based kagome compounds as ideal candidates for studying the topological nontriviality and its fingerprints on the electronic properties in kagome lattice.

Results and discussion

Crystal structures and physical properties for the bilayer kagome compounds

In Fig. 1a, b we illustrate the comparison of the crystal structures for the single-layer kagome compounds AV3Sb5 (A = K, Rb, Cs) and the bilayer kagome compounds: AV6Sb6 (A = K, Rb, Cs) and V6Sb4. All these materials consist of layered structural units stacking along the crystallographic c axis. A unit cell of AV3Sb5 hosts a single V3Sb layer in which the vanadium sublattice forms a perfect 2D kagome net and the Sb atoms locate at the center of all the kagome hexagons19 (upper panel in Fig. 1a); such V3Sb layers are separated by graphite-like Sb2 net and a triangular sublattice of alkaline cations A (left panel in Fig. 1b). The resulted hexagonal structure corresponds to the space group P6/mmm. By contrast, the bilayer compounds AV6Sb6 and V6Sb4 crystalize in the rhombohedral space group R\(\bar{3}\)m (No. 166); in their unit cells two adjacent V3Sb kagome slabs with in-plane offsets of V sites30 form a structural unit (lower panel in Fig. 1a). In AV6Sb6 these (V3Sb)2 bilayers are sandwiched by Sb2 sheets and triangular A sublattices that are the same as those in AV3Sb5 (Fig. 1b), whilst in V6Sb4 the intercalated A cations are absent and there is a single Sb2 net between two (V3Sb)2 bilayers. We note that the structure of V6Sb4 is identical to the ferromagnetic kagome compound Fe3Sn212,30, whereas the AV6Sb6 series adopts an unprecedented crystal structure of kagome compounds (for detailed structural parameters, see Supplementary Tables 1 and 2). Although the single-layer and bilayer compounds have different crystalline symmetries, we stress that they can be represented by a generic chemical formula (Am-1Sb2m)(V3Sb)n (m = 1, 2; n = 1, 2) with the values of (m, n) for AV3Sb5, AV6Sb6 and V6Sb4 being (2, 1), (2, 2) and (1, 2), respectively. Hence, the crystal structure of the entire series (Am-1Sb2m)(V3Sb)n can be viewed as an alternate stacking of the (Am-1Sb2m) blocks and the (V3Sb)n blocks.

Fig. 1: Structural and transport properties of the bilayer vanadium-based kagome compounds.
figure 1

a Top view of (top) the V3Sb kagome nets in single-layer compounds AV3Sb5 (A = K, Rb, Cs), (bottom) (V3Sb)2 bilayers in AV6Sb6 (A = K, Rb, Cs) and V6Sb4. The different offsets of the two adjacent V3Sb layers lower the rotational symmetry from sixfold to threefold. b Sketches of the structural unit cells of (left) AV3Sb5, (middle) AV6Sb6, (right) V6Sb4. The structures of all three series can be described as alternate stacking of the kagome unit (V3Sb)n and the spacing unit Am-1Sb2m. Single-crystal X-ray diffraction pattern for c the (00l) direction and d, e, the (hk0) plane measured in bilayer kagome compounds. f Temperature-dependent electrical resistivity of KV6Sb6 (orange), RbV6Sb6 (green, amplified by a factor of 2), CsV6Sb6 (blue), and V6Sb4 (red). Inset shows the Hall resistivity measured in CsV6Sb6 at T = 2 K. The solid dark blue curve is the linear fit corresponding to an electron-type carrier density of ne = 2.1 × 1021 cm−3.

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Single crystals of AV6Sb6 (A = K, Rb, Cs) and V6Sb4 were synthesized using a self-flux growth technique (Methods). The high quality of these single crystals is confirmed by our X-ray diffraction (XRD) measurements: the reconstructed (hk0) plane determined from single-crystal XRD displays sharp spots with sixfold rotational symmetry (Fig. 1d, e) and a 2θ-ω scan yields only a series of sharp (00l) Bragg peaks (Fig. 1c). We summarize the results of the single-crystal XRD analysis for V6Sb4, RbV6Sb6, and CsV6Sb6 in Supplementary Tables 1 and 2. Electrical transport and magnetization measurements identify all the bilayer compounds as nonmagnetic metals without indications of additional orderings (Fig. 1f and Supplementary Fig. S1). We note that no CDW ordering is observed in our bilayer kagome samples, contrary to the case in the single-layer AV3Sb5 (A = K, Rb, Cs) where a CDW transition occurs at 80–100 K19. Hall resistivity measured in CsV6Sb6 (inset of Fig. 1f) indicates dominant electron-type carriers with the density ne = 2.1 × 1021 cm−3.

First-principles calculations on CsV6Sb6 and V6Sb4

To further investigate the electronic structures of those bilayer kagome compounds, we performed first-principles calculations based on the density functional theory (DFT). The calculation results approve that AV6Sb6 (A = K, Rb, Cs) and V6Sb4 lack local magnetic interactions and possess nonmagnetic ground states, consistent with the experimental observations (Supplementary Fig. 1). Here, we mainly focus on the compounds CsV6Sb6 and V6Sb4. The calculated band structures for the other two members in the isostructural series AV6Sb6 with A = K, Rb are presented in Supplementary Fig. 2. In Fig. 2a, b we show the band structures as well as the projected density of states (DOS) for CsV6Sb6 and V6Sb4, respectively. The corresponding high-symmetry paths of the BZ of a rhombohedral lattice are depicted in Fig. 2c. The DOS in the vicinity of the Fermi level are dominated by V-3d orbitals for both CsV6Sb6 and V6Sb4, whereas the Sb-p orbitals have rather weak contributions (Fig. 2a, b). Remarkably, the calculated band structures of both compounds exhibit linear band crossings (i.e, Dirac points) that are close to the Fermi level along the specific high-symmetry paths, Г-Z-F-Г-L-Z-P (Fig. 2a, b). To be mentioned, the electronic structure of the bilayer kagome compounds is distinct from that of the single-layer AV3Sb5 which are hallmarked by multiple Dirac crossings and saddle points near the Fermi level20,31.

Fig. 2: Dirac nodal rings in the electronic structure of CsV6Sb6 and V6Sb4.
figure 2

The band structures and projected density of states (DOS) were obtained from DFT calculations for a CsV6Sb6 and b V6Sb4. The blue and yellow shaded areas highlight the topologically nontrivial bands near the Fermi level and the band gaps between them. The calculated parities are also shown for these bands at the TRIMs. The insets of panels a, b are zoom-ins of the Dirac band crossings along the Z-F direction without (left) and with (right) spin-orbit couplings. c The surface and bulk Brillouin zones of the rhombohedral AV6Sb6 and V6Sb4. The cross-section marked by yellow color is the middle plane in which the high-symmetry paths are selected for the DFT calculations in a, b. The two red curves denote the position of type-II Dirac nodal lines in CsV6Sb6. d The parity at TRIMs and the Z2 invariant for each band close to the Fermi level in CsV6Sb6 and V6Sb4.

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Our DFT calculations reveal that CsV6Sb6 is a Dirac nodal line semimetal. As shown in Fig. 2a, the band crossings occur along the high-symmetry paths from Γ/Z to the high-symmetry points at the boundaries of the Brillouin zone (BZ) such as the P, F, and L. All these high-symmetry paths lie in a middle plane of the BZ (highlighted in yellow in Fig. 2c); on this plane, the band crossings form two type-II Dirac nodal lines (shown as the red lines in Fig. 2c) characterized by tilted Dirac cones32. By further checking the little group of the BZ, we find that these type-II Dirac nodal lines are symmetry protected because the two intersecting bands along the above arbitrary high-symmetry paths belong to different irreducible representations (IR) Γ1 and Γ2 of the mirror symmetry Cs (see the insets in Fig. 2a). Due to the three-fold rotational symmetry, there are three equivalent middle planes, and thus six type-II Dirac nodal lines that are symmetrically distributed in the BZ of CsV6Sb6. On the other hand, the crossings of valence and conduction bands are absent along Γ/Z-L in the band structure of V6Sb4 (Fig. 2b). However, the preserved band crossings along Γ/Z-F can still form symmetry-protected nodal lines on three equivalent middle planes. Contrary to the type-II nodal lines in CsV6Sb6, these nodal lines in V6Sb4 are type-I and feature closed loops around the band inverted point F (Supplementary Fig. 2).

In the presence of the spin-orbit coupling (SOC), the spin-rotation symmetry is broken, subsequently, the nodal lines in a system with the coexistence of spatial inversion and time-reversal symmetries are always destroyed33. As shown in the insets of Fig. 2a, b, when the SOC effect is included, the two intersecting bands without SOC now belong to the same IR Γ4 of the mirror symmetry Cs. Thus the band crossings are avoided. Nonetheless, the SOC effect is rather weak in the vanadium bilayer kagome compounds: the gap opened at the Dirac band crossings is almost negligible; in particular, for CsV6Sb6 the gap width is less than 1 meV. Therefore, its type-II Dirac nodal lines are nearly intact. With the existence of the SOC gaps, we can use parity products of occupied bands at the time-reversal invariant momenta (TRIM) points to reveal the topological nontriviality34. For a nonmagnetic compound crystalizing in the R\(\bar{3}\)m space group, the three F (and the three L) points are equivalent, thus we only calculate the parity eigenvalues at four TRIM points, i.e., the Γ, Z, F, and L points (for detailed calculation results, see Supplementary Table 3). As illustrated in Fig. 2d, the parity analysis indicates that bands 115 and 117 (95 and 99) are topologically nontrivial in CsV6Sb6 (V6Sb4). These nontrivial bands are close to the Fermi level and their cooperation with nodal fermions would be expected to generate rich exotic quantum phenomena. It should be noticed that the inclusion of Hubbard U in the DFT calculations does not change the band topology (Supplementary Fig. 3), and the Dirac nodal lines remain intact with U = 2.0 eV.

ARPES measurements on CsV6Sb6

The band structure calculation results for CsV6Sb6 are supported by our angle-resolved photoemission spectroscopy (ARPES) measurements. As shown in Fig. 3a–f, the constant energy contours at binding energies Eb = 0, 200 and 400 meV, as measured with 60 eV photons, are similar to those of the DFT+ U calculations (U = 2eV). At the Fermi energy, we observe relatively high intensities close to the boundary of the projected 2D BZ (marked by yellow lines in Fig. 3b) and a hexagonal contour around the \(\bar{\Gamma }\) point; both of which are consistent with the DFT results (Fig. 3a). At Eb = 200 meV, the most prominent features of the calculated constant energy contours are the hexagonal pocket around the \(\bar{\Gamma }\) point and rounded-triangular pockets centered at the \(\bar{{{{{{\rm{K}}}}}}}\) points (Fig. 3c), whereas a gear-shaped pocket centered at the \(\bar{\Gamma }\) develops at higher binding energies (Fig. 3e). These features are well reproduced in the photoemission intensity maps (Fig. 3d, f). Figure 3g shows the calculated bulk band dispersion along the \(\bar{\Gamma }\)-\(\bar{{{{{{\rm{M}}}}}}}\) direction (red dashed line in Fig. 3b) with different kz ranging from 0 to 2π/c, and one can find that the kz dependence of the bulk bands in this material is very weak, which is also confirmed by the photon-energy-dependent ARPES measurements (Supplementary Figs. 4, 5). For a direct comparison, in Fig. 3h we display the corresponding ARPES-intensity plot. An overall agreement between the ARPES data and the calculated bulk bands (Fig. 3g). In particular, the two crossing bands (bands 117 and 119 in Fig. 2a) contributing to the type-II Dirac nodal lines in the \(\bar{\Gamma }\)-\(\bar{{{{{{\rm{M}}}}}}}\) direction are resolved, with the Dirac crossings located in close vicinity to the EF. We note that the band structure of CsV6Sb6 is significantly different from its single-layer counterpart CsV3Sb513,31, indicating the importance of inter-(V3Sb)-layer coupling in these kagome lattice compounds.

Fig. 3: Experimentally resolved electronic structure.
figure 3

a DFT + U-calculated Fermi surface contours at kz = 0.5 with U = 2 eV for CsV6Sb6. b Constant energy contours at binding energy Eb = 0 measured in CsV6Sb6 at around 12 K by ARPES using 60 eV photons. Yellow lines denote the boundary of the projected 2D Brillouin zone. c, d, e, f, Same as a, b, but for the constant energy contour at Eb = 200 meV and Eb = 400 meV. respectively. Red dotted lines in b, d, f are guides to the eye. g The bulk band structures of CsV6Sb6 at different kz ranging from 0 to 0.5 were obtained from DFT+U calculations with U = 2 eV. h Photoelectron intensity plot along the \(\bar{\varGamma }-\bar{{\rm M}}\) momentum cut (red dashed line in b), measured with 60 eV photons at T ≈ 12 K.

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Pressure-induced superconductivity in AV3Sb5

Despite that the bilayer vanadium-based kagome compounds, unlike AV3Sb5 (A = K, Rb, Cs)20,26, do not exhibit superconductivity at ambient pressure, we realize superconductivity in AV6Sb6 (A = K, Rb, Cs) by applying quasi-hydrostatic pressures. The results of high-pressure resistance measurements on two CsV6Sb6 samples are presented in Fig. 4a. The T-dependences of the normalized resistance R/R300K show metallic behavior in the entire pressure range with the residual resistivity ratio (RRR) gradually decreases below 15 GPa. At 15.8 GPa it drops to ~1.2. With pressure further increasing, superconducting transition emerges at 21.2 GPa manifested by a pronounced resistance drop (Fig. 4b). Magnetic fields can gradually suppress the transition temperature, which confirms that the resistance drop is due to a superconducting transition (Supplementary Fig. 6). The transition temperature determined by \({T}_{c}^{90 \% }\) (i.e., where the resistance drop to 90% of the normal state value) is 1.04 K. The evolution of \({T}_{c}^{90 \% }\) under applied pressure is nonmonotonic: it first increases rapidly and reaches a maximum of 1.48 K at 33.0 GPa, then starts to decrease slowly; superconductivity persists up to the highest pressure (79.5 GPa) achieved in this measurement, where \({T}_{c}^{90 \% }\) is ~1 K (Fig. 4b). Such nonmonotonic behavior gives rise to a broad dome-shaped superconducting regime in the high-pressure phase diagram (Fig. 4c), suggesting a complex interplay of the pressure-dependent DOS and structural instabilities35,36. Similar superconducting dome is also observed in RbV6Sb6 and KV6Sb6 under high pressure, yet with lower maximum Tc (Supplementary Fig. 7). Intriguingly, superconductivity in all three materials appears in the vicinity of the minimum of RRR (Fig. 4c and Supplementary Fig. 7). The correlation between Tc and RRR indicates that the emergence of superconductivity is associated with electronic structure modifications.

Fig. 4: Pressure-induced superconductivity in CsV6Sb6.
figure 4

a Temperature dependence of the resistance of CsV6Sb6 normalized using the room temperature (300 K) value under various pressures up to 79.5 GPa. The curves taken at P < 40 GPa and P > 40 GPa are measured in samples S1 and S2, respectively. Data are shifted vertically for clearance. The gray vertical bar denotes a scale of 0.25. b An expanded view of the low-temperature resistance of CsV6Sb6 in a pressure range of 21.2–79.5 GPa, showing the superconducting transitions. c Phase diagram for CsV6Sb6 under pressure. The superconducting transition temperature Tc (red solid circles) is determined as the temperature where the resistance drops to 90% of the normal state value. The shaded regimes shown in green and blue represents the rhombohedral (space group R\(\bar{3}\)m) and monoclinic (space group P2/m) structural phases, respectively (see Supplementary Figs. 8, 9).

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We note that such modification stems from a structural phase transition that occurs above ~20 GPa, where the structure changes from rhombohedral to monoclinic as revealed by our high-pressure XRD measurements (Supplementary Figs. 8, 9). It is most likely that the monoclinic phase hosts superconductivity. Refinements of the XRD data provide further details of the structural transition: the ambient-pressure rhombohedral phase evolves into the monoclinic phase via a lattice distortion at which the in-plane lattice parameter a develops into two unequal values a and c, whilst the angle β changes from 120° to ~110° (Supplementary Fig. 8). The pressure-induced superconductivity accompanied by a structural transition in AV6Sb6 resembles that observed in numerous topological semimetals37,38,39,40,41. Most notably, in some of these materials, the superconductivity is proposed to emerge from topological electronic bands37,39,40, offering a good opportunity to probe the feasible realization of topological superconductivity. Future studies are needed to determine the topological properties of the high-pressure monoclinic phase and to clarify how superconductivity develops in this phase with lower symmetry.

Our theoretical and experimental investigations reveal unusual topological metal phases in the bilayer vanadium-based kagome compounds. Distinct from the typical kagome physics concerning Dirac points and van Hove singularity in single-layered AV3Sb520,23, the most important characteristics of the bilayer compounds are denoted by the Dirac nodal lines near the Fermi level. The pressure-induced superconductivity discovered in AV6Sb6 further suggests promising emergent phenomena in the bilayer kagome materials. All these results provide inspiring perspectives for future explorations of the enriched topological physics in kagome lattice.

Methods

Single crystal growth and characterization

Single crystals of AV6Sb6 (A = K, Rb, Cs) and V6Sb4 were grown using a self-flux method. For AV6Sb6, K/Rb/Cs (ingot or liquid 99.5%), V (powder, 99.5%), Sb (shot, 99.999%) were loaded into an alumina container with the molar ratio of 2:3:6 and then sealed into a double-wall silica tube. Mixture was subsequently heated to 1150 °C and kept for 24 h, then slowly cooled to 1050 °C for 72 h. The excess flux was removed by centrifuging at 1050 °C. The products were single crystals with sizes of a few millimeters in ab plane and less than 100 μm in thickness. For V6Sb4, K (ingot, 99.5%), V (powder, 99.5%), Sb (shot, 99.999%) were mixed with the molar ratio of 2:3:6 and sealed in the same double-wall silica tube. The tube was heated to 1150 °C and kept for 24 h, then slowly cooled to 1050 °C in 72 h. After soaked at 1050 °C for 5 h, the temperature was increased to 1100 °C in 20 h. Large crystals of V6Sb4 with sizes of several millimeters were obtained from the flux by centrifuging at 1100 °C.

Single-crystal X-ray diffraction measurements were carried out on a XtaLAB AFC12 (RINC): Kappa single diffractometer (Rigaku, Japan) with a charge-coupled device detector and Cu source in Core Facility Center for Life Sciences, USTC. The data was processed and reduced using CrysAlisPro42. Using Olex-243, the structure was solved with the ShelXT structure solution program44 via direct methods and refined with the ShelXL refinement package45. Magnetization measurements were performed on a Quantum Design Magnetic Properties Measurement Systems (MPMS-5). Plate-shaped single crystals were attached to a quartz rod with the magnetic field applied parallel to and perpendicular to the c-axis. The transport properties were measured on the Quantum Design Physical Properties Measurement System (PPMS-9) using a standard six-probe configuration.

First-principles calculations

To depict electronic properties of these novel kagome compounds of AV6Sb6 and V6Sb4, we carried out first-principles calculations based on the density functional theory46 as implemented in the Vienna ab initio simulation package47. The exchange-correlation functional was described by generalized gradient approximation with Perdew–Burke–Ernzerhof formalism48. The core-valence interactions were treated by projector augmented-wave potentials49 with a plane-wave-basis cutoff of 450 eV. The Brillouin zone (BZ) was sampled by a 12 × 12 × 12 Monkhorst-Pack grid50 to simulate the rhombohedral structure. The crystal structures were fully relaxed by minimizing the forces on each atom smaller than 1.0 × 10−3 eV/Å, and the van der Waals interactions along the c-layer stacking direction were considered by the Crimme (DFT-D3) method51. The topological class was characterized by the Z2 invariants, which are calculated from the parity eigenvalues at TRIM points using IRVSP package52. We also employed the DFT + U method to calculate the band structure of CsV6Sb6, in which the Hubbard U correction represents the on-site Coulomb interactions on the d-orbital of vanadium; the band topology persists upon varying U values (Supplementary Information Fig. S3).

ARPES measurements

ARPES measurements were performed at the beamline 13 U of the National Synchrotron Radiation Laboratory at University of Science and Technology of China (photon energy 35 eV), and the beamline 03U of the Shanghai Synchrotron Radiation Facility (SSRF) (photon energy 42–60 eV). The samples were cleaved in situ with a base pressure less than 6 × 10−11 torr. We note that the terraced surfaces of the cleaved samples usually hamper a clear observation of the fine electronic features. Further ARPES investigations with improved resolution are required to reveal the possible topological surface states53 in the AV6Sb6 materials.

High-pressure transport measurements

Diamond anvils with various culets (200–300 µm) were used for high-pressure transport measurements. NaCl was used as a pressure transmitting medium and the pressure was calibrated by using the shift of ruby fluorescence and diamond anvil Raman at room temperature. For each measurement cycle, the pressure was applied at room temperature using the miniature diamond anvil cell. The transport measurements were performed in a dilution refrigerator (Kelvinox JT, Oxford Instruments) or a 3He cryostat (HelioxVT, Oxford Instruments). Single-crystalline samples of AV6Sb6 and V6Sb4 were cut into typical dimensions of 50 × 50 × 10 μm3. The resistivity was measured using a four-probe configuration. V6Sb4 does not show indication of superconducting transition up to the highest pressure we achieve, i.e., P ≈ 80 GPa (Supplementary Fig. 7).

High-pressure X-ray diffraction

The high-pressure synchrotron XRD measurements were performed at room temperature at the beamline BL15U1 of SSRF with a wavelength of λ = 0.6199 Å. A symmetric diamond anvil cell with a pair of 200 µm culet size anvils was used to generate pressure. 70 µm sample chamber is drilled from the Re gasket and Daphne 7373 oil was loaded as a pressure transmitting medium.