Superconductivity in (Ba,K)SbO3

(Ba,K)BiO3 constitute an interesting class of superconductors, where the remarkably high superconducting transition temperature Tc 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 BaSbO3−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 Tc = 15 K. This value is lower than the maximum Tc 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.

k-space. The negative U model may provide a possible framework to understand superconductivity in the bismuthates as well as some chalcogenides 19 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][21][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 bismuth 23 . 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 (6s 2 + 6s 0 ) but rather by the bond-length disproportionation as 6s 2 + 6s 2 L 2 , where L denotes a ligand hole. Spectroscopic evidence supports the oxygen-hole model [24][25][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 model 28 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 BaSbO 3 (BSO) have been previously conducted and compared with those of BBO [29][30][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 0.75 Sb 0.25 O 3 becomes superconducting 32 , 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 bonds 33 , and as a consequence, no perovskite antimonates have been realized to date except a highly distorted insulating NaSbO 3 (ref. 34 ). Here, we report superconducting antimonates Ba 1−x K x SbO 3 (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) method 10 , 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][30][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   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.
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 positive 29 or negative 31 , 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.
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 Fm3m) 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.
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 Fm3m to a tetragonal I4/mcm at x ≈ 0.3, and from I4/mcm to a primitive cubic Pm3m phase at x ≈ 0.65. This structural phase diagram is qualitatively similar to that of BKBO 37 , in which the CDW order is sequentially suppressed from the long range (I2/m) to short range (Ibmm) and then finally disappears (Pm3m). 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 BKBO 38 . 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 Pm3m phase 39 , the vanishing breathing-mode peak confirms that the crystal symmetry above x = 0.65 is indeed Pm3m 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 Pm3m 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.
The BKSO samples with x ≧ 0.65 and Pm3m symmetry shows bulk superconductivity with a maximum T c = 15 K at x = 0.65 (Fig. 4).  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 (σ 1 ) of BBO (ref. 50 ) is plotted as a reference, indicating the CDW gap of BaSbO 3−δ is larger than that of BBO.
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. 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 reference 41 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 Sb 3+ and Sb 5+ has been observed very recently in 121 Sb Mössbauer spectroscopy in BSO 43 . No such clear spectroscopic signature of Bi 3+ and Bi 5+ has been reported in BBO which can be attributed to the predominant oxygen holes [24][25][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.
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.
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 BBO 39 (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 electronphonon coupling, possibly linked with the enhanced covalency, must be incorporated in the enhancement of superconducti vity 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 ).  Fig. 2) and X-ray ( Supplementary Fig. 3) diffraction data. Black diamonds, tan crosses and red squares represent the face-centred cubic (fcc, Fm3m), tetragonal (T, I4/mcm) and primitive cubic (C, Pm3m) phases, respectively. The insets depict the local atomic structure of each phase, which shows transitions of the CDW order from the commensurate long range (Fm3m) to short range (I4/mcm), and finally to complete suppression (Pm3m). 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 Fm3m and I4/mcm phases disappears in the Pm3m phase (x ≥ 0.65), confirming the CDW order is completely suppressed. The inset shows a schematic picture of the breathing-mode phonon.
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 fluctuations 18 . 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 holes 20 . We also note that charge-or bond-disproportionated CDW states are not limited  40 . H is an applied magnetic field, and μ 0 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 0.35 K 0.65 SbO 3 (red open circles) at 300 K, plotted together with that of Ba 0.4 K 0.6 BiO 3 (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.  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.

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 BaO 2 (95%, Acros Organics), KO 2 (96.5%, Alfa Aesar), Sb (99.999%, ChemPur) and Sb 2 O 3 (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 Kα 1 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 KSbO 3 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 pressures 52 .
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 code 53 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 MT K 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.

Data availability
The data that support the findings of this work are available from the corresponding authors upon reasonable request. Fig. 1 | electronic density