Introduction

Charge correlations and the nature of charge density wave (CDW) order within the class of AV3Sb5 (A=K, Rb, Cs) kagome superconductors1,2,3,4 are hypothesized to play a crucial role in the anomalous properties of these compounds. Hints of pair density wave superconductivity5,6, magnetochirality and nonreciprocal transport7,8, as well as orbital magnetism9,10,11,12 in these compounds are all born out of a central CDW state13,14,15. The CDW order parameter itself is theorized to host both primary, real and secondary, imaginary components16, each of which is thought to play a role in the anomalous properties observed in AV3Sb5 compounds.

The real component of the CDW state manifests primarily as a 2 × 2 reconstruction within the kagome plane driven via a 3q distortion into either star-of-David (SoD) or (its inverse) tri-hexagonal (TrH) patterns of order17. In-plane distortions are further correlated between kagome layers13,18,19,20, either through correlated phase shifts of the same distortion type between neighboring layers, via alternation between distortion mode types, or a combination of both21.

The parent CDW state of CsV3Sb5 forms a lattice whose average structure is comprised of a modulation between SoD and TrH distortion modes along the interlayer c-axis below TCDW = 94 K19,22,23. Locally, the CDW supercell arises from a nearly degenerate mixture of states with 2 × 2 × 4 and 2 × 2 × 2 cells whose selection is dependent upon subtle effects such as thermal history and strain conditions imparted during growth24,25. While the interlayer stacking details are a low energy feature susceptible to small perturbations, the dominant feature of the CDW in all cases is the 2 × 2 reconstruction in the ab-plane, representing a commensurate charge modulation on the kagome lattice.

Upon cooling deeper into the CDW state, hints appear of a staged behavior within the in-plane charge modulation, suggestive of another coexisting or competing CDW instability. Scanning tunneling microscopy (STM) measurements resolve commensurate, quasi-1D charge stripes that form near T ≈ 60 K and coexist with the 2 × 2 in-plane CDW order14, while transient reflectivity26 and Raman measurements27 also resolve a shift/new modes in the lattice dynamics near this same energy scale. Sb NQR and V NMR measurements further observe a chemical shift in this temperature regime28, demonstrating a structural response to a modified CDW order parameter—one potentially driven by competing CDW correlations.

Further supporting the notion of a nearby charge state competing with the parent CDW order is the rapid suppression of thermodynamic/transport signatures of the CDW state in CsV3Sb5 under moderate pressure29,30 or via small levels of hole-substitution31. By substituting ≈ 6% holes per formula unit, the CDW state seemingly vanishes in thermodynamic measurements, whereas superconductivity undergoes a nonmonotonic response and generates two superconducting domes. Understanding the evolution of charge correlations between these two domes stands to provide important insights into in the origin of the unconventional coupling between CDW order and superconductivity reported in CsV3Sb5.

Here we track the evolution of charge correlations in CsV3Sb5−xSnx as holes are introduced via Sn-substitution and the in-plane 2 × 2 CDW state is suppressed. X-ray diffraction data resolve that very light Sn-substitution (x = 0.025) suppresses CDW correlations, and the CDW immediately becomes short-ranged along the interlayer axis. Increased hole-doping reveals continued shortening of interlayer correlations and the suppression of in-plane 2 × 2 CDW order; however, this suppression of commensurate 2 × 2 order is accompanied by the emergence of competing quasi-1D, incommensurate charge correlations (x = 0.15). Parallel STM measurements also observe the persistence of low-temperature quasi-1D charge stripes in the absence of 2 × 2 CDW order32. Our data unveil a complex landscape of competing charge correlations that evolve across the superconducting domes of this material.

Results

X-ray diffraction data and analysis

To understand the evolution of charge correlations across the electronic phase diagram of CsV3Sb5−xSnx, two Sn concentrations were chosen as shown in Fig. 1(a). The first x = 0.025 concentration possesses both a superconducting state with an enhanced Tc and a clearly observable CDW transition as shown in Fig. 1(b), (c). The second x = 0.15 concentration retains a SC phase transition but the thermodynamic signature of 2 × 2 CDW order in susceptibility has vanished as shown in Fig. 1(d), (e).

Fig. 1: Evolution of electronic order in CsV3Sb5−xSnx.
figure 1

a Electronic phase diagram of Sn-doped CsV3Sb5 showing the evolution of both CDW and SC order with hole-doping in powder samples. Data are reproduced from ref. 31. b and c Show susceptibility data characterizing the superconducting and CDW states of a crystal with the x = 0.025 composition in the first SC 'dome' and (d) and (e) show susceptibility data characterizing the superconducting and CDW states of a crystal with the x = 0.15 composition in the second SC 'dome'.

Full size image

Looking first at the x = 0.025 crystal, maps of x-ray diffraction data were collected with representative data plotted in Fig. 2(a) and (b). Figure 2(a) plots scattering within the (H, K, 1.5)-plane. Reflections centered at (H, K)=(0.5, 0.5)-type positions indicate that the parent 2 × 2 in-plane CDW order remains in the x = 0.025 compound. However, interlayer correlations are altered. Fig. 2(c) plots scattering within the (H, 1.5, L)-plane, showing that c-axis correlations shift to become substantially shorter-range and center primarily at the L = 0.5 positions. This marks a suppression of 2 × 2 × 4 correlations in the undoped material and a transition into a short-range CDW state whose q vectors match those of undoped (K,Rb)V3Sb513.

Fig. 2: X-ray scattering from a x = 0.025 crystal.
figure 2

a Map of x-ray scattering intensities in the (H, K, 1.5)-plane for the x = 0.025 sample at T = 11 K. b One dimensional H-cuts through the (−3, −2.5, 1.5) position for both x = 0 and x = 0.025. Solid lines are Gaussian fits to the data. c Map of x-ray scattering intensities in the (H, 1.5, L) plane for the x = 0.025 sample. d One-dimensional L-cuts along H=1 for both the x = 0 and x = 0.025 samples. Solid lines are pseudo-Voigt fits for the x = 0.025 sample with the Gaussian component fixed to the instrument’s resolution.

Full size image

The in-plane correlation lengths associated with CDW peaks in the x = 0.025 sample are slightly reduced, shortening from resolution-limited in the undoped material to ξH = 367 ± 6 Å. Interplane correlation lengths shorten dramatically, reducing to ξL = 70 ± 2 Å. CDW peak intensities and positions are symmetric with respect to ± L, and Fig. 2(c) provides a narrower field of view for clarity. Weak reflections also appear at integer L positions with shorter correlation lengths ξL = 40 ± 2 Å. Similar weak, integer L reflections also appear in the undoped x = 0 compound, and their presence likely reflects that interlayer correlations are heavily impacted by local minima upon rapid cooling24,25,27. The difference in correlation lengths between half-integer and integer L CDW reflections in the x = 0.025 sample reflects two distinct patterns of c-axis modulation present prior to reaching a doping level where the CDW becomes truly two-dimensional.

At this small doping level, the immediate disappearance of L=0.25 type peaks demonstrates a reduction in the mixed character of CDW order and suggests a switch from a state with modulating SoD and TrH order into one with phase-shifted planes of a single distortion type, similar to (K,Rb)V3Sb522. This crossover into another CDW phase at light doping may drive the formation of the first SC dome in the phase diagram of CsV3Sb5−xSnx; however a quantitative refinement of the isolated 2 × 2 × 2 CDW state will be required to further understand the mechanism.

Examining charge correlations outside of the nominal 2 × 2 CDW phase boundary, x-ray scattering data for the x = 0.15 sample are plotted in Fig. 3. Panels (a) and (b) show a representative schematic of the scattering and data in the (H, K, − 0.5)-plane. Data collected at half-integer L values indicate a superposition of three quasi-1D patterns of charge scattering. This can be understood in a model of charge correlations forming preferentially along one unique in-plane axis (i.e., H or K), reducing the sixfold rotational symmetry to twofold, and forming three domains rotated by 120° in real space. These quasi-1D domains vanish upon warming as shown in Fig. 3(d), similar to CDW domain formation in the undoped x = 0 system observed in optical and STM measurements9,14.

Fig. 3: X-ray scattering from a x = 0.15 crystal.
figure 3

a Schematic of x-ray scattering in the (H, K)-plane about a representative zone center for the x = 0.15 sample. Scattering from three domains is illustrated and cut directions for corresponding panels are labeled. b Map of x-ray scattering intensities for x = 0.15 at T = 11 K plotted about (H, K, −0.5) (c) One-dimensional cut along H as illustrated in (a), (d) Map of x-ray scattering intensities for x = 0.15 at T = 260 K (e, f) One-dimensional cuts along K and L as illustrated in (a). Solid lines are the results of pseudo-Voigt fits to the peak lineshapes with the Gaussian component constrained to the instrument’s resolution.

Full size image

Looking at scattering from a single domain, charge correlations form an incommensurate state with qinc = 0.37 along a preferred in-plane axis. This is illustrated via a representative cut along H plotted in Fig. 3(c). Within the (H, K)-plane, correlations along qinc are short-ranged with ξH = 66 ± 2 Å and are substantially longer-ranged orthogonal to the direction of modulation with ξK = 176 ± 7 Å (Fig. 2(e)). As shown in Fig. 3(f), the peak of these quasi-1D correlations is centered at the L = − 0.5 position with a short-correlation length of ξL = 18 ± 1 Å, reflecting an anti-phase modulation between neighboring kagome layers correlated only between neighboring V-planes. We note here that all of these charge density correlation lengths are substantially longer than the projected distance between Sn-dopants assuming an isotropic distribution. Analysis of scattering attributed to the other two domains is presented in Supplementary Figs. 1–4.

Scanning tunneling microscopy data and analysis

To further investigate the local evolution of charge correlations, STM measurements were performed on the x = 0.15 sample at T = 4.5 K. Figure 4(a), (b) show STM topographs of the Sb surface over different fields of view where dark hexagonal defects correspond to individual Sn dopants. Counting these defects is consistent with the expected Sn concentration x = 0.15. Specifically, STM analysis counts Sn-dopants on the surface at a concentration between x=0.08 and x=0.10, within the ≈ 1 atm % resolution of EDS measurements. One-dimensional, stripe-like features are apparent in the STM topograph (Fig. 4(a) and (b)), which can be more easily quantified via the Fourier transform plotted in Fig. 4(c). In this Fourier map, quasi-1D correlations are observed along one of the atomic Bragg peak directions with a map-averaged qinc ≈ 0.2, reminiscent of the previously identified 4a0 charge stripes in the undoped system14. The superlattice peaks at the 2 × 2 (or q2D-CDW) CDW positions are notably absent. This is further demonstrated via the line cuts through the Fourier map along the three lattice directions, where no scattering peaks can be observed at 2 × 2 positions (Fig. 4(d)).

Fig. 4: Scanning tunneling microscopy data for a x = 0.15 crystal.
figure 4

a and b show STM topography images of CsV3Sb5−xSnx with x = 0.15. Red arrows in (b) highlight several representative Sn dopants that can be seen as dark hexagons in the STM topograph, (c) Fourier transform of the STM topography showing the presence of quasi-1D, q1D-CO correlations, and the absence of 2 × 2 (q2D-CDW) correlations, (d) One dimensional line cuts through the Fourier map in (c), (e–g) Quasiparticle interference spectra collected at 0 mV, −105 mV, and −210 mV biases respectively. The circular scattering from q1 due to the Sb pz states is marked. h The dispersion of the QPI pattern showing the bottom of the Sb pz band has risen to ≈ − 500 meV. Label q1D-CO denotes the momentum-transfer space (q-space) position of the 1D CDW wave vector; the label q2D-CDW marks the q-space location where FT peaks associated with the 2 × 2 CDW state would be expected.

Full size image

To gain insight into the electronic band structure, quasiparticle interference (QPI) imaging is plotted in Fig. 4. Fourier transforms of STM dI/dV maps in Fig. 4(e)–(g) show the electron scattering and interference pattern as a function of increasing STM bias (binding energy). The dominant dispersive scattering wave vector is the nearly isotropic central circle (labeled q1), which arises from scattering within the Sb pz band that crosses through EF. Hole-doping is predicted to be orbitally-selective and should preferentially dope this band31,33, pushing the bottom of the band closer to EF. Figure 4 (h) shows the resulting dispersion of q1, where it can be seen that the bottom of the Sb pz band has been pushed up from below − 600 meV in the x = 0 parent system14 to ≈ − 500 meV in the x = 0.15 sample. This is consistent with DFT expectations of hole-doping achieved via the replacement of in-plane Sb atoms with Sn.

The persistence of stripe-like correlations on the surface of the x = 0.15 sample in the absence of the 2 × 2 CDW state suggests that the interactions driving this surface order are linked to the formation of the quasi-1D order resolved in the bulk via x-ray scattering measurements. In STM data, the only charge correlations that break translational symmetry are inhomogeneous, incommensurate stripes, and, diffraction measurements show that incommensurate charge modulations should be present. We therefore hypothesize that the quasi-1D correlations sampled in diffraction and STM data arise from the same instability, with the precise wave vector of the quasi-1D stripes modified by the surface in STM studies. The wave vector could be modified by potential surface doping due to the polar surface and removal of Cs for STM measurements or the correlations could be modified by surface strain. Future measurements will be required to prove the hypothesis that both quasi-1D correlations sampled in x-ray and STM measurements arise from a common origin.

Quasi-1D correlations were observed in STM measurements to pin at the surface below ≈ 60 K in undoped CsV3Sb514 and coherent, quasi-1D band features appear in the differential conductance dI/dV maps at low temperature34, reflective of a strong coupling between these correlations and the electronic structure. Estimates of the onset temperature of quasi-1D correlations in the x = 0.15 sample show that they persist to 60 K and optical data suggest they form in a similar temperature range (Supplementary Fig. 5). We note here that the short-range nature of the charge-correlations in the x = 0.15 sample means that there is no clear thermodynamic anomaly in heat capacity or magnetization data that makes their onset temperature readily apparent.

Discussion

The incommensurate character of the CDW correlations in the x = 0.15 sample stresses the importance of electron-electron interactions in this regime of the phase diagram. A 2kf nesting instability can, in principle, arise once the 2 × 2 reconstruction of the original Fermi surface is lifted and the Fermi level is shifted downward via hole-doping. In the absence of the reconstructed 2 × 2 cell, the nesting wave vector should be doping dependent, and future studies at higher Sn-concentrations can test this conjecture. Parallels to reported pressure-tuned phase diagrams of CsV3Sb5 can also be suggested. Both hydrostatic pressure29,35 and hole-doping31 have been shown to create ’double dome’ type superconducting phase diagrams featuring the rapid suppression of long-range CDW order. A recent NMR study has also suggested the presence of a stripe-like CDW state that emerges in the second superconducting dome once the parent triple-q CDW order is suppressed36.

More broadly, our experiments establish AV3Sb5 as a promising platform for the studies of charge-stripe physics and draw comparisons with the extensively studied 4a0 charge ordering in cuprates37. For example, the sizable doping dependence of charge ordering in Bi-based cuprates38 appears qualitatively similar to observations in CsV3Sb5−xSnx. Given the suppression of charge ordering in cuprates in the overdoped regime, it will be of interest to explore the fate of stripe-like correlations in CsV3Sb5 at an even higher doping level, as samples with higher Sn composition are developed in the future and the multigap superconducting phase is completely suppressed39. Initial STM data suggest that, in the low doping regime, the surface wave vector of the quasi-1D correlations evolves with Sn-concentration (Supplementary Figs. 6–8).

In summary, our results demonstrate a complex landscape of charge correlations in the hole-doped kagome superconductor CsV3Sb5−xSnx. Light hole-doping eliminates 2 × 2 × 4 supercell charge correlations and suppresses long-range interlayer correlations. Continued hole-doping results in the suppression of the 2 × 2 commensurate CDW state and the striking stabilization of quasi-1D, incommensurate charge correlations. These emergent, quasi-1D correlations demonstrate an underlying electronic rotational symmetry breaking present across the phase diagram of this system and are suggestive of a 2kf nesting instability at the Fermi surface. These results provide important experimental insights into competing charge correlations in the class of AV3Sb5 superconductors and crucial input for modeling the unconventional interplay between charge density wave order and the low-temperature superconducting ground state.

Methods

Crystal growth

CsV3Sb5−xSnx crystals with x = 0.025 and x = 0.15 were made with a flux of Cs20V15Sb90Sn30 and Cs20V15Sb106Sn34 respectively. Fluxes were ball-milled for 60 mins and then packed into alumina crucibles, and sealed under inert atmosphere within stainless steel tubes. Tubes were heated to 1000 °C and kept at 1000 °C for 12 h and then cooled quickly to 900 °C, and then slowly cooled (2 °C/hour) to 500 °C. Undoped x = 0 crystals were grown using the method previously reported2.

Single crystal X-ray diffraction

Temperature-dependent synchrotron x-ray diffraction were collected at the ID4B (QM2) beamline, CHESS. In ID4B measurements, temperature was controlled by a stream of cold helium gas flowing across the single-crystal sample. An incident x-ray of energy 26 keV (λ = 0.6749 Å) was selected using a double-bounce diamond monochromator. Bragg reflections were collected in transmission mode, and the sample was rotated with full 360° patterns, sliced into 0.1° frames.

Scanning tunneling microscopy measurements

STM data were acquired using a Unisoku USM1300 STM at approximately 4.5 K. Spectroscopic measurements were made using a standard lock-in technique with 915 Hz frequency and bias excitation. STM tips were custom-made chemically-etched tungsten tips, annealed in UHV to bright orange color prior to the measurements.

Optical pump-probe reflectivity measurements

Optical pump-probe reflectivity measurements similar to those in Ratcliff et al.26 were performed on a cleaved single crystal of nominal composition CsV3Sb4.8Sn0.15 mounted in an optical cryostat. Pump and probe pulses were linearly polarized in-plane and configured in a cross-polarized geometry, with the pump center wavelength at 760 nm and the probe center wavelength at 800 nm. The ≈ 50 fs optical pulses were incident at a repetition rate of 250 kHz with a fluence of 100 μ J cm2. A lock-in amplifier and optical chopper were used to measure the pump-induced transient change in reflectivity of the probe. To isolate coherent phonon oscillations, an exponential background was subtracted from the transient response before Fourier transforming to the frequency domain. Scans at different temperatures were normalized to the intensity of the fully symmetric phonon at 4.1 THz.