Superconductivity in (Ba,K)SbO₃

Abstract

(Ba,K)BiO₃ constitute an interesting class of superconductors, where the remarkably high superconducting transition temperature T_c of 30 K arises in proximity to charge density wave order. However, the precise mechanism behind these phases remains unclear. Here, enabled by high-pressure synthesis, we report superconductivity in (Ba,K)SbO₃ with a positive oxygen–metal charge transfer energy in contrast to (Ba,K)BiO₃. The parent compound BaSbO_3−δ shows a larger charge density wave gap compared to BaBiO₃. As the charge density wave order is suppressed via potassium substitution up to 65%, superconductivity emerges, rising up to T_c = 15 K. This value is lower than the maximum T_c of (Ba,K)BiO₃, but higher by more than a factor of two at comparable potassium concentrations. The discovery of an enhanced charge density wave gap and superconductivity in (Ba,K)SbO₃ indicates that strong oxygen–metal covalency may be more essential than the sign of the charge transfer energy in the main-group perovskite superconductors.

High-pressure synthesis is used to stabilize superconducting (Ba,K)SbO₃, whose properties provide a fresh perspective on the origin of superconductivity in these types of materials.

Main

Superconducting bismuthates, BaPb_1–xBi_xO₃ (BPBO)¹ and Ba_1–xK_xBiO₃ (BKBO)^2,3, have attracted considerable research interest since their discovery more than three decades ago. The parent compound BaBiO₃ (BBO) is known to be a non-magnetic, commensurate charge density wave (CDW) insulator. The CDW order is accompanied by a breathing octahedral distortion; that is, two octahedra with different sizes order in a three-dimensional chequerboard pattern^4,5. As the CDW order is suppressed via chemical substitution of Bi with Pb or Ba with K (refs. ^6,7), the compounds become superconducting up to a maximum T_c of 12 K in BPBO, and 30 K in BKBO. Numerous experiments have established that the mechanism of superconductivity is largely conventional; the pairing symmetry is s-wave⁸, and the oxygen isotope effect is consistent with the Bardeen–Cooper–Schrieffer (BCS) theory⁹, meaning electron–phonon interaction plays the important role in superconductivity. Nevertheless, the unexpectedly high T_c of BKBO, despite a rather low carrier density, has triggered various critical questions as to the driving mechanism and the correct model of the CDW order and superconductivity in these materials. For example, recent studies suggest that the additional consideration of long-range exchange interactions and many-body effects can be crucial for the quantitative description of the CDW gap^10,11 as well as for superconductivity^12–14.

Superconducting bismuthates have long been considered as archetypal candidates for unconventional superconductors in which an effective electron–electron interaction U is negative ^15,16, leading to electron pairing in real as well as in momentum spaces^17,18. The real-space pairing occurs in the parent compound BBO, which is argued to be a typical valence-skipping compound with unstable tetravalent bismuth (6s¹) disproportionated into tri- (6s²) and pentavalent (6s⁰). As the charge disproportionation on the bismuth sites is suppressed via chemical doping and the bismuth valence starts to dynamically fluctuate, negative U, which causes pairing of two electrons in the Bi³⁺–O₆ octahedra, could also pair them in k-space. The negative U model may provide a possible framework to understand superconductivity in the bismuthates as well as some chalcogenides¹⁹ with valence-skipping elements.

While the negative U model emphasizes the role of bismuth, an alternative model asserts the role of oxygen and its hybridization with bismuth^6,20–22. This model’s foundation is that the charge transfer energy Δ_CT of the bismuthates is negative, as the on-site energy of the Bi 6s orbital is lower than that of the oxygen 2p, owing to the large scalar relativistic effect of heavy bismuth²³. Consequently, electronic states around the Fermi level (which originate from the strongly hybridized spσ* states) show predominantly oxygen 2p character. This crucially modifies the preceding understanding of the CDW order in BBO; it should be described not by the charge disproportionation (6s² + 6s⁰) but rather by the bond-length disproportionation as 6s² + 6s²L², where L denotes a ligand hole. Spectroscopic evidence supports the oxygen-hole model^24–26. As the CDW order is suppressed, oxygen holes become delocalized, giving rise to superconductivity, possibly via strong electron–phonon coupling^21,27. The importance of oxygen holes has previously been demonstrated in the Zhang–Rice model²⁸ for cuprates, in which holes on the copper and oxygen sites form a strongly hybridized singlet state, highlighting their potential role in understanding the CDW order and high-T_c superconductivity in the bismuthates as well.

In spite of their scientific importance, a contrastive analysis of the effects of bismuth and oxygen has so far been limited due to lack of compounds analogous to the bismuthates. Perovskite antimonates are ideal candidates to study; antimony is isovalent to bismuth. Higher on-site energy of the Sb 5s orbital compared to the Bi 6s may enable us to tune the Δ_CT of the material from negative to almost zero or even positive; therefore the states around the Fermi level are expected to show stronger metal s character. First-principles calculations of a hypothetical primitive cubic perovskite BaSbO₃ (BSO) have been previously conducted and compared with those of BBO^29–31. The results clearly indicate that the Sb 5s level is well above the Bi 6s level, increasing Δ_CT from established negative values in BBO to higher energy values in BSO. It would therefore be enlightening to see the impact of this drastic change of Δ_CT on both superconductivity and CDW in antimonates, which should give us a hint to identify the key ingredient of high-T_c superconductivity in BKBO.

Several attempts have been made to synthesize superconducting antimonates, but with limited success. It was reported that partially doped BaPb_0.75Sb_0.25O₃ becomes superconducting³², but its T_c is substantially decreased compared to that of BPBO. However, superconducting perovskite antimonates, with only antimony occupying the octahedral sites of perovskites, have yet to be experimentally reported, to the best of our knowledge. This is probably because the strongly covalent Sb–O bond is known to hamper forming 180 degree Sb–O–Sb bonds³³, and as a consequence, no perovskite antimonates have been realized to date except a highly distorted insulating NaSbO₃ (ref. ³⁴). Here, we report superconducting antimonates Ba_1−xK_xSbO₃ (BKSO), which we were able to stabilize via high-pressure high-temperature synthesis routes, enabling clarification of possible driving mechanisms for CDW and superconductivity in the compounds by comparing their properties with the sibling compound, BKBO.

To shed light on the effects that varying Δ_CT has on the electronic structure, the band structures of BKSO as well as BKBO are calculated via a hybrid density functional theory (DFT) method¹⁰, as shown in Fig. 1 (total and projected density of states (DOS) are in Extended Data Fig. 1). The calculations are conducted for primitive cubic structures without the breathing distortions, which were experimentally obtained at the potassium concentration x = 0.65. The band structure of BKBO in Fig. 1b comprises the spσ* band around the Fermi level and the spσ band below –7 eV, which lie above and below the non-bonding flat O 2p_π bands (around –2 and –4 eV), respectively. The band structure of BKSO in Fig. 1d shares these common overall features, but the locations of the O 2p_π bands are pushed down appreciably, demonstrating the elevated Sb 5s orbital energy relative to the Bi 6s, as pointed out previously^29–31. In Fig. 1b,d, the sum of the O 2p_σ and Bi-6s/Sb-5s contributions and their composition are indicated by the thickness and colour; blue denotes predominant O 2p_σ character and red denotes predominant Bi-6s/Sb-5s character (the O 2p_π contribution is in Extended Data Fig. 2). The analysis of the orbital composition indeed demonstrates that Δ_CT for BKSO is almost zero and slightly positive, in contrast to BKBO with negative Δ_CT, as schematically shown in Fig. 1a. In BKBO, the red region with predominant Bi 6s character can be identified at the Γ point. Its energy, E = − 5.4 eV, is a good measure of the Bi 6s orbital energy, as the Bi 6s state does not hybridize with O 2p states at Γ in the cubic symmetry^31,34,35. Clearly, the energy of the Bi 6s state is below the average energy of the flat O 2p_π bands, E = –2.9 eV (Extended Data Fig. 2 and Supplementary Table 1). By sharp contrast, the location of the red region at the Γ point in BKSO, a measure of the Sb 5s orbital energy, is at E = –4.0 eV, which is only slightly above the average energy of the O 2p_π bands, E = –4.8 eV. The clear contrast of predominant orbital character between the lower spσ and higher spσ* bands, the Bi 6s (red) and O 2p_σ (blue) characters, respectively, is evident for BKBO in Fig. 1b, indicating that the orbital energy of O 2p_σ is higher than that of Bi 6s, namely, Δ_CT < 0. In BKSO (Fig. 1d), the red/blue contrast is reversed, with more O 2p_σ character (blue) in the spσ band and more Sb 5s character (red) in the spσ* band, meaning Δ_CT ≥ 0. The more covalent character of BKSO, closer to the covalent limit Δ_CT = 0 compared to BKBO, can be seen as the strongly reduced contrast between the spσ and spσ* bands in the ratio of Sb 5s and O 2p_σ contributions to the DOS in Extended Data Fig. 1. We note that the previous estimates of Δ_CT in a hypothetical BSO based on a tight-binding fitting gave the sign of Δ_CT as either positive²⁹ or negative³¹, depending on the model used. Incidentally, a fitting of the present band calculation based on Wannierization (Supplementary Fig. 1 and Supplementary Table 2) gives a positive value. The estimates of Δ_CT are quite useful in visualizing material trends within the same model, but are subject to model-dependent uncertainties in quantitative comparison across different models, as each model uses limited and different varied orbital bases and hopping terms to obtain ‘effective’ orbital energies and transfers. Here, we rely only on the qualitative arguments based on the orbital composition of the band structure to position BKSO in Fig. 1a.

Fig. 1. Inverted charge transfer energy in between BKSO and BKBO.

a, A schematic diagram of different regimes of metallicity in BKBO and BKSO. When charge transfer energy Δ_CT is positive (negative), Bi or Sb s electrons (oxygen holes) are predominant. b, The fat-band representation of the electronic band structure of BKBO at x = 0.65 calculated via hybrid DFT. The thickness is proportional to the sum of O 2p_σ and Bi 6s contributions, and the colours represent their ratio, with predominant O 2p_σ character shown by blue and predominant Bi 6s character by red. The plot shows the predominant O 2p_σ (Bi 6s) character in the spσ* (spσ) band. A band with predominant Bi 6s character at Γ at −5.4 eV is formed by non-bonding Bi 6s states (Extended Data Fig. 2 for the O 2p_π contribution). E_F, Fermi energy. c, The molecular-orbital diagram of BKBO derived from b. The Bi 6s orbital energy is markedly lower than the O 2p energy, consistent with negative Δ_CT. Therefore, BKBO is located in the scheme of the oxygen-hole metal^20,21, as illustrated in a. d, The fat-band representation of the electronic band structure of BKSO at x = 0.65 calculated via hybrid DFT. Sb 5s and oxygen 2p are found to be highly mixed in both spσ and spσ* bands. The much enhanced Sb 5s character in the spσ* band is clear compared to that of Bi 6s in BKBO. The non-bonding Sb 5s states at Γ are at −4.0 eV (Extended Data Fig. 2 for the O 2p_π contribution). e, The molecular-orbital diagram for BKSO derived from d. The Sb 5s orbital energy is marginally higher than the O 2p energy, indicating that Δ_CT is slightly positive while being close to zero (Δ_CT ≳ 0). Thus, BKSO is located in the region of the Bi/Sb s-orbital metal while critically close to the covalency limit in a.

Extended Data Fig. 1. Electronic density of states of Ba_0.35K_0.65SbO₃ and Ba_0.35K_0.65BiO₃.

The results are consistent with those suggested from the molecular-orbital diagrams (Figs. 1c and 1e); Ba_0.35K_0.65BiO₃ with negative Δ_CT shows predominant Bi 6s and O 2p_σ characters in the spσ and spσ* bands, respectively. The projected density of states (PDOS) of O 2p_σ at the Fermi level is larger than that of Bi 6s [PDOS (Bi 6s) / PDOS (O 2p_σ) ≅ 0.552]. On the contrary, for Ba_0.35K_0.65SbO₃ with Δ_CT slightly positive while close to zero, the ratio between Sb 5s and O 2p_σ PDOS is not so different between the spσ and spσ* bands, and very close to unity at the Fermi level [PDOS(Sb 5s) / PDOS (O 2p_σ) ≅ 1.06)]. Thus, metal s character with respect to O 2p_σ at the Fermi level is stronger in Ba_0.35K_0.65SbO₃ than Ba_0.35K_0.65BiO₃. Total DOS at the Fermi level shows almost no difference between the two compounds (Ba_0.35K_0.65SbO₃: 0.223 states/eV, Ba_0.35K_0.65BiO₃: 0.227 states/eV).

Extended Data Fig. 2. Metal s and oxygen 2p characters of Ba_0.35K_0.65SbO₃ and Ba_0.35K_0.65BiO₃.

The fat-band representations of the band structure of Ba_0.35K_0.65BiO₃ calculated via the hybrid-DFT showing a, Bi 6s, b, O 2p_π, and c, O 2p_σ orbital characters. The black dashed circle in a denotes a band at Γ at which Bi 6s (a_1g symmetry) do not hybridize with any O 2p states in the cubic structure. The energy of this band can be used to estimate the on-site energy of Bi 6s^31,34,35, if one neglects weak Bi 6s–O 2s hybridization. The two black dashed circles in b denote triply degenerate bands at R at which the O 2p_π states have the t_2g and t_1g symmetries, respectively, and do not hybridize with Bi 6s or 6p states. The on-site energy of O 2p_π can be reasonably approximated by averaging the energies of these two bands, which cancels out the effect of O 2p–O 2p hybridization. The fat-band representations of the electronic band structure of Ba_0.35K_0.65SbO₃ calculated via the hybrid-DFT showing d, Sb 5s, e, O 2p_π, and f, O 2p_σ orbital characters. The black dashed circles in d and e denote the bands with Sb 5s (a_1g) and O 2p_π t_2g and t_1g characters as in the case of Ba_0.35K_0.65BiO₃.

Having clarified the inverted Δ_CT of BKSO as compared to that of BKBO, we next reveal how the inversion modifies physical properties of the materials. Polycrystalline samples of BKSO with potassium content x from 0 to 0.75 were synthesized under a high-pressure, high-temperature condition of 12 GPa and 1,300 °C (Methods for details of sample synthesis and characterization). The parent compound BaSbO_3−δ is found to be a robust insulator with a large CDW gap. Rietveld refinement of neutron powder diffraction data (Supplementary Fig. 2a) confirms face-centred cubic symmetry (space group Fm$\overline{3}$m) with the breathing distortion, and furthermore reveals two distinct Sb–O bond lengths, 2.24(1) and 2.01(1) Å (Fig. 2a). Surprisingly, the difference between the two bond lengths Δd = 0.23 Å is larger than that of BBO (Δd = 2.28 − 2.11 = 0.16 Å, Fig. 2b)⁴. The observation of the breathing distortion establishes the commensurate CDW order from the structural point of view, which results in a bandgap in the material. Using diffusive reflectance spectroscopy, the bandgap in BSO is determined to be 2.54 eV (Fig. 2c). The value is appreciably larger than that in BBO (2.02 eV)³⁶, consistent with the larger bond-length disproportionation observed in the neutron diffraction.

Fig. 2. Three-dimensional CDW order in undoped BaSbO_3−δ.

a,b, Schematic diagrams of expanded and contracted octahedra in BaSbO_3−δ (a) and BBO (b). d denotes bond length between metal and oxygen ions. From the neutron diffraction investigations (Supplementary Fig. 2), two distinct Sb–O bond lengths are estimated to be 2.24(1) and 2.01(1) Å, respectively (Supplementary Table 3 for detailed structural parameters). The difference between the two bond lengths is found to be larger than that of BBO (ref. ⁴). c, Optical absorbance of BaSbO_3−δ at 300 K shows a wide bandgap E_CDW of 2.54 eV caused by the formation of the CDW order. By comparison, the optical conductivity (σ₁) of BBO (ref. ⁵⁰) is plotted as a reference, indicating the CDW gap of BaSbO_3−δ is larger than that of BBO.

The CDW order of the antimonate can be suppressed by substituting Ba with K up to 65%. X-ray and neutron powder diffraction measurements enable us to map out the structural phase diagram of BKSO, as shown in Fig. 3a (detailed refinement profiles and refined parameters are in Supplementary Figs. 2 and 3 and Supplementary Table 3). As x increases, two structural transitions are found, namely, from Fm$\overline{3}$m to a tetragonal I4/mcm at x ≈ 0.3, and from I4/mcm to a primitive cubic Pm$\overline{3}$m phase at x ≈ 0.65. This structural phase diagram is qualitatively similar to that of BKBO³⁷, in which the CDW order is sequentially suppressed from the long range (I2/m) to short range (Ibmm) and then finally disappears (Pm$\overline{3}$m). The structural transitions trigger drastic successive changes in Raman scattering, as shown in Fig. 3b. The undoped compound shows a pronounced peak at 672 cm⁻¹, which corresponds to the breathing-mode phonon, that is, the symmetric movement of oxygen ions with A_1g symmetry, and is also known to be crucial to superconductivity in BKBO³⁸. The phonon peak is first marginally softened as x increases, and next its amplitude completely vanishes for x ≥ 0.65. Because all the phonon modes become Raman-inactive in the Pm$\overline{3}$m phase³⁹, the vanishing breathing-mode peak confirms that the crystal symmetry above x = 0.65 is indeed Pm$\overline{3}$m with the ideal cubic perovskite structure without any distortion; that is, the CDW order is completely suppressed. Interestingly, the critical potassium concentration x_IMT at which the structure symmetry becomes Pm$\overline{3}$m is larger in BKSO (x_IMT ≈ 0.65) than in BKBO (x_IMT ≈ 0.35). The larger x_IMT is plausibly related to the bigger CDW gap, which may necessitate more holes for its suppression in the antimonates.

Fig. 3. Suppression of the CDW order via potassium doping.

a, The structural phase diagram of BKSO based on neutron (Supplementary Fig. 2) and X-ray (Supplementary Fig. 3) diffraction data. Black diamonds, tan crosses and red squares represent the face-centred cubic (fcc, Fm$\overline{3}$m), tetragonal (T, I4/mcm) and primitive cubic (C, Pm$\overline{3}$m) phases, respectively. The insets depict the local atomic structure of each phase, which shows transitions of the CDW order from the commensurate long range (Fm$\overline{3}$m) to short range (I4/mcm), and finally to complete suppression (Pm$\overline{3}$m). b, Raman spectra of BKSO measured with the excitation wavelength of 632 nm at 300 K. ω denotes the Raman shift in the unit of wavenumber. As highlighted in the dashed box, the breathing-mode phonon peak observed in the Fm$\overline{3}$m and I4/mcm phases disappears in the Pm$\overline{3}$m phase (x ≥ 0.65), confirming the CDW order is completely suppressed. The inset shows a schematic picture of the breathing-mode phonon.

The BKSO samples with x ≧ 0.65 and Pm$\overline{3}$m symmetry shows bulk superconductivity with a maximum T_c = 15 K at x = 0.65 (Fig. 4). The superconducting transition of the optimally doped sample (x = 0.65) is clearly identified at T_c = 15 K in resistivity (Fig. 4a). In the magnetic susceptibility (Fig. 4b), a diamagnetic signal corresponding to a superconducting volume fraction near 100% is observed below T_c = 15 K. The specific heat shows a jump with an onset at 15 K due to the superconducting transition, which is suppressed by applying a magnetic field of 1 T (Fig. 4c). The magnitude of the jump is on the order of the linear specific heat coefficient γ (0.924 mJ mol⁻¹ K⁻²; Supplementary Fig. 4), confirming the bulk nature of superconductivity. The maximum T_c = 15 K of BKSO at x = 0.65 is found to be lower than that of BKBO at x = 0.4, T_c ≈ 30 K, but at comparable potassium concentrations, is higher than that of BKBO (7.0 K at x = 0.66 (ref. ⁴⁰)) by more than a factor of two, as seen in Fig. 4b.

Fig. 4. Superconductivity and weakened oxygen-hole character in Ba_0.35K_0.65SbO₃.

a, Superconducting transition observed in the resistivity (ρ) of optimally doped antimonate (x = 0.65). T denotes temperature. The superconducting transition temperature T_c, defined by the clear onset of the transition, is ~15 K. b, The superconducting transition of the same sample is observed in zero-field-cooled magnetic susceptibility (χ) measured at μ₀H = 0.001 T (red), in comparison with that of Ba_0.34K_0.66BiO₃ (grey)⁴⁰. H is an applied magnetic field, and μ₀ is the vacuum permeability. The diamagnetic volume fraction is near 100%, indicating bulk superconductivity. Here, T_c is 15 K, defined as a temperature where the volume fraction started increasing by 0.1%. c, The superconducting transition of the same sample observed in the specific heat. ΔC denotes the difference between specific heats (C) under each field and 14 T. T_c is estimated to 15 K from the clear onset of jump, which can be suppressed by applying a field of 1 T. The observed jump is broadened, perhaps indicating sample inhomogeneity from the high-pressure synthesis. d, Oxygen K-edge X-ray absorption spectrum of Ba_0.35K_0.65SbO₃ (red open circles) at 300 K, plotted together with that of Ba_0.4K_0.6BiO₃ (ref. ⁴¹; grey open triangles). The intensity of each spectrum is normalized by that at a high energy ~550 eV above the edge. The arrows indicate the prepeak structure originating from oxygen 2p holes in the spσ* band. The suppression of the prepeak intensity in the antimonate indicates the decrease of oxygen holes compared to the bismuthate.

Reduced oxygen-hole character in BKSO is revealed via X-ray absorption spectroscopy, consistent with its positive Δ_CT. The oxygen K-edge, which probes unoccupied oxygen 2p states, is measured for the optimally doped BKSO and compared with a BKBO reference⁴¹ at similar x in Fig. 4d. The BKBO (x = 0.6) exhibits a pronounced prepeak structure at E = 528.8 eV, indicating predominant oxygen holes in the conduction band. The BKSO (x = 0.65) sample shows a similar prepeak at the same energy, but its intensity is appreciably diminished, indicating the reduction of the oxygen-hole density. The suppression of the prepeak intensity in BKSO compared with BKBO^41,42 is observed not only around x = 0.65, but also in all the available x range including x = 0 (BSO; Extended Data Fig. 3). We also note that a clear signature of charge disproportionation of Sb³⁺ and Sb⁵⁺ has been observed very recently in ¹²¹Sb Mössbauer spectroscopy in BSO⁴³. No such clear spectroscopic signature of Bi³⁺ and Bi⁵⁺ has been reported in BBO which can be attributed to the predominant oxygen holes^24–26. The stark contrast between BKSO and BKBO supports the strong metal s character and the reduced O 2p character of the spσ* band and hence the positive sign of Δ_CT in BKSO.

Extended Data Fig. 3. The oxygen K-edge X-ray absorption spectra of Ba_1-xK_xSbO₃ (0 ≤ x ≤ 0.75).

a, The spectra of the BKSO samples with various K contents were measured at 300 K in the total fluorescence yield mode. All the samples show the pre-peak structure (black arrows) analogous to the Ba_0.35K_0.65SbO₃ sample depicted in Fig. 4d. This indicates a strong admixture of Sb 5s with O 2p throughout the entire x range, but the intensity of the pre-peak is appreciably reduced compared with that of BKBO at comparable x values^41,42,55. The position of the pre-peak shifts to a lower energy with increase of x, which can be understood as the suppression of the CDW gap by doping holes^41,55. The high-energy peak (grey arrows) shifts to a higher energy, which may be associated with the Ba 5d and K 3d states that change upon the chemical substitution⁴¹. For the x = 0, 0.65, and 0.75 samples, the extra peak around 531 eV (black asterisks) likely originates from a degraded surface, because of its pronounced intensity in the surface-sensitive total electron yield mode data (not shown). Further quantitative analysis has so far been limited at present, as the Sb M₅-edge gives rise to an additional structure around the pre-peak because its energy is so close to that of the oxygen K-edge⁵⁶. b, The spectra of the x = 0.65 sample at 300 and 25 K, showing no apparent change within the temperature range investigated. We note that the x = 0.65 sample shown here is different from that in Fig. 4d.

A phase diagram of BKSO, compiled from these results, offers a comprehensive view of the interplay between the CDW order and superconductivity in main-group oxide superconductors (Fig. 5). First, a common tendency in the phase diagram can be found in both compounds; as the CDW insulating phase is suppressed, a half-dome of superconductivity arises with T_c maximized at the border of the insulator-to-metal transition and gradually decreasing with x increasing. Nevertheless, a crucial difference between the two compounds is that the suppression of the CDW phase occurs at higher x in BKSO, possibly related to its larger CDW gap. As BKSO shows a higher T_c at x ≥ 0.65, its T_c could exceed that of BKBO if it were possible to stabilize metallic BKSO at lower x and if the same trend of T_c based on x held. In reality, this has so far been prohibited by the strong CDW instability in BKSO, setting a limit on enhancing the superconductivity further.

Fig. 5. Phase diagram of BKSO and BKBO.

Red circles are the T_c values of superconductivity (SC) in the antimonates with the same definition as in Fig. 4, and grey triangles are T_c of BKBO (refs. ^40,51). T_c values of the antimonates show a half-dome shape (red region), which is similar to that of the bismuthates (dark grey). The crucial difference is that the CDW order in the bismuthates (light grey region) is suppressed at x = 0.4, whereas that of the antimonates (green region) continues to exist up to x = 0.65.

The superconducting T_c that is more than doubled in BKSO at x = 0.65 suggests a mechanism associated with strong metal–oxygen covalency. The electronic structure in Fig. 1e and Extended Data Fig. 1 points to the close proximity of the orbital energies of Sb 5s and O 2p, Δ_CT ≈ 0, indicating the strong covalency in BKSO. This leads to the Sb–O bonds being stiffer than the Bi–O bonds, and the relevant phonon energies of BKSO being higher than those of BKBO, as supported by the following experiments. First, the Debye temperature of the optimally doped BKSO was found to be 535 K (Supplementary Fig. 4), which is greater than that of BKBO, typically ~330 K (ref. ⁴⁴). Second, the breathing-mode phonon in the parent compounds showed its frequency increased by about 19% in BSO (672 cm⁻¹), as compared to BBO³⁹ (565 cm⁻¹; Supplementary Fig. 5). The increase of the phonon frequencies can be a factor in increasing T_c but alone cannot fully account for the more than twofold enhancement of T_c in BKSO at x = 0.65 in terms of the Macmillan’s formula for superconducting T_c. This implies that the increase of the electron–phonon coupling, possibly linked with the enhanced covalency, must be incorporated in the enhancement of superconductivity as well (Supplementary Note 1 for more detailed discussion). The stronger CDW instability in BKSO could also be related to such an enhanced electron–phonon coupling, which is reminiscent of covalent superconductors in which too large electron–phonon coupling sometimes leads to lattice instability instead of higher T_c (refs. ^45,46).

Finally, yet importantly, our study affords insight into the role of negative Δ_CT and predominant oxygen holes. On one hand, it is evident from the results that BKSO, which has slightly positive Δ_CT, demonstrates both CDW insulating and superconducting phases, analogous to BKBO. Therefore, the emergence of the two phases is not necessarily dependent on the sign of Δ_CT. In addition, at x ≥ 0.65, BKSO shows even higher T_c than BKBO, in spite of its decreased oxygen-hole character. Hence, it could be inferred that predominant oxygen holes may not be a necessary condition for enhancement of superconductivity. On the other hand, BKBO, which has more oxygen holes, shows a smaller amplitude of the CDW order than that in BKSO, which results in a smaller x_IMT as well. Since the electronic DOS at the Fermi level as well as the electron–phonon interaction become larger with decreasing x (ref. ¹⁴), a smaller x_IMT would lead to an increased T_c. Therefore, the weakened CDW order in BKBO, likely by predominant oxygen holes, could be vital to show a higher T_c. In this respect, predominant oxygen holes may be a sufficient condition for a higher T_c.

We have reported superconducting perovskite antimonates with a maximum T_c of 15 K. The modification of Δ_CT via the substitution of Bi with Sb has allowed us to address long-standing questions as to the different roles of metal and oxygen ions for the CDW and superconductivity in the main-group oxide superconductors. Furthermore, these results provide fascinating possibilities for approaching novel regimes in the future. For example, it would be intriguing to modify Δ_CT either to be more positive or negative by utilizing appropriate elements at the octahedral site: As and Sn would give an on-site energy of a metal s level higher than Sb, and thus more positive Δ_CT value than antimonates. Assuming these compounds can be stabilized, they would show more prominent effects of the cations, providing ideal model systems to examine the negative U model and the effects of valence fluctuations¹⁸. On the other hand, Te (ref. ⁴⁷) and I (ref. ⁴⁸) would give an on-site energy of a metal s level lower than Sb, and perhaps comparable or even lower than Bi. Thus, their Δ_CT values would be more negative than those of the antimonates and possibly bismuthates, providing additional model systems to comprehensively examine the effect of oxygen holes²⁰. We also note that charge- or bond-disproportionated CDW states are not limited to oxides but extend to other families, including perovskite halides CsTlCl₃ or CsTlF₃ (ref. ⁴⁹).

Methods

Sample synthesis and characterization

Polycrystalline samples of BKSO (x = 0.0, 0.36, 0.50, 0.65 and 0.75) were fabricated using a high-pressure high-temperature synthesis technique with a Walker-type multi-anvil module. Precursors of BaO₂ (95%, Acros Organics), KO₂ (96.5%, Alfa Aesar), Sb (99.999%, ChemPur) and Sb₂O₃ (99.999%, Aldrich) were mixed in stoichiometric ratios and transferred into a Pt capsule. The samples were obtained from high-pressure high-temperature treatment at 12 GPa and 1,300 °C for an hour, followed by quenching to room temperature and slow decompression. A dense pellet of the samples was recovered from the Pt capsule, after which its outer face was polished using a diamond file. Powder X-ray and neutron diffraction data were collected in the Debye–Scherrer geometry using a Mo Kα₁ source and a time-of-flight neutron source, respectively, with the instrument WISH at ISIS. The structural refinements based on neutron and X-ray diffraction patterns, shown in Supplementary Figs. 2 and 3, indicate that the samples consist of an almost pure BKSO perovskite phase with only a very minor trace of BaSbO_2.5 for x = 0 and KSbO₃ for x ≠ 0 as the impurity phases. The X-ray refinements reveal no clear signature of cation non-stoichiometry and the K contents, x, are in good agreement with the nominal values for all the samples. The neutron refinement suggests an oxygen deficiency on the order of a few percent only for BaSbO_3−δ (x = 0). The oxygen deficiency in BaSbO_3−δ is not large as compared with its sibling compound BaBiO_3−δ, which is known to be easily reduced at relatively low temperatures and oxygen partial pressures⁵².

Physical property measurements

Magnetic susceptibility was measured via a Quantum Design magnetic property measurement system, and resistivity and heat capacity were measured via a Quantum Design physical property measurement system. Optical absorbance was measured via diffuse reflectance spectroscopy at room temperature. X-ray absorption spectroscopy was measured in partial fluorescence yield mode using a silicon drift detector to select the O K-edge fluorescence at the Spherical Grating Monochromator beamline and in total fluorescence yield mode using a microchannel plate at the Resonant Elastic and Inelastic X-ray Scattering beamline of the Canadian Light Source.

First-principles calculation

The band structures of BKSO and BKBO were calculated using the WIEN2k code⁵³ with full hybrid functionals (YS-PBE0, similar to HSE06 (ref. ⁵⁴)). We found that a 12 × 12 × 12 reciprocal-space k mesh is sufficient for the calculations well converged. R_MTK_MAX was set to  7.0, where R_MT is the smallest atomic sphere radius and K_MAX is the maximal k in the plane wave expansion. The virtual crystal approximation was used to take into account the solid solution of Ba and K ions. The atomic structures reported from experiments were used.

Online content

Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41563-022-01203-7.

Author contributions

M.K. and H.T. conceived the project. M.K. prepared and characterized the samples. T.T., M.I. and R.K.K. helped with the analysis. M.K., G.M.M., A.S.G. and P.M. conducted the neutron diffraction experiments. M.K. and H.-H.K. conducted the Raman experiments. M.K., U.W. and A.Y. performed the first-principles calculations. M.O., R.J.G. and R.S. conducted the X-ray absorption spectroscopy experiments. M.K. and H.T. wrote the manuscript, and all authors commented on it.

Peer review

Peer review information

Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.

Funding

Open access funding provided by Max Planck Society.

Data availability

The data that support the findings of this work are available from the corresponding authors upon reasonable request.

Competing interests

The authors declare no competing interests.

Extended data

is available for this paper at 10.1038/s41563-022-01203-7.

Supplementary information

The online version contains supplementary material available at 10.1038/s41563-022-01203-7.