Main

Superconductivity often emerges in the vicinity of other ordered electronic states with a broken symmetry, such as antiferromagnetic order and charge density wave. Their interdependence has been widely studied in cuprate and iron-based superconductors21,22, but persists as a key issue for understanding high-temperature superconductivity. In certain cases, the ordered state and superconductivity can even coexist23, which may indicate an unconventional pairing and have a dramatic impact on the superconducting mechanism. Because of the unique lattice geometry and unusual electronic features in a kagome lattice1,3,4, the recently discovered kagome superconductors stand out as a new platform for inspecting the superconductivity emerging from a complex landscape of electronic orders5,7,24. Of particular interest is the non-magnetic family of AV3Sb5 (A = K, Rb, Cs)5,24, in which a variety of intriguing phenomena have been uncovered, including a tantalizing time-reversal symmetry-breaking charge density wave (CDW) order9,25,26, a pair density wave10, electronic nematicity8,27,28, double superconducting domes under pressure29,30 and giant anomalous Hall effect31,32. All these phenomena point out exotic intertwined effects in kagome superconductors AV3Sb5.

To illuminate the microscopic pairing mechanism and the cooperation/competition between multiple phases in such kagome superconductors, a fundamental issue is to determine the superconducting (SC) gap symmetry. This prominent issue remains elusive owing to the great challenge in resolving such small energy scales and the existence of several conflicting experimental results. Taking CsV3Sb5 as an example, certain V-shaped gaps, as well as residual Fermi-level states measured by scanning tunnelling spectroscopy10,11 and a finite residual thermal conductivity towards zero temperature12, seem to support a nodal SC gap. By contrast, the observations of the Hebel–Slichter coherence peak in the spin-lattice relaxation rate from 121/123Sb nuclear quadrupole resonance measurements13 and the exponentially temperature-dependent magnetic penetration depth14,15, are more consistent with a nodeless superconductivity. On the theoretical side, both unconventional and conventional superconducting pairing were proposed18,19,20. Therefore, an unambiguous characterization of the SC gap structure and its connection with the intertwined CDW order becomes an urgent necessity. During the long-term research of superconductors, angle-resolved photoemission spectroscopy (ARPES) has been proved to be a powerful tool to directly measure the SC gap in the momentum space33. Nevertheless, the relatively low transition temperature (Tc) and correspondingly small gap size render a thorough ARPES measurement extremely challenging.

In this work, we utilize an ultrahigh-resolution and low-temperature laser-ARPES, together with a chemical substitution of V in CsV3Sb5 that raises Tc, to precisely measure the gap structure in the superconducting state. CsV3Sb5 crystallizes in a layered structure with V atoms forming a two-dimensional kagome net, as shown in the inset of Fig. 1a. At low temperatures, the material exhibits a CDW transition at TCDW ≈ 93 K, and eventually becomes superconducting at Tc ≈ 3 K. To finely tune the competition between superconductivity and CDW, we take two elements to substitute V in CsV3Sb5. As shown in Fig. 1, both substitutions show a similar trend in the phase diagram, but with distinctions—Nb substitution enhances Tc more efficiently, whereas Ta dopant concentration can be increased to fully suppress the CDW order. Considering the accessibility in terms of temperature and the possible influence of CDW, we select Cs(V0.93Nb0.07)3Sb5 and Cs(V0.86Ta0.14)3Sb5, from two typical regions in the phase diagram, for the SC gap measurement (denoted hereafter as Nb0.07 and Ta0.14, respectively). The Nb0.07 sample exhibits a Tc of 4.4 K and a TCDW of 58 K, whereas the Ta0.14 sample exhibits a higher Tc of 5.2 K, but no clear CDW transition. Strikingly, as we shall present below, the gap structures of both samples are isotropic, regardless of the disappearance of CDW, hinting at a robust nodeless pairing in CsV3Sb5-derived kagome superconductors.

Fig. 1: Evolution of CDW and superconductivity in CsV3Sb5 on chemical substitution.
figure 1

a, Phase diagrams for Cs(V1−xNbx)3Sb5 and Cs(V1−xTax)3Sb5. Inset, the lattice structure of V–Sb layer, illustrating the Ta or Nb substitution of V atoms within the kagome lattice. b, Temperature dependence of in-plane resistivity for the pristine and two substituted samples studied in this work. The arrows indicate the anomalies associated with CDW transitions. The inset shows the differential resistivity to highlight the CDW transitions, with the curves vertically shifted for clarity. Note that there is no CDW order observed in Cs(V0.86Ta0.14)3Sb5. c, Normalized resistivity curves in the low-temperature range showing clear superconducting transitions. AU, arbitrary unit.

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Spectroscopic evidence of the superconducting gap

Mapping out the Fermi surface (FS) is critical to investigate the SC gap structure, especially for a multiband system. Due to the limited detectable momentum area of the 5.8 eV laser source, Fig. 2a shows a joint FS of the Ta0.14 sample by combining three segments, which is validated by whole-FS mapping with a larger photon energy (Extended Data Fig. 1). Similar to the pristine CsV3Sb5 sample6,34,35, the Ta0.14 sample has a circular electron-like pocket (marked as α) and a hexagonal hole-like pocket (marked as β) at the Brillouin zone (BZ) centre Γ point, and a triangle pocket (marked as δ) at the BZ corner K point. The α FS is formed by Sb 5p orbitals, whereas the β and δ FS are derived from V 3d orbitals35 and are close in momentum. As shown in Figs. 2a and 3b, the β and δ FS are well distinguished due to the high momentum resolution of the laser source. Moreover, the intensities of the β and δ FS are enhanced under different polarizations of light (Extended Data Figs. 2 and 3, and see Methods for details), which further makes the determination of the Fermi momentum (kF) reliable.

Fig. 2: Isotropic superconducting gap in Cs(V0.86Ta0.14)3Sb5.
figure 2

a, ARPES intensity integrated over ±5 meV around EF. The broken lines represent the FS contours. b, Temperature dependence of EDC at kF in a cut marked as a black line in a. Inset, temperature-dependent SC gap amplitude determined by the fitting procedure based on the BCS spectral function. The blue broken curve represents BCS-like temperature dependence. c–e, EDCs at kF measured at T = 2 K and 7 K along with the α (c), β (d) and δ (e) FS, respectively. f, Summary of the kF positions of the EDCs shown in c–e, shown as black thick circles. The black lines are the curves fitted by the BCS spectral function. The dashed lines mark the peak of the EDCs. g, SC gap amplitude estimated from the fits to EDCs shown in c–e. The shaded areas represent the error bars determined from the standard deviation of EF. The square makers are the SC gap results from an independent sample and the corresponding kF are shown as thin squares in f.

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Fig. 3: Isotropic superconducting gap in charge-ordered Cs(V0.93Nb0.07)3Sb5.
figure 3

a, ARPES intensity integrated over ±5 meV around EF. The broken lines represent the FS contours. b, ARPES intensity plot along a red line shown in a. The intensity is measured using circular polarization to capture both β and δ bands. The white dotted line represents the MDC integrated over ±2 meV around EF and the black line is a double-peak Lorentzian fit. Two peaks distinguished in the MDC show kF positions of the β and δ bands. c–e, EDCs at kF taken along the α (c), β (d) and δ (e) FS, respectively. f, Summary of the kF positions of the EDCs in c–e. The black lines are the curves fitted by the BCS spectral function. The dashed lines mark the estimated peak position of the EDCs. g, SC gap amplitude estimated from the fits to EDCs shown in c–e. The square makers are the SC gap results from an independent sample and the corresponding kF are shown as thin squares in f. The shaded areas represent the error bars determined from the standard deviation of EF.

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Before investigating the SC gap structure, we first present the spectral evidence of the superconductivity below Tc. Using the Ta0.14 sample as an example, the temperature-dependent energy distributed curves (EDCs) at kF of a cut indicated in Fig. 2a are shown in Fig. 2b. At T = 2 K, far below the Tc, the emergence of the particle–hole symmetric quasiparticle peaks around the Fermi level (EF) clearly indicate the opening of an SC gap. With temperature gradually increasing, the growing intensity at EF and the approaching quasiparticle peaks suggest that the SC gap becomes smaller and eventually closes. Quantitatively, the SC gap amplitude can be extracted from the fitting procedure based on a Bardeen–Cooper–Schrieffer (BCS) spectral function (Methods). The inset of Fig. 2b summarizes the SC gap amplitudes Δ(T) at different temperatures, which fit well with the BCS-like temperature function. The fitted SC gap amplitude at zero temperature, Δ0, is approximately 0.77 meV, and the estimated Tc of approximately 5.2 K is consistent with the bulk Tc determined by resistivity measurements (Fig. 1c). These results demonstrate the high quality of the samples and the high precision of our SC gap measurements.

Superconducting gap structure in CDW-suppressed Cs(V0.86Ta0.14)3Sb5

We then study the momentum dependence of the SC gap in the Ta0.14 sample, in which the CDW order is fully suppressed (Fig. 1b). Considering the six-fold symmetry of the FS, we select various kF points to cover the complete FS sheets and thus capture the symmetry of the SC gap, as shown in Fig. 2f. The EDCs at kF of the α, β and δ Fermi surfaces are presented in Fig. 2c–e. For each kF point, we take spectra below and above Tc, to ensure a precise in situ comparison. In the vicinity of EF, the leading edge of the EDCs at 2 K all show a shift compared to that at 7 K. Moreover, they universally show a strong coherence peak at a binding energy EB of approximately 1 meV, indicating a rather isotropic SC gap structure. Fitting these EDCs to a BCS spectral function, the quantitatively extracted SC gap amplitudes are summarized in Fig. 2g. These SC gaps of different Fermi surfaces have rarely fluctuated amplitudes with an average ΔTa of 0.77 ± 0.06 meV, yielding a ratio 2ΔTa/kBTc of 3.44 ± 0.27 (where kB is the Boltzmann constant; Extend Data Table 1), which is close to the BCS value of approximately 3.53. These results clearly demonstrate an isotropic SC gap in the Ta0.14 sample.

Superconducting gap structure in charge-ordered Cs(V0.93Nb0.07)3Sb5

Next, we turn to examine the possible influence of the CDW order in the normal state on the superconducting pairing symmetry16,29,30. We measure the SC gap structure of the Nb0.07 sample, where TCDW gets slightly suppressed, and Tc smoothly increases from that of the pristine CsV3Sb5 (Fig. 1a). In this sense, the superconductivity in the Nb0.07 sample is expected to have a similar SC gap structure to CsV3Sb5. As shown in Fig. 3a, the FS topology of the Nb0.07 sample is also similar to that of CsV3Sb5, consisting of the circular α FS, hexagonal β FS and triangular δ FS, which is consistent with the helium-lamp-based ARPES measurements (Extended Data Fig. 1) and the calculations based on density function theory36. The EDCs at kF positions indicated in Fig. 3f, on these three Fermi surfaces, are presented in Fig. 3c–e. Just like the case for the Ta0.14 sample, coherence peaks arise at a similar energy position for all EDCs at 2 K, albeit of a slightly broader shape due to a smaller SC gap and lower Tc. By fitting the EDCs to the BCS spectral function, the SC gap amplitudes along the Fermi surfaces are summarized in Fig. 3g. The data clearly show a nearly isotropic SC gap structure in the Nb0.07 sample, with the gap amplitude ΔNb of 0.54 ± 0.06 meV, giving a ratio 2ΔNb/kBTc of 2.83 ± 0.32 (Extended Data Table 2), which is smaller than the BCS value. Our results show that an isotropic SC gap robustly persists in the Nb0.07 sample with CDW order.

As the kagome metals AV3Sb5 have a three-dimensional electronic structure34,35, we further study the z-direction momentum (kz) dependence of the SC gap by tuning the photon energy from 5.8 eV to 7 eV. We find that the SC gap remains nearly the same at these two kz planes within our experimental uncertainties (Extended Data Fig. 4). Giving the direct momentum-resolving capability of ARPES and the prominent features of SC gap opening, our data reveal a nodeless, nearly isotropic and orbital-independent SC gap in both Nb0.07 and Ta0.14 samples (Fig. 4a,b).

Fig. 4: Robust isotropic SC gap on suppression of CDW.
figure 4

a,b, Schematic momentum dependence of the SC gap amplitude of the Nb0.07 (a) and Ta0.14 (b) samples, respectively. c, Schematic phase diagram in which TCDW and Tc are plotted as a function of the lattice expansion due to the chemical substitutions. The lattice expansion is represented by \(\delta a/{a}_{0}\), where \(\delta a=a-{a}_{0}\) is the change of the in-plane lattice constant (a) from that of pristine CsV3Sb5 (a0). The inset shows the lattice structures of the CDW (left) and undistorted (right) phases, representing the states above Tc for two distinct regions in the phase diagram. The black solid lines in the insets mark the corresponding single-unit cells. The isotropic SC gap symmetry persists through two such regions, regardless of the existence of CDW order.

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Discussions and perspectives

These results shine a light on the interplay between superconductivity and CDW in CsV3Sb5. As shown in Fig. 4c and Extended Data Fig. 5, the isovalent substitutions of Nb/Ta for V in our experiments can be viewed as an effective in-plane negative pressure, which suppresses the CDW order while it enhances the superconductivity. In the absence of the CDW order, our measurements on the Ta0.14 sample reveal a nearly isotropic gap structure (Fig. 4b). When the CDW order associated with an anisotropic gap34,37 comes into play in the Nb0.07 sample, the SC gap remains isotropic and nodeless (Fig. 4a), different from the muon spin relaxation (μSR) observation of a nodal-to-nodeless transition in the sister compounds KV3Sb5 and RbV3Sb5 under hydrostatic pressure16. The difference between the two regimes, represented by the Nb0.07 and Ta0.14 samples, is that the ratio 2Δ/kBTc is smaller when superconductivity emerges inside the CDW order. This may be attributed to the CDW order partially gapping out the Fermi surfaces and generating spin polarizations before entering the superconducting phase.

We further discuss the pairing symmetry in CsV3Sb5-derived kagome superconductors. Although the SC gap structure in pristine CsV3Sb5 with a relatively low Tc is not examined, the nodeless gap is probably retained according to the similarities between the pristine and Nb0.07 samples in terms of electronic structure (Extended Data Figs. 1, 7 and 8), charge ordering and transport properties (Fig. 4c). The robust isotropic SC gaps with small 2Δ/kBTc in the presence or absence of the CDW seem to be consistent with a conventional s-wave pairing. This is also supported by the observed band dispersion kinks37,38 stemming from a non-negligible electron–phonon coupling, as well as the positive correlation between the coupling strength and Tc (Extended Data Fig. 6). Precisely, these results do not rule out other nodeless pairing states due to the lack of phase information in ARPES measurements. Recent μSR studies25,39 report a possible time-reversal symmetry breaking associated with the CDW state in CsV3Sb5 and the SC state in pressurized CsV3Sb5. Additionally, our recent μSR measurements on the CDW-suppressed Ta0.14 sample, which will be published elsewhere, also provide evidence for the potential presence of time-reversal symmetry-breaking superconductivity, highlighting the need for further examination. Our direct determination of the robust isotropic SC gap significantly narrows down the pairing symmetry and offers crucial insights into the pairing mechanism, thus laying a foundation for deciphering the nature of the superconductivity and its intertwined orders in these kagome quantum materials.

Methods

Growth of single crystals

High-quality single crystals of Cs(V0.86Ta0.14)3Sb5 and Cs(V0.93Nb0.07)3Sb5 were synthesized from Cs bulk (Alfa Aesar, 99.8%), V pieces (Aladdin, 99.97%), Ta powder (Alfa Aesar, 99.99%) and Sb shot (Alfa Aesar, 99.9999%) via a self-flux method using Cs0.4Sb0.6 as the flux. The above starting materials were put into an aluminium crucible and sealed in a quartz tube, which was then heated to 1,000 °C in 24 h and maintained for 200 h. After that, the tube was cooled to 200 °C at a rate of 3 °C h−1, followed by cooling down to room temperature with the furnace switched off. To remove the flux, the obtained samples were soaked in deionized water. Finally, shiny single crystals with hexagonal features were obtained.

Electronic transport measurements

Electronic transport properties of Cs(V0.86Ta0.14)3Sb5 and Cs(V0.93Nb0.07)3Sb5 crystals were measured on a physical property measurement system (Quantum Design) at a temperature range from 300 K to 1.8 K. A five-terminal method was used, at which the longitudinal resistivity and Hall resistivity can be taken simultaneously. The direct current magnetic susceptibility was measured on a magnetic property measurement system (Quantum Design) with a superconducting quantum interference device magnetometer.

High-resolution laser-ARPES measurements

Ultrahigh-resolution ARPES measurements were performed in a laser-based ARPES setup, which consisted of a continuous wave laser (hυ = 5.8 eV) provided from OXIDE Corporation and a vacuum ultraviolet laser40 (hυ = 6.994 eV, called ‘7 eV’ for convenience), a Scienta HR8000 hemispherical analyser and a sample manipulator cooled by decompression-evaporation of the liquid helium. The samples were cleaved in situ and measured under a vacuum better than 3 × 10−11 torr. The sample temperature was varied from 2 to 7 K, and the energy resolution for the superconducting gap measurements was better than 0.6 meV for the 5.8 eV laser, and 1.5 meV for the 6.994 eV laser. We checked the linearity of the detector41, and the Fermi level EF was calibrated with an in situ connected gold reference.

Summary of Fermi surface and identification of k F

The FS was obtained by integrating the ARPES intensity over ±5 meV around EF. Due to the limited detectable momentum area of the 5.8 eV laser source, we measured multiple samples to cover all the FS contours. We summarize the FS maps of the measured samples and the corresponding kF points in Extended Data Figs. 2 and 3 for Cs(V0.86Ta0.14)3Sb5 (denoted as Ta0.14) and Cs(V0.93Nb0.07)3Sb5 (denoted as Nb0.07), respectively. The kF was determined directly from the peak position of the integrated momentum distributed curve (MDC) at T > Tc over EF ± 2 meV (white dotted line in Fig. 3b). The peak position was obtained from a Lorentzian fit. It is worth noting that although the β and δ Fermi surfaces are close in momentum, the corresponding bands can be well distinguished. As shown in Extended Data Figs. 2b–d and 3b–d, the intensity of the β and δ bands are enhanced under different polarizations due to different V 3d orbital characters—s polarization for the β FS and p polarization for the δ FS.

Fitting procedure to obtain the amplitude of the SC gap

The SC gap amplitude was quantitatively determined by the fits based on the BCS spectral function42,43,44, which has the form

$${A}_{{\rm{BCS}}}(k,\omega )=\frac{1}{\pi }\left[\frac{{| {u}_{k}| }^{2}\varGamma }{{(\omega -\sqrt{{\varepsilon }_{k}^{2}+{| \Delta (k)| }^{2}})}^{2}+{\varGamma }^{2}}+\frac{{| {v}_{k}| }^{2}\varGamma }{{(\omega +\sqrt{{\varepsilon }_{k}^{2}+{| \Delta (k)| }^{2}})}^{2}+{\varGamma }^{2}}\right]$$
(1)

where |uk|2 and |vk|2 are coherence factors for the occupied and unoccupied quasiparticles, respectively, Γ is the line width broadening factor due to the finite quasiparticle lifetime, \({E}_{k}=\sqrt{{\varepsilon }_{k}^{2}+{|\Delta (k)|}^{2}}\) is the Bogoliubov quasiparticle band dispersion, εk is the band dispersion near EF in the normal state and |Δ(k)| is the SC gap amplitude. To fit the ARPES data, the BCS spectral function is multiplied by the Fermi–Dirac function and convoluted with a Gaussian function corresponding to the experimental energy resolution. Then, the EDCs at kF, obtained by integrating the ARPES intensity over kF ± 0.02 Å−1, were fitted to extract the SC gap |Δ(k)|.

Statistics of the fitted SC gap amplitude measured on different samples

By applying the fitting procedure to the EDCs at kF on the different Fermi surfaces, we obtain the momentum dependence of the SC gap amplitude, which directly reflects the pairing symmetry. As presented in Figs. 2g and 3g in the main text, we observed that the SC gap amplitudes of both the Ta0.14 and Nb0.07 samples are nearly isotropic in the momentum space. To demonstrate the small fluctuation of the SC gap amplitudes, we present the statistics of the fitted SC gap amplitudes for the Ta0.14 samples in Extended Data Table 1, and for the Nb0.07 samples in Extended Data Table 2. The average deviations are less than 0.04 meV, which means a very small fluctuation around the average value of the SC gap amplitude (\(\bar{\Delta })\). Moreover, the difference between the maximum and minimum values of the SC gap amplitudes, Δmax − Δmin, is comparable to two times the standard deviation of EF (approximately 0.06 meV), which determines the error bars for the SC gap. These demonstrate that the SC gap amplitude is almost constant in different momenta, supporting a nearly isotropic pairing gap structure. The consistent SC gap observed in different samples demonstrates the high quality of the single crystals and excludes sample-dependent influences on the SC gap.

Superconducting gap at difference k z

The FS maps of the Nb0.07 sample measured with 5.8 eV and 7 eV lasers are plotted in Extended Data Fig. 4a,d. Here we apply an inner potential of 7.3 eV (ref. 45) to calculate kz for different k//, as shown in the inset of Extended Data Fig. 4g. The EDCs at kF on the β FS are shown in Extended Data Fig. 4b for the 5.8 eV laser and Extended Data Fig. 4e for the 7 eV laser. The corresponding symmetrized EDCs are shown in Extended Data Fig. 4c,f. Because the energy resolution for the measurements with the 7 eV laser is about twice as large as that with the 5.8 eV laser, the coherence peak of the EDCs measured with the 7 eV laser is broader than that measured with the 5.8 eV laser. To effectively compare the SC gap at these two different kz, the EDCs were fitted with equation (1), with the energy resolution taken into account. The extracted SC gap amplitudes at these two kz planes are summarized in Extended Data Fig. 4g, which clearly shows that they are nearly the same within experimental uncertainties, implying a nearly isotropic SC gap along the kz direction.

Spectral evidence of electron–phonon coupling

Electron–phonon coupling (EPC) is ubiquitous in quantum materials, which could induce kinks in the band dispersion at the frequencies of the coupled phonons46,47. As shown in Extended Data Fig. 6a–c, kinks are observed on the α and β bands for all the pristine, Nb0.07 and Ta0.14 samples. These kinks are more prominent in the extracted band dispersions from the fits of the MDCs, as shown in Extended Data Fig. 6d–f. For the α band, the kink is at the binding energy EB of approximately 30 meV, whereas for the β band two kinks are distinguished at EB of approximately 10 meV and 30 meV. The EPC is enhanced for the Nb0.07 and Ta0.14 samples, which have a higher Tc compared to the pristine sample. The EPC strength can be roughly estimated by the ratio between the Fermi velocity and the velocity of the bare band47,48. Here the bare band is the band dispersion without the effect of EPC, which is assumed as a line between a high EB and EF. As shown in Extended Data Fig. 6g, with the V partially substituted by the Nb/Ta, the EPC strength on the β band (derived from V 3d orbitals) is prominently enhanced, whereas the EPC strength on the α band (derived from Sb 5p orbitals) remains nearly constant. Such enhancements of EPC in the samples with higher Tc suggest an important role of the EPC in promoting the superconductivity of the CsV3Sb5 family of materials.

Evolution of the van Hove singularities via Nb/Ta substitutions

We performed additional ARPES measurements to study the evolution of van Hove singularities (VHS) in the pristine CsV3Sb5, Nb0.07 and Ta0.14 samples. To avoid the influence of the CDW gap, the ARPES spectra were taken in the normal state (above the TCDW) along the K–M–K direction. As shown in Extended Data Fig. 7, one can find that the energy positions of the VHS show a moderate shift, whereas the corresponding superconducting gaps are always isotropic and nodeless. Such a shift of VHS is consistent with our density functional theory calculations shown in Extended Data Fig. 8. We note that two VHS can be distinguished around EF at low temperatures34,35, although only one VHS is observed here at high temperatures. Theoretically, although there are multiple VHS near the Fermi level, and electronic interactions may generate pairings with close pairing strengths, the further inclusion of electron–phonon coupling, experimentally evidenced by the band kinks shown in Extended Data Fig. 6, may lift the quasi-degeneracy and one pairing may always be dominant. Therefore, the variation of the energy position of VHS should have little effect on the pairing symmetry in realistic materials. Despite this, the unique sublattice feature at van Hove fillings and enhanced non-local electronic interactions in the kagome lattice can play an important role in generating unconventional pairing2,3,4.