Electron-hole asymmetry in the phase diagram of carrier-tuned CsV 3 Sb 5

In this work, we study the effect of electron doping on the kagome superconductor CsV 3 Sb 5. Single crystals and powders of CsV 3 Sb 5− x Te x are synthesized and characterized via magnetic susceptibility, nuclear quadrupole resonance, and x-ray diffraction measurements, where we observe a slight suppression of the charge density wave transition temperature and superconducting temperature with the introduction of electron dopants. In contrast to hole doping, both transitions survive relatively unperturbed up to the solubility limit of Te within the lattice. A comparison is presented between the electronic phase diagrams of electron- and hole-tuned CsV 3 Sb 5.

The interplay between charge density wave (CDW) order and superconductivity (SC) in the A V 3 Sb 5 (A = K, Rb, and Cs) class of kagome superconductors remains a focus of ongoing research (Ortiz et al. (2020, 2021); Yin et al., 2021). The band structure of A V 3 Sb 5 hosts a series of saddle points near the Fermi level (Ortiz et al., 2019), giving rise to Van Hove singularities theorized to promote the formation of unconventional electronic states (Kang et al., 2022; Hu et al., 2022; Wang et al., 2013; Kiesel et al., 2013). At high temperatures, nesting effects combined with electron–phonon coupling are proposed to stabilize the formation of a CDW state (Tan et al., 2021; Li et al., 2021; Xie et al., 2022). At lower temperatures, superconductivity arises from this CDW state, and the coupling between the two phase transitions can provide insights into several proposed instabilities in this class of materials.

Specifically, the coupling between CDW order and SC in A V 3 Sb 5 compounds has been experimentally explored through several approaches. These include tracking the evolution of both order parameters as the system is perturbed via chemical pressure (Ortiz et al., 2023; Li et al., 2022; Liu et al., 2022a,b; Zhou et al., 2023), change in dimensionality (Song et al., 2021; Wang et al., 2021; Song et al., 2023), external pressure (Wang et al., 2021; Feng et al., 2023; Yu et al., 2021; Chen et al., 2021; Du et al., 2021; Zhang et al., 2021; Chen et al., 2021; Zhu et al., 2022; Wang et al., 2021; Du et al., 2022; Yu et al., 2022; Zheng et al., 2022), uniaxial strain (Qian et al., 2021), and chemical doping (Oey et al., 2022a; Oey et al., 2022b; Liu Y. et al., 2022; Yang et al., 2022; Liu et al., 2023; Ding et al., 2022; Sur et al., 2023). One function of these perturbations is to shift the chemical potential about the multiple Van Hove singularities nearby; however, the dominant perturbation in the case of doping is often considered to be the orbitally selective modification of the Sb p z pocket at the Γ point in the Brillouin zone (LaBollita and Botana, 2021).

In the case of carrier doping, hole doping has been shown to rapidly drive the suppression of long-range CDW order and an accompanying increase in the SC transition temperature (T c) (Oey et al., 2022b; Yang et al., 2022; Oey et al., 2022a). In the case of CsV 3 Sb 5, T c evolves in a non-monotonic fashion, and two SC domes emerge. The second dome appears in the regime where the long-range CDW is fully suppressed, and there are qualitative similarities observed in the pressure-tuned phase diagram of CsV 3 Sb 5 (Yu et al., 2021; Chen et al., 2021; Zhang et al., 2021). The evolution of charge correlations into an incommensurate, quasi-1D regime beyond the phase boundary of 3D CDW order suggests a link between the formation of two SC domes and a crossover in the character of charge correlations (Kautzsch et al., 2022; Feng et al., 2023).

One less explored question is whether there exists an electron-hole asymmetry in the carrier-tuned phase diagram of CsV 3 Sb 5. In a rigid band shift model, the relative shift of the Van Hove points relative to E F should be important to the response of the system, and in the more realistic case of orbitally selective doping, the impact of the relative changes in the Sb p z mixed bands on the CDW state should inform more about their role in the formation of charge order. Prior studies have partially explored hole and electron doping via substitution on the vanadium sites of Ti (Yang et al., 2022) and Cr (Ding et al., 2022), respectively. While Ti doping shows a non-monotonic evolution of SC as CDW order is suppressed, Cr doping instead shows a slower suppression of CDW order and a rapid quenching of T c. Given the strong disorder potential introduced by directly replacing the kagome net atoms, the impact of dopant-induced disorder remains uncertain in interpreting these phase diagrams. Naively, a cleaner means of introducing holes has been demonstrated via the substitution of Sn onto the Sb sites of CsV 3 Sb 5− x Sn x which preserves the core V-based kagome matrix (Oey et al., 2022b). This doping away from the V-sites generates an anomalous double-dome evolution in T c as long-range CDW order is destabilized. The electron-doping counterpart to this can be achieved via Te substitution onto the Sb sites in CsV 3 Sb 5− x Te x, which is the focus of this paper.

Here, we present x-ray diffraction, nuclear quadrupole resonance, and susceptibility measurements characterizing the Te-substituted (electron-doped) phase diagram of CsV 3 Sb 5. Our data demonstrate a limited solubility of Te into the CsV 3 Sb 5− x Te x matrix before phase separation occurs near x ≈ 0.08 and that Te preferentially occupies the Sb sites in the V-kagome plane. In contrast to hole doping, the introduction of electrons results in a relatively weak perturbation to the system—where the CDW onset temperature is only slightly suppressed and SC is weakly suppressed in a monotonic fashion. The likely dominant driver of the weak suppression of both states is the introduction of disorder via Sb substitution, establishing a sharp contrast to the hole-doped phase diagram of this system.

2.1 Powder and single crystal synthesis

Powders of CsV 3 Sb 5− x Te x were synthesized inside a glovebox filled with argon (water and oxygen levels at < 0.5 ppm) by measuring stoichiometric amounts of elemental Cs (solid, Alfa 99.98%), V (powder, Sigma 99.9%, previously purified using a 1:10 ratio of EtOH and HCl), Sb (shot, Alfa 99.999%), and Te (lump, Alfa 99.999%). For each composition of Te doping, 6 g batches of the starting materials were ball-milled inside a tungsten carbide vial for 60 min in a SPEX 8000D high-energy ball mill. The resulting powders were extracted inside a glovebox, ground, and sieved through a 106 micron sieve. Powders were then placed inside an alumina crucible, sealed inside an argon-filled quartz tube, and annealed at 550°C for 48 h. A post-anneal grind and sieve was performed followed by a second anneal at 450°C for 12 h. The final powders are gray and reasonably air-stable.

Single crystals of CsV 3 Sb 5− x Te x were grown by a self-flux method. Different Te concentrations were targeted by the formula Cs 20 V 15 Sb 120 − x Te x, with x = 7.2 and 9.6. Elements were weighed inside a glovebox to make 4 g batches of fluxes; each batch was loaded into tungsten carbide vials and ball-milled for 60 min. Precursors were then extracted, loaded into alumina crucibles, and sealed inside carbon-coated quartz tubes. Previous attempts at synthesizing CsV 3 Sb 5− x Te x crystals were performed inside sealed steel tubes but were unsuccessful, given that elemental Te corrodes steel. The sealed tubes were heated at 900 ° C for 12 h and then cooled to 500°C at 2°C/h. Single crystals were extracted manually using isopropyl alcohol.

2.2 Experimental details

Powder x-ray diffraction data were collected on a PANalytical Empyrean powder diffractometer. Pawley and Rietveld refinements were performed using TOPAS-Academic software (Coelho, 2018). A tabletop scanning tunneling microscope (SEM) (Hitachi TM4000Plus) was used to analyze concentrations of Te in single crystal samples. Magnetization data for both powders and crystals were measured inside a Quantum Design Magnetic Property Measurement System (MPMS) using the vibrating sample mode (VSM) to detect the superconducting transitions under a field of 5 Oe and measure the charge density wave transition under 10,000 Oe. Low-temperature susceptibility data were collected using a Quantum Design Physical Property Measurement System (PPMS) with a dilution refrigerator insert and the AC susceptibility option. Room-temperature 121 Sb zero-field nuclear quadrupole resonance (NQR) measurements were performed using a laboratory-made NMR spectrometer and probe. Quadrupole lines from the I = 5 / 2 Sb nuclei were collected from Fourier transforms of the spin-echo using the same sequence and approach as detailed in the work of Oey et al. (2022b). Two distinct Sb chemical sites are present in the unit cell, which we label Sb1 and Sb2, and they generate unique frequencies.

Powders and single crystals of CsV 3 Sb 5− x Te x were synthesized in the composition range 0 ≤ x ≤ 0.1. The 300 K structure remains P 6 /mmm across this composition range, and the tellurium dopants occupy the Sb1 site in the kagome plane, as shown in Figure 1. Demonstrating this, NQR data plotted in Figure 1C, D show the preferential chemical shift of only the Sb2 sites at both NQR transitions probed. Using the same reasoning as that presented by Oey et al. (2022b), this indicates that Te preferentially occupies the in-plane Sb1 positions, as only changes to Sb1–Sb2 field gradients are observed and (similar distance) Sb2–Sb2 field gradients are unaffected.

Lattice parameters derived from Pawley refinements of powder x-ray data are shown in Figure 2. The resulting c/a ratio plotted in Figure 2A reveals a continuous decrease up to a concentration of x ≈ 0.07, and for concentrations greater than x = 0.08, impurity peaks are observed in the x-ray powder patterns, shown as ‘*’ in Figure 2C. This suggests that the solubility limit is x ≈ 0.07–0.08 of Te within the lattice, and a similar deviation from a linear Vergard-like behavior is suggested in the a - and c -axis lattice parameters plotted in Figure 2B on the left and right sides (although the changes are small and at the boundary of resolution).

Now turning to the characterization of CsV 3 Sb 5− x Te x below the solubility limit, magnetization and susceptibility data are plotted in Figure 3. Figure 3A shows low-field susceptibility data characterizing the superconducting transition of polycrystalline CsV 3 Sb 5− x Te x up to x = 0.08. Susceptibility data collected using a dilution insert (4 K–80 mK) was normalized to overlapping low-field magnetization-derived susceptibility data above 2 K. Within the uncertainty of this normalization procedure and variable packing fractions between powders, all specimens show a bulk superconducting transition in Figure 3A. In contrast to the effect of hole doping, T c shows a monotonic and gradual decrease as a function of Te concentration.

Magnetization measurements collected under 10,000 Oe were performed at higher temperatures to characterize the CDW instability. These measurements can detect the onset of a CDW state via a decrease in the density of states at the Fermi level, reflected in a decrease in the Pauli spin susceptibility. Magnetization data plotted in Figure 3C reveal that a well-defined CDW transition remains observable for all compositions up to x = 0.08. This strongly contrasts the response observed upon hole doping, where the introduction of Sn immediately broadens and shifts the CDW transition. Quantifying the shift in the CDW onset temperature, Figure 3D plots the derivative δMT/δT, revealing a smooth shift downward in the CDW temperature upon Te doping with minimal broadening of the CDW anomaly in the magnetization data. This is again distinct from the response driven via hole substitution, where a rapid broadening immediately onsets and the CDW transition vanishes near x = 0.05 holes per formula unit. We note here that an upturn in the susceptibility at lower temperatures is also observed in all samples, and this can be modeled by a small fraction of paramagnetic ions in the powders (≈0.1% S = 1/2 moment per vanadium ion).

Our results are summarized in Figure 4, where the electronic phase diagram of hole- versus electron-doped CsV 3 Sb 5 is plotted (i.e., Sn versus Te doped). Both electron and hole dopants result in the suppression of the CDW transition temperature; however, the suppression is more rapid for hole doping, and the transition vanishes near x = 0.05. In contrast, the suppression of the CDW temperature is more gradual with electron doping, and crucially, the CDW transition remains well defined until the solubility limit of Te is reached. The SC transition evolves smoothly downward with electron doping and does not follow a trivial enhancement via a trade-off in the density of states as the parent CDW state is weakened. This simultaneous suppression of the CDW onset temperature and T c suggests that disorder introduced via chemical alloying may play a role in the suppression of each phase.

To test this, select single crystals of CsV 3 Sb 5− x Te x were measured, and their transition temperatures were overplotted with those from powder samples in Figure 4. The apparent onset temperature of the CDW state is always higher in powders than in crystals, but both crystals and powders show a qualitatively similar smooth decrease in the CDW transition up to the solubility limit. However, the superconducting T c in powders is often degraded relative to single crystals due to disorder effects (such as strain and plastic deformation) incurred during powder preparation. As a result, trends in T c as a function of doping are often more reliable in crystals. Figure 4 shows that the T c for single crystals of CsV 3 Sb 5− x Te x is indeed higher than that of powders and that the suppression of T c with Te doping is severely reduced. This supports the notion of a disorder-induced suppression of T c as a function of impurity concentration rather than electron doping. Notably, the canonical trade-off between the suppressed CDW order and enhanced SC due to density of states effects is absent, further supporting the idea of a dominant role of the dopant-induced disorder.

The aforementioned results are derived using chemical dopants that avoid the V-sites in the kagome network; however, qualitatively similar trends in the evolution of CDW and SC order parameters have been reported in individual studies leveraging V-site substitution. Ti-doped CsV 3 Sb 5 renders a phase diagram qualitatively similar to Sn-doped CsV 3 Sb 5 (Yang et al., 2022), and Cr-doped CsV 3 Sb 5 also reveals an asymmetric persistence of the CDW order (Ding et al., 2022). We note one difference: T c is reported to be rapidly suppressed in Cr-doped samples, which is distinct from our Te-doped data. This is likely due to a stronger impurity potential native to the Cr dopants residing directly within the kagome network, and we hypothesize that the slow, simultaneous suppression of the CDW and SC is primarily driven by the dopant disorder.

In conclusion, our results illustrate a strong electron–hole asymmetry in the electronic phase diagram of carrier-doped CsV 3 Sb 5. Electron doping via Te substitution in CsV 3 Sb 5− x Te x largely preserves the CDW state, whereas hole doping rapidly suppresses the long-range CDW order and renormalizes the nature of charge correlations. At lower temperatures, light electron doping also largely preserves the superconducting state, whereas hole doping creates a non-monotonic, “double-dome” response. We suggest that the slight suppression in the onset temperatures of both the CDW and SC orders observed upon Te substitution arises from alloy-induced disorder rather than a doping-driven effect and that both transitions are robust to light electron doping. Our findings motivate a deeper theoretical exploration of electron–hole asymmetries in the carrier-tuned band structure of CsV 3 Sb 5 and related compounds as a means of isolating the dominant Van Hove points and other band features responsible for driving electronic order in this family of compounds.