Steven D Conradson
email: st3v3n.c0nrads0n@icloud.com

Theodore H Geballe
email: geballe@stanford.edu

Andrea Gauzzi

Maarit Karppinen

Changqing Jin

Gianguido Baldinozzi

Wenmin Li

Lipeng Cao

Edmondo Gilioli

Jack M Jiang

Matthew Latimer

Oliver Mueller

Venera Nasretdinova

Ivan Bozovic

Douglas J J Scalapino

Local lattice distortions and dynamics in

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A common characteristic of many "overdoped" cuprates prepared with high-pressure oxygen is T c values ≥ 50 K that often exceed that of optimally doped parent compounds, despite O stoichiometries that place the materials at the edge or outside of the conventional boundary between superconducting and normal Fermi liquid states. X-ray absorption fine-structure (XAFS) measurements at 52 K on samples of high-pressure oxygen (HPO) YSr 2 Cu 2.75 Mo 0.25 O 7. [START_REF] Lima | High-resolution molybdenum K-edge X-ray absorption spectroscopy analyzed with time-dependent density functional theory[END_REF] , T c = 84 K show that the Mo is in the (VI) valence in an unusually undistorted octahedral geometry with predominantly Mo neighbors that is consistent with its assigned substitution for Cu in the chain sites of the structure. Perturbations of the Cu environments are minimal, although the Cu X-ray absorption near-edge structure (XANES) differs from that in other cuprates. The primary deviation from the crystal structure is therefore nanophase separation into Mo-and Cu-enriched domains. There are, however, indications that the dynamical attributes of the structure are altered relative to YBa 2 Cu 3 O 7 , including a shift of the Cu-apical O two-site distribution from the chain to the plane Cu sites. Another effect that would influence T c is the possibility of multiple bands at the Fermi surface caused by the presence of the second phase and the lowering of the Fermi level.

cuprates | high-pressure oxygen | overdoped | local structure T he common, or "conventional," phase diagram for what we will refer to as "conventional" hole-doped cuprates [START_REF] Keimer | From quantum matter to high-temperature superconductivity in copper oxides[END_REF] shows the superconducting dome beginning at p ∼ 0.06, where p is defined as the number of excess holes/CuO 2 -type Cu, T c rising to its maximum at p ∼ 0.16, followed by T c of "overdoped" materials decreasing rapidly to 0 as they transition to a normal Fermi liquid at p ∼ 0.27. This widely accepted diagram, however, overlooks cuprates synthesized with high-pressure oxygen (HPO) using either chlorate or peroxide compounds (2) that have T c values greater than 50 K, despite O stoichiometries [START_REF] Krekels | Order and disorder in (Nd,Ce) n O 2n SR 2 GaCu 2 O 5 and YSr 2 CoCu 2 O 7[END_REF][START_REF] Babu | Critical hole density for superconductivity in Sr-containing phases related to YBa2Cu3O7-Structure, superconductivity and cation substitutions in YSr 2 Cu 2.8 Cr 0.2 O 7[END_REF][START_REF] Babu | Chemical control of superconducting properties of (Y,Ca)(Sr,Ba)2Cu2.7Ga0.3O7-delta[END_REF][START_REF] Greaves | The chemical control of superconductivity in (Y1-yCay)(Sr2-xBax)Cu2.7Co0.3O7+/-delta[END_REF][START_REF] Babu | Synthesis, composition, and structure of superconducting (Y,Ca)(Sr,Ba)(2)Cu2GaO7-delta[END_REF][START_REF] Ono | Critical-temperature optimization in Sr 2 YCu 3 O z and Sr 2 TmCu 3 O z[END_REF][START_REF] Ono | Oxygenation and critical-temperature optimization in M-1212 cuprates (Sr, Ba)(2)YCu(2.8)M[END_REF][START_REF] Shi | Effect of high-pressure oxygen annealing in promoting superconductivity in YSr2Cu2.7Fe0.3Oy: Evidence for Fe coordination number change in the chains[END_REF][START_REF] Ren | Fe 0.5 Cu 0.5 (Ba 1-x Sr x ) (2) YCu 2 O 7+delta (x=0, 0.5, and 1) superconductors prepared by high-pressure synthesis[END_REF][START_REF] Shiraki | Bulk superconductivity observed in (Co,Cu)(Sr,Ba)2(Y,Ca)Cu2Oy[END_REF] so high that they are outside the superconducting region when made with O 2 . In addition, T c of these substituted HPO compounds can be substantially higher than the parent materials from which they derive, e.g., 84 K for YSr 2 Cu 2.75 Mo 0.25 O 7.54 (YSCO-Mo) (13) vs. 63 K for YSr 2 Cu 3 O 7+δ [START_REF] Gilioli | Structure and superconductivity of YSr2Cu3O7-d[END_REF]. One type of HPO materials derives from the La 2 CuO 4+δ structure family and consists of Sr 2 CuO 3.3 (SCO) [START_REF] Hiroi | A new family of copper-oxide superconductors Sr N+1 Cu N O 2N+1+delta stabilized at high-pressure[END_REF][START_REF] Laffez | Synthesis of superconducting Sr 2 CuO 3+delta using high-pressure techniques[END_REF][START_REF] Liang | Growth of Sr 2 CuO 3+delta superconductor single crystals at high pressure[END_REF][START_REF] Liu | A new modulated structure in Sr 2 CuO 3+delta superconductor synthesized under high pressure[END_REF], Ba 2 CuO 3.2 (BCO) [START_REF] Hiroi | A new family of copper-oxide superconductors Sr N+1 Cu N O 2N+1+delta stabilized at high-pressure[END_REF][START_REF] Takano | Superconductivity in the Ba-Sr-Cu-O system[END_REF][START_REF] Li | Synthesis and structure stability of Ba2CuO3+delta under high pressure[END_REF][START_REF] Li | Superconductivity in a unique type of copper oxide[END_REF], and related compounds with T c values of 73 to 95 K. The second type is isostructural with YBa s Cu 3 O 7 (YBCO), consisting of Y(Ba 1-x Sr 1+x )(Cu 3-y M y )O 7+δ -type compounds [START_REF] Skakle | Crystal chemical substitutions and doping of YBa 2 Cu 3 O x and related superconductors[END_REF] with Ba and Sr interchanging and M=Cr, Co, Fe, Ga, Mo, etc. substituting for 5 to 100% of the Cu in the chain sites. For the YBCO type where data from many O stoichiometries are often available, p can be estimated by assigning a valence to M consistent with the high O activity (Mo = +6, Fe = +3, Ga = +3, etc.) and keeping the chain Cu charge at its already high value of +2.64 that is derived from the peak T c occurring at p = 0.16 in YBa 2 Cu 3 O 6.98 . These assumptions give p ∼ 0.3 for several compounds and still greater p values for others, even as their T c values are constant or still increasing (Fig. 1). Even if a substantial amount of the excess charge goes onto the chain Cu, HPO compounds still differ significantly from the phase diagram as it applies to conventionally "overdoped" materials [START_REF] Bozovic | The vanishing superfluid density in cupratesand why it matters[END_REF][START_REF] He | Persistent low-energy phonon broadening near the charge-order q vector in the bilayer cuprate Bi2Sr2CaCu2O8+delta[END_REF], in that T c shows no indication of rolling over up to the highest p values. X-ray measurements [START_REF] Grigoraviciute | Electronic structures, hole-doping, and superconductivity of the s = 1, 2, 3, and 4 members of the (Cu,Mo)-12s2 homologous series of superconductive copper oxides[END_REF] and valence-bond sum calculations (26) that concur with the optimum p value for O 2 -doped cuprates do, however, confirm that p does exceed 0.3 for HPO YSCO-Mo and related (Cu-Mo)-12s2 superconductors. In addition, the inception of superconductivity for some of these HPO compounds may begin below the standard p ∼ 0.06. Although there may be some disagreement on the exact placement of these materials on the diagram, it is apparent that the superconductivity in the HPO Y 1 (Ba 1-x Sr 1+x )(Cu 3-y M y )O 7+δ

Significance

This report Q:10 uses X-ray absorption fine-structure spectra of the title compound and a review of the literature to show that a second-phase diagram is needed to describe "overdoped" cuprates prepared by high-pressure oxygen methods. The critical temperatures of these HPO compounds continue to increase, even past the values of O stoichiometry and Cu charge, where T c values of conventional materials go to zero. The Mo and Cu maintain their preferred geometries, despite the higher Cu charge via clustering of the Mo. The principal effect of the Mo and excess O is therefore nanophase separation into Mo-and Cu-enriched domains. The high degree of similarity between the HPO and normal structures, including a Cu2-apical O two-site distribution, therefore suggests that the elevated T c of YSCO-Mo may originate in a combination of the dynamical properties and the nanophase separation.

compounds (2-8, 10-13, 22, 27, 28), SCO, and BCO does not conform to the dome of the conventional phase diagram and that the consistent behavior of these systems necessitates this second whose much broader and highly modified superconducting region challenges.

There are additional differences between the conventional and HPO materials. HPO compounds are tetragonal instead of orthorhombic. The projection of the heat capacity to a finite value at 0 K indicates that, although it is single phase, YSCO-Mo [START_REF] Gauzzi | Bulk superconductivity at 84 K in the strongly overdoped regime of cuprates[END_REF] and BCO [START_REF] Li | Superconductivity in a unique type of copper oxide[END_REF] retain some Fermi liquid electrons to give coexisting superconducting and normal metallic electronic phases. The highly contracted Cu-Oap distances of the HPO compounds contradict the correlation (21) between higher T c and increased distance from the apical O (Oap) to the Cu of the CuO 2 layer [START_REF] Sakakibara | Origin of the material dependence of T c in the single-layered cuprates[END_REF][START_REF] Rybicki | Perspective on the phase diagram of cuprate high-temperature superconductors[END_REF][START_REF] Bozin | Charge-screening role of c-axis atomic displacements in YBa 2 Cu 3 O 6+x and related superconductors[END_REF][START_REF] Peng | Influence of apical oxygen on the extent of in-plane exchange interaction in cuprate superconductors[END_REF] or its opposite cation [START_REF] Kim | Apical charge flux-modulated in-plane transport properties of cuprate superconductors[END_REF]. This multitude of changes in composition and structure poses the questions of what are the effects of the separate modifications, how do they sum to stabilize the superconductivity to such an extent, and what is the microscopic mechanism underlying this second phase diagram? We address these questions via an X-ray absorption fine-structure (XAFS) study of YSCO-Mo at 52 K, using samples magnetically aligned along the c axis and in the aa plane. XAFS probes the local order of each element separately without the restrictions imposed by the space-group symmetry, so that it is not constrained to the average structure of the periodic fraction of the material. In addition, its structure factor, S(q, ω) (or S[q, t = 0]) [START_REF] Salkola | Dynamic polaron tunneling in YBa 2 Cu 3 O 7 : Optical response and inelastic neutron scattering[END_REF][START_REF] Salkola | Correlation-function analysis of nonlinear and nonadiabatic systems: Polaron tunneling[END_REF][START_REF] De Leon | X-ray absorption fine structure applied to the study of systems with lattice instabilities[END_REF], includes time and energy scales in the range of dynamical processes coupled to collective phenomena. XAFS therefore often provides key insights into the structure-property relationships of complex correlated materials.

We use the existing labels for YSCO-Mo (14) (Fig. 1A and SI Appendix, Fig. S1), T c = 84 K (13) (SI Appendix, Fig. S2), derived from YBCO. Mo(IV-VI) in oxides is found in distorted octahedral geometries. These are incompatible with the square or highly elongated square pyramid or bipyramid displayed by Cu 2+∂ as occurs in the YBCO/YSCO structure. The problem in YSCO-Mo and related materials is, therefore, how the Cu1 layer is arranged to minimize the stress between the different stable geometries of the Cu and substitutional element, M. The Cu1-M layer can easily take up the adventitious or superstoichiometric O if the substitutional element prefers more than four O neighbors at short distances, but only if the M-Cu pairs are accommodated in a way that minimizes the stress by maintaining their individual geometries. This includes conserving the square geometry of the Cu by limiting the number of Cu1-O4 pairs to two per Cu1 in addition to the two Cu-Oap, which constrains the relative positions of the Cu and M. The structure reported from neutron diffraction [START_REF] Gauzzi | Bulk superconductivity at 84 K in the strongly overdoped regime of cuprates[END_REF] with random, isomorphic substitution of the Cu by the Mo and the partially occupied, off-axis O sites in the Cu1-Mo plane may therefore only approximate the disorder in the atom positions, especially if the local symmetry is lower than the average tetragonal symmetry under which the structure was refined. Our XAFS results supplement these to provide a more precise depiction of the structure.

The information on the local structure around the Cu and Mo is obtained from the extended XAFS (EXAFS) spectra by observation of the spectra, comparison with related compounds, curve fits, and separation of the contributions of individual neighbors of particular interest. (A detailed discussion with additional figures is contained in SI Appendix.) The EXAFS spectra are presented as their Fourier Q:11 transforms (FTs) that take χ(k) into χ(R) to give a modulus that approximates the Cu partial pair-distribution function. The caveats in this interpretation are that: the phase shifts cause a neighbor-element-specific reduction from the actual distance; the modulus only contains half of the total information, with the remainder in either the real or imaginary component; and the width of the modulus peak derives from the finite range of the data and is not only much wider than the actual distribution, but also wider than the inherent resolution of the spectrum (ΔR = π/2k max ), so that the contributions of various neighbors whose FTs overlap are actually easily separable. The Cu spectra of YSCO-Mo (Fig. 2 A andB) are very similar to those of YBCO [START_REF] Conradson | The axial oxygen and superconductivity in YBa2Cu3O7[END_REF][START_REF] Boyce | Temperature dependence of the local structure of YBa 2 Cu 3 O 7-delta with varying oxygen content: An x-ray-absorption study[END_REF][START_REF] Maruyama | Temperature-dependence of the EXAFS spectrum in YBa2Cu3O7-delta compounds[END_REF][START_REF] Booth | Comparison of local structure measurements from c-axis polarized XAFS between a film and a single crystal of YBa 2 Cu 3 O 7-delta as a function of temperature[END_REF], with the O nearest neighbors giving the features at R ∼ 1.6 Å, the Y and Sr at R ∼ 2.8 Å, and the Cu at R ∼ 3.5 Å. The lower numbers of O and Cu neighbors account for the lower amplitudes of the Ejjc spectrum. Excellent fits are obtained for both spectra by using only the crystallographic neighbors of the Cu. The distances calculated by the fits (Table 1) are within the standard EXAFS uncertainties of the crystallographic values. Uncorrelated thermal motion from weak bonding and resulting damping of the EXAFS signal accounts for the absence of contributions from the Cu1-Sr [START_REF] Piazza | Study of atomic motions in EuBa 2 Cu 3 O 7-delta Mossbauer and EXAFS spectroscopies[END_REF][START_REF] Haskel | Altered Sr environment in La 2-x Sr x CuO 4[END_REF] and Cu2-Cu2 pairs, which is typical of YBCO-type compounds [START_REF] Maruyama | Temperature-dependence of the EXAFS spectrum in YBa2Cu3O7-delta compounds[END_REF][START_REF] Booth | Comparison of local structure measurements from c-axis polarized XAFS between a film and a single crystal of YBa 2 Cu 3 O 7-delta as a function of temperature[END_REF][START_REF] Oka | X-ray absorption study of oxygen configurations in YBa 2 Cu 3 O 7-delta single crystals annealed by two step heat treatments[END_REF][START_REF] Sahiner | Pressure-induced bond buckling in YBa2Cu3O7-delta[END_REF].

The Mo EXAFS for both orientations shows a similar pattern with three peaks (Fig. 2 C andD) that are the contributions of the O, Sr, and Cu/Mo. However, the substantial differences in the shapes of the Moj(P) relative to the Cu beyond the difference from the lack of a Y neighbor demonstrate that the local structure around the Mo site is not identical to that of the Cu, as expected from the difference in their geometries in their oxides. The preference of the Mo for a distorted octahedral environment is found in that the Mo EXAFS requires O neighbors at more than one Mo-O distance for a complete fit (Table 1). In contrast to Cu1, the Mo-Sr contribution is large. The Mo-Cu pair distribution obtained from the EXAFS addresses the crucial issue of the Mo substitution mechanism. Of the four possibilities for the Cu or Mo neighbor, Cu or Mo with or without bridging O, curve fits showed that the Mo-M contribution was not only fit best, but also could be solely fit by the EXAFS from an Mo-O-Mo moiety. Mo-Mo and Mo-O-Cu were ruled out by being π out of phase, and the larger error with a Mo-Cu fit gave a likelihood of less than 0.01 [START_REF] Hamilton | Significance tests on crystallographic r factor[END_REF] for that atom pair (SI Appendix, Fig. S4). This predominance of Mo neighbors indicates that the Mo is clustered so that the Cu1-Mo plane is separated into Moand Cu-enriched domains. Insofar as some Cu neighbors are required, it was found that up to one-fourth of the neighbors could be Cu without bridging O before the error in the fit became significantly worse (Fig. 2C). Consistent with the larger average size of Mo and the resulting strain from its substitution in the Cu site, the Mo-Mo distance is 3.95 Å, and the Mo-Cu is This analysis of the EXAFS therefore confirms that the YBCOtype crystal structure is conserved. The YBCO/YSCO structure is virtually identical for the Cu, with modifications around the Mo that result in its preferred distorted octahedral geometry, with the exception of the absence of O neighbors with Mo-O distances less than 1.8 Å that are typical of Mo(VI). This Q:12 mechanism may apply to additional compounds; the Fe in YSr 2 Cu 2.7 Fe 0.3 O 7+δ has also been stated to display its preferred geometry that differs from Cu [START_REF] Shi | Effect of high-pressure oxygen annealing in promoting superconductivity in YSr2Cu2.7Fe0.3Oy: Evidence for Fe coordination number change in the chains[END_REF]. The EXAFS therefore indicates that the mechanism enabling this structure is clustering of the Mo, resulting in nanophase separation or nanoscale heterogeneity that divides the material into Mo-and Cu-type domains. The ordered Mo-O-Mo moieties are the internal or edge pairs of the cluster, with O bridges in four or three directions in the Cu1-Mo plane. The atoms constituting the disordered component are the Mo-Cu1 pairs at the edges of the clusters, many or most of which are not bridged to the Mo because the Cu already has its preferred O four neighbors at distances less than 2 Å, two each from the chain and Oap. Those that are bridged must have a wide range of distances, indicative of a disordered interface. The absence of a bridging O for the neighboring Cu ions and the presence of an interstitial O found in both orientations imply a rotation of a cohort of the O ions out of the aa plane. The limit on the relative numbers of Mo and Cu neighbors, the requirement of the domains being below the diffraction limit in size, and the accumulating stress as the domain size increases are all consistent with these clusters being three to four × four to five unit cells in size (Fig. 3). One fourth of the aa plane in the Cu1 layer would then be composed of these MoO 3 clusters, with the other three-quarters consisting of Cu-O chains isomorphic with the parent YSCO. The Mo domains limit Cu-O chain length, and the random orientations of these shorter chains would produce the average tetragonal symmetry. The greater number of O in the Mo domains may couple more strongly with the Sr, which would account for it being more correlated with the Mo than Cu1. At this size, a significant number of both types of atoms will also belong to the interfaces between the Cu and Mo domains.

An additional finding is that, like other EXAFS studies of cuprates [START_REF] Batistic | Polaron origin for anharmonicity of the axial oxygen in YBa2Cu3O7[END_REF][START_REF] Heald | Orientation-dependent x-ray-absorption near-edge studies of high-T c superconductors[END_REF][START_REF] Bianconi | Electronic structure of Bi 2 CaSr 2 Cu 2 O 8 determined by a combined analysis of various polarized x-ray-absorption spectra[END_REF][START_REF] Chou | Orientation-dependent x-ray absorption fine-structure (XAFS) of the Bi-Sr-Ca-Cu-O system[END_REF][START_REF] Akeyama | Cu K-edge XANES and electronic-structure of trivalent, divalent, and monovalent Cu oxides[END_REF][START_REF] De Groot | The 1s x-ray absorption pre-edge structures in transition metal oxides[END_REF], the Cu2-Oap pair resides in a two-site distribution with Cu-O distances of 2.06 and 2.22 Å, so that the average Errors are 0.01 to 0.02 Å. The resolution limit for the Cu EXAFS is 0.11 Å and for the Mo EXAFS 0.12 Å. Because of the Cu/Mo and additional disorder, the referenced crystal structure found multiple Cu1-O positions labeled O5 and O6, none of which were along the Cu1-Cu1 vectors. In contrast, the EXAFS finds O positions very similar to YBa 2 Cu 3 O 7 for both the Cu and the Mo (see

Q:19
text), and, because there is apparently only a single O site, we labeled it O4. These differences are not unexpected; the diffraction analysis must describe the disorder under the constraints of the space-group symmetry derived from the average Cu and Mo positions that, as described in the text, are not equivalent. As discussed in the text and shown in Fig. 3A, the single Cu2-Oap distance listed here is the average position of its actual two-site distribution. The two-site Cu-Oap distribution was analyzed separately. The two Cu2-Sr distances are from the Ejjaa and Ejjc spectra. Cu1-Sr did not make an identifiable contribution to the EXAFS in both orientations. In the Cu EXAFS, the Cu1-Cu1 and Cu2-Cu2 contributions are combined; the Mo EXAFS will contain Mo-Cu1 and Mo-Mo. The Q:20 analysis of the Mo Ejjaa EXAFS spectrum found four Mo-O4 distances separated by more than the resolution limit; the Mo E⊥jjc found 3. The Mo-O pairs with Mo-O distances 2.33 and 2.39 Å Mo-O found in the analysis of the spectra from the two orientations most likely represent the same O neighbor that would be at an interstitial position off of the crystallographic axes through the Cu and Mo sites because it makes contributions to both orientations. The Mo-Mo, Mo-Cu2, and Cu1-Cu1/Cu2-Cu2 distances were obtained by using amplitudes and phases that are the sum of the two-, three-, and four-leg paths calculated by FEFF9 (69) from the crystal structure. location of the O is the same as the crystallographic one. The associated double-well potentials have been ascribed to tunneling polarons that are components of the dynamic structure. In contrast to a conventional polaron that transfers its excess charge and lattice distortion to a neighboring site by hopping, a tunneling polaron is a fixed set of atoms that oscillate between two conformations denoted by distinct geometries and charge distributions that in chemical terms would involve changes in the valence and resulting speciation of the affected atoms [START_REF] Salkola | Dynamic polaron tunneling in YBa 2 Cu 3 O 7 : Optical response and inelastic neutron scattering[END_REF][START_REF] Salkola | Correlation-function analysis of nonlinear and nonadiabatic systems: Polaron tunneling[END_REF][START_REF] De Leon | X-ray absorption fine structure applied to the study of systems with lattice instabilities[END_REF][START_REF] Batistic | Polaron origin for anharmonicity of the axial oxygen in YBa2Cu3O7[END_REF]. The signature for a tunneling polaron is that the two sites give individual signals in the EXAFS of only the Cu atom with that correlation for the Cu-O pair distribution, in this case Cu2 (SI Appendix, Fig. S5), but not in the signal from Cu1 atom or in diffraction. Although the location of the double-well potential in the Cu2-Oap bond is the same as for La 2 CuO 4+δ and Tl-cuprates, in YBCO, it was associated with the Cu1-Oap bond. The 0.16-Å separation between the two sites in YSCO-Mo is quite close to these others, despite its unusually short Cu2-Oap distance. The quality of the fit indicates that all of the O atoms are located at one of these two positions. The Cu2-Oap double well therefore occurs for both Cu1 and Mo being the cation on its far side. The Cu and Mo valences are probed by their X-ray absorption near-edge structure (XANES) that is interpreted by direct comparison with the spectra from related compounds and relevant standards (a more detailed discussion of the XANES is found in SI Appendix). The overall shape does not resemble those of YBCO, other cuprates [START_REF] Heald | Orientation-dependent x-ray-absorption near-edge studies of high-T c superconductors[END_REF][START_REF] Bianconi | Electronic structure of Bi 2 CaSr 2 Cu 2 O 8 determined by a combined analysis of various polarized x-ray-absorption spectra[END_REF][START_REF] Chou | Orientation-dependent x-ray absorption fine-structure (XAFS) of the Bi-Sr-Ca-Cu-O system[END_REF], or Cu 2 O, CuO, and NaCuO 2 [START_REF] Akeyama | Cu K-edge XANES and electronic-structure of trivalent, divalent, and monovalent Cu oxides[END_REF]. Since the local structures of the Cu are so similar, the origins of this difference must be a combination of modifications to the electronic structure and the dynamics that influence the oscillator strengths of forbidden transitions. The overall shift of the Cu absorption edge to higher energies relative to YBCO and the greater amplitude of certain spectral features (51, 52) (Fig. 4) show that the charge on the Cu atoms is significantly higher in YSCO-Mo. Similarly, the overlap in energy for the Mo XANES of YSCO-Mo with that of MoO 3 indicates that the Mo valence is (VI), as expected from the HPO synthesis. A second important characteristic centers on the 20,008-eV feature in MoO 3 that is assigned to the forbidden 1s → 4d transition at 20,008 eV and augmented by terminal, multiply bound, nonbridging O neighbors [START_REF] Kutzler | Single-crystal polarized x-ray absorption-spectroscopy-Observation and theory for (MoO 2 S 2 ) 2[END_REF][START_REF] Lima | High-resolution molybdenum K-edge X-ray absorption spectroscopy analyzed with time-dependent density functional theory[END_REF]. Consistent with the EXAFS, the absence of this spectral feature in the YSCO-Mo spectra demonstrates the corresponding absence of this type of O neighbor that is typical of Mo(VI).

Summarizing, the basic YBCO structure remains intact, in particular, the CuO 2 planes with their Y "glue" and the Cu1-O4-Oap 2 chains. Any impacts of the Mo substitution and higher O stoichiometry on the Cu local structure are therefore minimal. This is consistent with the clustering of the Mo that results in the excess O being located in the Mo-enriched domains, so that the local environments of most of the Cu atoms are unaffected. It is also consistent with overdoping with O 2 , where the YBCO structure is retained at comparable stoichiometries. Although the substitution of the Cu1 with its +2.64 charge by Mo that is +6 takes up most of the charge from the additional O, the larger amount of O still significantly increases the charge on the Cu. This increased charge on Cu2 may also contribute to the overall contraction of the Cu1/Mo-Oap-Cu2 unit that in YSCO-Mo is intermediate in size between YBCO and the smaller YSCO. Apart from the Cu2-Oap contraction, the most notable difference relative to the structure of YBCO is that the Cu-Oap double well is shifted from its Cu1 location that is unique to YBCO, where the Cu-O bond length is 1.85 Å, to the Cu2-Oap pair with its 2.16-Å distance. This occurs for both Cu1 and Mo, both of which also display a single-site Cu-Oap distribution. This difference in the Cu-Oap distribution between Cu1 and Cu2 is one of the dynamical aspects of its structure expected for a tunneling polaron.

In attempting to explain the difference between overdoping with O 2 vs. HPO, since the overall structure is only minimally affected, the most likely change is that reaction with O 2 results in interstitial O atoms, whereas the much stronger conditions under HPO cause the observed clustering of the substitutional element and resulting nanoscale heterogeneity. Insofar as this does not alter the basic structure, the two factors that could enhance the superconductivity are therefore the dynamics [START_REF] Piazza | Study of atomic motions in EuBa 2 Cu 3 O 7-delta Mossbauer and EXAFS spectroscopies[END_REF] and modifications to the Fermi surface from the lowering of the Fermi level and the second nanophase. Changes in the dynamics are evident in the shift of the tunneling polaron from Cu1 to Cu2 and the large amplitude of the Mo-Sr pair relative to the complete damping of the Cu1-Sr. These two factors effect a division of the YBCO-type structure into two dynamical domains derived from these correlations. In YBCO, these are the CuO 2 -Y-Ba-Oap and the Cu1-O4 layers, with the Cu2-Oap being the more highly correlated pair because it shows only a single position. In YSCO-Mo, the dynamically correlated domains are the CuO 2 -Y-Sr, the Cu1-O4-Oap, and the Mo-O4-Sr-Oap domains. The heterogeneity would diminish the correlation lengths of the phonons to the interdomain spacing, making them intermediate between their normal size in a uniform crystal and local modes. These results for YSCO-Mo therefore point to a large role in exotic superconductivity for the dynamical properties and, in particular, dynamics outside of the harmonic regime. They also inform about the tunneling polarons that are coupled to the superconductivity [START_REF] Batistic | Polaron origin for anharmonicity of the axial oxygen in YBa2Cu3O7[END_REF][START_REF] Conradson | Axial oxygen-centered lattice instabilities and high-temperature superconductivity[END_REF][START_REF] Conradson | Evidence for an axial oxygen-centered lattice fluctuation associated with the superconducting transition in YBa 2 Cu 3 O 7[END_REF][START_REF] Allen | Characterization of a split axial-oxygen site in TlBa 2 Ca 3 Cu 4 O 11 by extended x-ray-absorption fine-structure spectroscopy[END_REF][START_REF] Conradson | Correlation between axialoxygen anharmonicity and Tc in YBa2Cu3O7 and related compounds[END_REF][START_REF] Egami | Local structural anomaly near Tc observed by pulsed neutron-scattering[END_REF][START_REF] Conradson | Axial oxygen-centered lattice instabilities in YBa2Cu3O7: An application of the analysis of extended x-ray-absorption fine structure in anharmonic systems[END_REF][START_REF] Arai | Local structural instability of high-T c oxide superconductors studied by inelastic neutron-scattering[END_REF]. The model that was used for the original theoretical analysis was the simplest one utilizing a symmetric cluster with a degenerate double well [START_REF] Salkola | Dynamic polaron tunneling in YBa 2 Cu 3 O 7 : Optical response and inelastic neutron scattering[END_REF][START_REF] Salkola | Correlation-function analysis of nonlinear and nonadiabatic systems: Polaron tunneling[END_REF][START_REF] De Leon | X-ray absorption fine structure applied to the study of systems with lattice instabilities[END_REF]. This approximation may be valid in materials with a single CuO 2 layer or when the polaron is on the chain Cu of YBCO. However, in compounds with two or more layers where the polaron is on a CuO 2type Cu, the square pyramidal geometry renders the two minima of the potential nondegenerate. The tunneling polaron forms within certain Cu-O bonds, but not for Mo-O. Nevertheless, it is sufficiently stable on or characteristic of Cu that the substitution of the Cu1 by Mo, or the Ba by Sr, does not eliminate it, but causes it to shift to the opposite Cu2-O pair. A final point is that since this shift occurs on all of the Cu2 ions, including the ones where the opposite ion is Mo, it is a collective rather than a local phenomenon. The significance of this observation is that the oscillatory exchange between the two conformations of the tunneling polarons would be facilitated by the cooperative action of a large number of atoms constituting a domain within a crystal where clustering of defects or substitutional atoms may already have caused the composition to differ from the bulk [START_REF] Conradson | Possible Bose-condensate behavior in a quantum phase originating in a collective excitation in the chemically and optically doped Mott-Hubbard system UO2+x[END_REF][START_REF] Conradson | Possible demonstration of a polaronic Bose-Einstein(-Mott) condensate in UO2(+x) by ultrafast THz spectroscopy and microwave dissipation[END_REF]. Collective behavior will then synchronize the oscillations over the domain.

Electronically, it is possible or even likely that the additional holes from the excess doping are the origin of the observed normal Fermi liquid carriers that are separate from the superconducting ones. It is possible that these reside in the Mo-enriched domains, so that this separation extends into real as well as momentum space. Insofar as the overall structure is conserved, the band structure in the Cu1-enriched domains will also be similar to that of the parent compound. If the Fermi level is lowered sufficiently, bands that are below it in the parent compound may intersect the Fermi surface [START_REF] Bianconi | 10th International Conference on Materials and Mechanisms of Superconductivity[END_REF]. In addition, there is a second effect of the heterogeneity that must be considered; even if the band structure in the Cu1 domains is mostly similar to YBCO/YSCO, it will be modified within the Mo-enriched domains. The new Fermi level and second phase may cause the emergence of a second band, which has been shown to significantly enhance T c in cuprates and other compounds [START_REF] Miloševi C | Emergent phenomena in multicomponent superconductivity: An introduction to the focus issue[END_REF][START_REF] Bussmann-Holder | The road map toward room-temperature superconductivity: Manipulating different pairing channels in systems composed of multiple electronic components[END_REF]. If this does occur, then the pairing and condensation mechanism in the "overdoped" HPO cuprates may simply be an extension of the mechanism in the conventional one that does not necessarily require novel physics [START_REF] Bozovic | The vanishing superfluid density in cupratesand why it matters[END_REF].

Materials and Methods

YSCO-Mo was the same sample as in the previous report [START_REF] Gauzzi | Bulk superconductivity at 84 K in the strongly overdoped regime of cuprates[END_REF] reannealed to give the same T c , superconducting fraction, and other properties as before (SI Appendix, Fig. S2), although with a somewhat broader transition [START_REF] Gauzzi | Bulk superconductivity at 84 K in the strongly overdoped regime of cuprates[END_REF]. Atom labels were the same as used previously (SI Appendix, Fig. S1). The material was ground with a mortar and pestle and suspended in epoxy, and the epoxy was allowed to set and cure in the bore of a 16-T magnet at the Institute of Physics, Chinese

Fig. 1 .

 1 Fig. 1. (A) Conventional phase diagram for YBCO with the addition of YSCO-Mo and other HPO compounds whose superconducting regions (9, 10, 13, 27, 70, 71) do not conform to the "dome" found for materials prepared by oxidation with O 2 . (B) Half of the unit cell from the crystallographic structure (13) of YSCO-Mo, with labels as in SI Appendix, Fig. S1. The c axis is across the figure, through the Cu2-O1-Cu1 axis, with the CuO 2 plane adjacent to the Y and the Cu of the chains on the right side going vertically on and out of the page. One-fourth of the Cu1 are replaced by Mo. Cu1 and the substituting Mo are in the chains, Cu2 is in the CuO 2 planes, O1 or Oap is the apical O bridging Cu1/Mo with Cu2, O2 bridges between the Cu2 sites in the CuO2 planes (this is also O3 in orthorhombic YBCO because YSCO-Mo is tetragonal), O4 bridges the Cu1/Mo sites, and the XAFS results do not require the O5 or O6 sites of the YSCO-Mo crystal structure (SI Appendix, Fig. S1). Although the crystal structure places the O5 and O6 atoms of the Cu-Mo layer off of the Cu-Cu axes as in the crystal structure, the Cu-O and Mo-O distances determined by the XAFS locate the O4 atoms directly between the Mo-Mo and Cu-Cu pairs.

Fig. 2 .

 2 Fig. 2. (A) Cu K-edge XANES of oriented YBCO and YSCO-Mo. (B) Mo Kedge XANES of MoO 3 parallel (light blue) and perpendicular (dark blue) to the very short, terminal Mo-O multiple bond, MoO 2 parallel and perpendicular to the directions of its Mo-Mo chains, and the YSCO-Mo along its two orientations.

Fig. 3 .

 3 Fig. 3. EXAFS (FT or χ(R) representation) of YSCO-Mo. (A) For Cu measured in the aa plane, the main graph shows the data and fit in real space, Upper Right Inset shows the same in k, and Lower Right Inset shows the FT moduli of the data, fits, and differences in their upper halves and the contributions of the individual neighbor shells, inverted for clarity, in their lower halves with red, O; violet, Y; purple, Sr; green, Cu; and orange, Mo. The relative numbers of atoms are reflected by the peak amplitudes, reduced by 1/R 2 and the Debye-Waller factor. (B) The same as A, but for Cu measured in the c direction. (C) The same as A, but for Mo measured in the aa plane. (D) The same as B for Mo in the c direction.

Q: 13

 13 Academy of Sciences (IOP-CAS). X-ray; 14 diffraction (XRD) analysis showed only the diffraction pattern of YSCO-Mo and the essentially complete cylindrical orientation of the YSCO-Mo along the c axis coincident with the applied field (SI Appendix, Figs. S6-S9). Its behavior was therefore identical with all other cuprates [except Sr s CuO 3.3[START_REF] Conradson | Local structure of Sr 2 CuO 3.3 , a 95 K cuprate superconductor without CuO2 planes[END_REF]], giving Ejjc and E⊥cjjaa (in the aa plane) spectra. XAFS measurements at 52 K were performed at the Stanford Synchrotron Radiation Lightsource on beamline 2-2 in the continuous-scanning mode. Transmission data were analyzed by standard methods, with one recent description in ref.[START_REF] Conradson | Nanoscale heterogeneity, premartensitic nucleation, and a new plutonium structure in metastable delta fcc Pu-Ga alloys[END_REF]. Curve fits of the EXAFS were performed with amplitudes and phases calculated by FEFF9[START_REF] Rehr | Parameter-free calculations of X-ray spectra with FEFF9[END_REF]. The data ranges and other specific parameters are given in the text or figures. XRD data were obtained on powder diffractometers at IOP-CAS and the Commissariat Q:15 à l'Énergie Atomique Saclay laboratory. More detailed descriptions of the materials and methods, the capabilities of XAFS vis-à-vis these results and their interpretations, the two-site Oap distribution, and the interpretation of the XANES are in SI Appendix. Data Availability. Data are available by request to S.D.C. ACKNOWLEDGMENTS. S.D.C. and V.N. were supported by Slovenian Research Agency Research Core Funding P1-0040. Work at Washington Q:16 State University is partially supported by NSF Division of Materials Research Early Concept Grants for Exploratory Research Grant 1928874. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences Contract DE-AC02-76SF00515. Work at Stanford and SLAC is supported by the Stanford Institute for Materials and Energy Science, SLAC National Accelerator Laboratory, under Department of Energy, Office of Basic Energy Sciences Contract DEAC02-76SF00515. Work at IOP-CAS was supported by the Ministry of Science and Technology of China and the National Natural Science Foundation of China through Research Projects 2018YFA03057001, 2017YFA0302901, 11820101003, 2016YFA0300301, 2015CB921000, and 112111KYS820150017.

Fig. 4 .

 4 Fig. 4. Conceptual depiction of Cu1-Mo plane. As described in the text, the Mo is clustered into domains 12 to 20 unit cells (= 20 to 30 Mo atoms) in size, in which it can exert its preference for a distorted octahedral geometry, allowing the Cu1 to be in its preferred square geometry with its two Oaps. The disorder at the interfaces that results in some interstitial O out of this plane and the minimized contribution of the Mo-Cu pairs with bridging O caused by the strain from the average Mo-O distances being longer than the Cu-O ones is not fully shown. The alteration of the directions of the Cu-O chains at the Mo clusters result in the average tetragonal symmetry.

  Oap and Mo-Cu2 distances the same as for Cu. The extra features in the spectrum are fit by O neighbors at 2.39 and 2.69, with low numbers of atoms indicating less than one atom per Mo. Together with the finding of an O at 2.33 to 2.39 Å for both orientations, implying an off-axis interstitial, these O atoms are most likely at the interfaces between the Mo and Cu domains.

3.79 Å, bracketing the Cu-Cu distance of 3.83 Å. In contrast to Ejjaa, the Ejjc EXAFS gives a local structure very similar to the Cu, with Mo-

Table 1 .

 1 Relevant interatomic distances

		Cu2-O2 Cu1-O5/6 Cu1-Cu1 Cu2-Cu2	Cu1-Oap	Cu2-Oap Cu2-Cu2: Ejjc Cu1-Cu2 Cu2-Y Cu2-Sr Cu1-Sr
	xtal (14)	1.92	3.83	1.88	2.16	3.46	4.05	3.21	3.31	3.46
	Cu EXAFS	1.91	3.81	1.88	2.14	3.45	4.04	3.19 3.35/3.31
	Mo EXAFS 1.84/2.04/2.33/2.54 3.79 (Cu1)/3.95 (Mo) 1.88/2.39/2.69			4.05			3.48

of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1918704117 Conradson et al.

of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1918704117 Conradson et al.


Steven D Conradson

Theodore H Geballe
email: geballe@stanford.edu

Changqing Jin

Lipeng Cao

Gianguido Baldinozzi

Jack M Jiang

Matthew J Latimer

Oliver Mueller

Ivan Bozovic

Douglas J J Scalapino

Local structure of Sr 2 CuO 3.3 , a 95 K cuprate superconductor without CuO 2 planes

The local structure of the highly "overdoped" 95 K superconductor Sr 2 CuO 3.3 determined by Cu K X-ray absorption fine structure (XAFS) at 62 K in magnetically oriented samples shows that: 1) the magnetization is perpendicular to the c axis; 2) at these levels of precision the Cu sublattice is tetragonal in agreement with the crystal structure; the O sublattice has: 3) continuous -Cu-O-chains that orient perpendicular to an applied magnetic field; 4) approximately half-filled -Cu-O-chains that orient parallel to this field; 5) a substantial number of apical O vacancies; 6) O ions at some apical positions with expanded Cu-O distances; and 7) interstitial positions that imply highly displaced Sr ions. These results contradict the universally accepted features of cuprates that require intact CuO 2 planes, magnetization along the c axis, and a termination of the superconductivity when the excess charge on the CuO 2 Cu ions exceeds 0.27. These radical differences in charge and structure demonstrate that this compound constitutes a separate class of Cu-O-based superconductors in which the superconductivity originates in a different, more complicated structural unit than CuO 2 planes while retaining exceptionally high transition temperatures.

overdoped cuprate | CuO 2 plane | high-temperature superconductivity | X-ray absorption fine structure spectroscopy A lthough 135 K has remained the highest transition temper- ature in cuprates since 6 y after their initial discovery [START_REF] Bednorz | Possible high-tc superconductivity in the Ba-La-Cu-O system[END_REF][START_REF] Keimer | From quantum matter to high-temperature superconductivity in copper oxides[END_REF], given that an accurate theory remains lacking still higher transition temperatures cannot be ruled out. Here we report X-ray absorption fine structure (XAFS) experiments on Sr 2 CuO 3.3 (SCO) prepared by high-pressure oxygen (HPO) methods that show that this compound lacks the CuO 2 planes found in all other cuprates while retaining a T c of 95 K. The HPO cuprates [START_REF] Ono | Superconductivity in Cr-1212 cuprates Sr2-xBaxYCu2.8Cr0.2Oz[END_REF][START_REF] Ono | Oxygenation and critical-temperature optimization in M-1212 cuprates (Sr, Ba)(2)YCu(2.8)M[END_REF][START_REF] Haskel | Altered Sr environment in La 2-x Sr x CuO 4[END_REF] give a second, T c vs. Cu-charge phase diagram whose superconducting region differs radically from the "dome" (6) common to the "conventional" materials that are doped by reaction with O 2 . Instead of the superconductivity terminating with the formation of a Fermi liquid when the excess charge on the Cu atoms in the CuO 2 planes reaches ∼0.27 per Cu, T c plateaus or even continues to increase, opening a new region of superconductivity on the high Cu-charge side of the phase diagram. In addition, these HPO cuprates are tetragonal, their heat capacities demonstrate coexisting Fermi liquid and superconducting electrons [START_REF] Gauzzi | Bulk superconductivity at 84 K in the strongly overdoped regime of cuprates[END_REF][START_REF] Li | Superconductivity in a unique type of copper oxide[END_REF], and they do not adhere to the empirical correlation between T c and the Cu-apical O (Oap) [START_REF] Rybicki | Perspective on the phase diagram of cuprate high-temperature superconductors[END_REF][START_REF] Bozin | Charge-screening role of c-axis atomic displacements in YBa 2 Cu 3 O 6+x and related superconductors[END_REF][START_REF] Peng | Influence of apical oxygen on the extent of in-plane exchange interaction in cuprate superconductors[END_REF] or apical cation [START_REF] Kim | Apical charge flux-modulated in-plane transport properties of cuprate superconductors[END_REF] distance. Ba 2 CuO 3.2 [START_REF] Li | Superconductivity in a unique type of copper oxide[END_REF][START_REF] Takano | Superconductivity in the Ba-Sr-Cu-O system[END_REF][START_REF] Li | Synthesis and structure stability of Ba2CuO3+delta under high pressure[END_REF], a structural analog of SCO, exhibits an oblate Cu geometry with its Cu-Oap distance of less than 1.9 Å presumably inverting the ordering of the d x

2

-y 2 and d z 2 states (8). SCO and related compounds were first prepared shortly after the initial discovery of cuprates [START_REF] Hiroi | A new family of copper-oxide superconductors SrN+1CuNO2N+1+delta stabilized at high-pressure[END_REF]. Jin and co-workers subsequently found multiple phases [START_REF] Yang | TEM and EELS characterization of a Sr2CuO3+delta superconductor post-annealed at different temperatures: Enhancement of T-c by apical oxygen reordering[END_REF][START_REF] Liang | Growth of Sr 2 CuO 3+delta superconductor single crystals at high pressure[END_REF][START_REF] Liu | A new modulated structure in Sr 2 CuO 3+delta superconductor synthesized under high pressure[END_REF], but recent improvements in the synthesis now produce single-phase SCO with T c = 95 K (SI Appendix, Fig. S1) [START_REF] Liang | Growth of Sr 2 CuO 3+delta superconductor single crystals at high pressure[END_REF][START_REF] Liu | A new modulated structure in Sr 2 CuO 3+delta superconductor synthesized under high pressure[END_REF] Between La 2 CuO 4+δ and Sr 2 CuO 3+δ (SCO) the structure changes radically. La 2 CuO 4+δ exhibits the common cuprate geometry [START_REF] Hafliger | Quantum and thermal ionic motion, oxygen isotope effect, and superexchange distribution in La2CuO4[END_REF] with fully ordered CuO 2 planes with 3.78-Å Cu-Cu distances with O midway between, fully occupied Cu-Oap sites at 2.41 Å, and Cu-La at 3.24 Å. The structure of the other parent, Sr 2 CuO 3 [START_REF] Teske | Alkaline earth metals oxocuprate. 2. Sr 2 CuO 3[END_REF], is notable for its highly orthorhombic symmetry with -Cu-Ochains with a 3.91-Å Cu-Cu distance in the a direction and 3.48-Å Cu-Cu distances in the b direction that lacks bridging O. The disparate nature of the connections between the Cu sites along the crystallographic axes results in Sr 2 CuO 3 being a "nearly ideal . . . [one-dimensional] . . . Heisenberg antiferromagnet" [START_REF] Thurber | O NMR study of q = 0 spin excitations in a nearly ideal S = 1 / 2 1D Heisenberg antiferromagnet, Sr2CuO3, up to 800[END_REF]. The Oap sites are all occupied with the same 1.95 Cu-Oap distances as in the chains. This gives c-oriented SrCuO 2 planes with 3.22-Å Cu-Sr distances. Increasing the O stoichiometry by only ∼10% in HPO SCO results in its transformation to a tetragonal space group with a Cu-Cu distance of 3.8 Å that is typical of cuprates. However, its bulk stoichiometry with a fractional number of O atoms differs from the formula of its unit cell that is constrained to integers, and the absence of superlattice peaks demonstrates that these excess O atoms are distributed aperiodically (or dynamically). This disorder within the constraints of the tetragonal symmetry that presumably does not apply to the O sites causes ambiguities in the crystallographic determination of its structure that include the possibility of vacancies in the CuO 2 planes [START_REF] Laffez | Synthesis of superconducting Sr 2 CuO 3+delta using high-pressure techniques[END_REF][START_REF] Geballe | Enhanced superconductivity in Sr2CuO4-v[END_REF].

XAFS is arguably the most incisive experimental method for probing these behaviors in mixed valence, transition metal, correlated materials. It complements the crystallographic analysis of Significance CuO 2 planes are a universal component of cuprate superconductors. Sr 2 CuO 3+δ that has a T c of 95 K despite its excessively high doping level has been reported to have vacancies in these planes. Extended X-ray absorption fine structure measurements not only provide definitive proof but furthermore show that in magnetically oriented samples not only are there also apical O vacancies but that the -

Q:8
Cu-O-chains normal to the orienting field are complete

Q:9
while the O sites of the chains parallel with this field are only half filled. These unique characteristics of a material with such a high transition temperature demonstrate that there are still substantial gaps in our knowledge of exotic superconductivity, including such fundamental aspects as the types of structures that support it.

SCO because: 1) it does not depend on long-range order or translational symmetry and therefore reveals aperiodic local lattice distortions; 2) its element selectivity separates and isolates many of the atom pairs to give a better basis for detailed analysis than X-ray or neutron pair distribution function analysis; and 3) its intrinsic time and energy scale that correspond to collective dynamical phenomena in correlated materials make it sensitive to the dynamical and instantaneous aspects of the structure, S(q, ω) or S(q, t = 0) [START_REF] Egami | Local structural anomaly near Tc observed by pulsed neutron-scattering[END_REF][START_REF] Salkola | Dynamic polaron tunneling in YBa 2 Cu 3 O 7 : Optical response and inelastic neutron scattering[END_REF][START_REF] Salkola | Correlation-function analysis of nonlinear and nonadiabatic systems: Polaron tunneling[END_REF][START_REF] Deleon | Applications of Synchrotron Radiation Techniques to Materials Science III[END_REF][START_REF] Bishop | Signatures of mesoscopic Jahn-Teller polaron inhomogeneities in high-temperature superconductors[END_REF]. The differences between the extended XAFS (EXAFS) [START_REF] Conradson | Axial oxygen-centered lattice instabilities and high-temperature superconductivity[END_REF][START_REF] Young | Reverse Monte Carlo study of apical Cu-O bond distortions in YBa2Cu3O6.93[END_REF] and complementary diffraction and neutron scattering measurements [START_REF] Egami | Local structural anomaly near Tc observed by pulsed neutron-scattering[END_REF][START_REF] Arai | Local structural instability of high-T c oxide superconductors studied by inelastic neutron-scattering[END_REF] were therefore key in originally identifying and characterizing the Cu-Oap double-well potential [START_REF] Conradson | Evidence for an axial oxygen-centered lattice fluctuation associated with the superconducting transition in YBa2Cu3O7[END_REF], its assignment to a tunneling polaron [START_REF] Salkola | Dynamic polaron tunneling in YBa 2 Cu 3 O 7 : Optical response and inelastic neutron scattering[END_REF][START_REF] Deleon | Applications of Synchrotron Radiation Techniques to Materials Science III[END_REF][START_REF] Batistic | Polaron origin for anharmonicity of the axial oxygen in YBa2Cu3O7[END_REF], and its coupling to the superconductivity in other cuprates [START_REF] Bishop | Signatures of mesoscopic Jahn-Teller polaron inhomogeneities in high-temperature superconductors[END_REF][START_REF] Allen | Characterization of a split axial-oxygen site in TlBa 2 Ca 3 Cu 4 O 11 by extended x-ray-absorption fine-structure spectroscopy[END_REF][START_REF] Deleon | Planar oxygen-centered lattice instabilities in Tl-based hightemperature superconductors[END_REF]. Tunneling polarons differ from the common small polarons that exhibit thermally activated hopping between neighboring sites in a crystal, exchanging the normal crystal structure adopted by the atoms at the second site with the distorted polaron structure and excess charge that had been at the first. A tunneling polaron is the oscillatory interchange between two distinct arrangements of a given set of atoms that contain the excess charge, with the two structures denoted by the charges and positions/local geometries of the constituent atoms. The tunneling polaron remains in the same location within a crystal, where it could be pinned because of stationary defects or special aspects of the atoms of its location. In addition, in contrast to the original, elementary, three-atom model of a Cu atom bracketed by two Oap, it may involve a large number of atoms and the two structures will be nondegenerate [START_REF] Conradson | Possible demonstration of a polaronic Bose-Einstein(-Mott) condensate in UO 2(+x) by ultrafast THz spectroscopy and microwave dissipation[END_REF][START_REF] Conradson | Closure of the Mott gap and formation of a superthermal metal in the Frohlich-type nonequilibrium polaron Bose-Einstein condensate in UO2+x[END_REF].

A procedure that was key in these studies was the enhancement of the sensitivity of EXAFS to the different components of the structure ( 38) by orienting the samples in a magnetic field to align them along a unique crystallographic axis. The spectra therefore measure the projections of the neighbor atoms on the axis parallel to the orienting magnetic field and the plane perpendicular to it, rendering the problem one of cylindrical symmetry. The EXAFS will therefore help elucidate the characteristics of a crystallographically modulated structure [START_REF] Liu | A new modulated structure in Sr 2 CuO 3+delta superconductor synthesized under high pressure[END_REF], the widths of the distributions and whether they are continuous or consist of discrete, separated distances. The diffraction peaks of these samples were measured with the incident and diffracted X-rays in the plane normal to the axis along which the XAFS was measured (SI Appendix, Fig. S2). The (001) reflections of a YBa 2 Cu 3 O 7 and the two SCO samples were analyzed by the method of March and Dollase [START_REF] Dollase | Correction of intensities for preferred orientation in powder diffractometry-Application of the march model[END_REF]. The corresponding angular probability functions of the c crystallographic axis (Fig. 1) show that the EjjH sample and E⊥H samples are oriented, although to a somewhat lesser degree than for YBa 2 Cu 3 O 7 . The alignment of its c axis normal to YBa 2 Cu 3 O 7 EjjH is evident. The induced magnetization in SCO is therefore orthogonal to the c axis, unlike all other cuprates where the c axis orients strongly along the field direction. SCO maintains at least some of the magnetic anisotropy from the CuO 2 chains in undoped Sr 2 CuO 3 [START_REF] Schlappa | Probing multi-spinon excitations outside of the two-spinon continuum in the antiferromagnetic spin chain cuprate Sr2CuO3[END_REF] despite its tetragonal space group. This confirms the prior suggestion that the crystal structure is incomplete, augmented by showing that the properties of SCO are coupled to these extracrystallographic factors. The unique direction parallel to the magnetization will be labeled "a," the orthogonal direction in the Cu planes "b."

The capabilities and limitations of EXAFS in elucidating structure and dynamics in correlated materials are described in SI Appendix. EXAFS, χ(k), is best presented as its Fourier transform, χ(R), because the modulus peaks that originate in the constituent waves of the original χ(k) correspond to the contributions of the neighbor atom shells arranged from short to long absorber-neighbor distances to give an approximate representation of the partial pair distribution. Inspection of the Fourier transforms of the Cu K EXAFS of the two orientations (Fig. 2) show the same Sr and Cu contributions at, respectively, R = 2.9 and 3.5 Å. The contribution of the Cu neighbors in both the a and bc-oriented spectra differs from all other cuprates where it occurs only in Ejjab spectra, corroborating this unique orientation found in the diffraction. Curve-fitting analysis finds 3.79 Å Cu-Cu distances. An identical Cu-Cu distance for both orientations demonstrates that the tetragonal symmetry found crystallographically is intrinsic and not the result of small, orthorhombic domains averaging to tetragonal. The amplitudes of the Cu signals that are ∼40% of the amount displayed by other cuprates [START_REF] Conradson | Axial oxygen-centered lattice instabilities and high-temperature superconductivity[END_REF][START_REF] Conradson | Correlation between axial-oxygen anharmonicity and Tc in YBa2Cu3O7 and related compounds[END_REF] are also consistent with a division of the Cu contribution between the two orientations. The Cu-Sr pair is best fit with the principal and a smaller shell separated by an amount just above the resolution limit, 3.22/3.35-Å Cu-Sr distances for EjjH and 3.24/3.38 Å for E⊥H. These are equal within the uncertainty for the two orientations. This result is indicative of an overall anharmonic distribution. The Cu-Cu and principal Cu-Sr distances are within 0.01-0.02 Å of the crystallographic values.

If the O sublattice is tetragonal then all of the Cu-O distances in the EjjH spectrum from the aa plane must be found in the E⊥H spectrum, with any additional ones belonging to the c component. Deviation of the O positions from the tetragonal symmetry of the Cu-Sr sublattice is evident in the comparison of the locations of the peaks of the two spectra (Fig. 2). Unlike the tetragonal arrangement of the Cu and Sr atoms, the O sublattice is therefore orthorhombic with distinct a and b axes but insufficiently ordered to give a clear signature in the diffraction pattern dominated by the Cu and Sr. The EjjH spectrum measures the a components of the Cu pair distribution. The O region of the spectrum for EjjH is dominated by a single peak (Fig. 2A) [START_REF] Conradson | Axial oxygen-centered lattice instabilities and high-temperature superconductivity[END_REF][START_REF] Conradson | Axial oxygen-centered lattice instabilities in YBa2Cu3O7: An application of the analysis of extended x-ray-absorption fine structure in anharmonic systems[END_REF]. Complete curve fits, however, require three O neighbors at 1.92, 2.09, and 2.31 Å, with a fourth low-amplitude shell at 2.64 Å giving a small improvement in the fit (Fig. 2 A, Inset and SI Appendix, Fig. S3). The 1.92-Å Cu-O distance is close to half of the 3.79-Å Cu-Cu distance. The E⊥H spectrum displays three distinct peaks in the O neighbor region. The lower position of the first one demonstrates a shorter Cu-O distance than in the a direction, just as the other peaks at higher R signify longer ones. This complicated spectrum is fit by four O neighbors at 1.83, 2.00, 2.27, and 2.61 Å (Fig. 2 B,Inset). An additional small feature in both spectra at R ∼ 2.5 Å is fit by Sr and/or O at ∼2.8-2.9 Å. The 1.83-and 2.00-Å distances with their equivalent amplitudes could be the two parts of an off-center O in a b-oriented -Cu-O-chain and/or two Cu-Oap distances of a distorted square Cu site with O vacancies in the ab plane. The differences between 1.83, 1.92, 2.00, and 2.09 Å are significantly larger than the normal EXAFS error ±0.02 Å, confirming the separate a and b Cu-O distributions and division of the spectra into a and the combined bc component. Since the Cu-Cu wave in χ(k) in both spectra is defined by the amplitudes and phases of the Insofar as the most significant finding of this study is the location of the O ions and vacancies in the aa-oriented Cu planes a thorough analysis was performed that provides a graphic presentation of the relevant results. As explained previously, the 0.11-Å resolution derived from the upper limit of the spectra ensures that the individual Cu-O waves in χ(k) in the Ejja spectrum are easily separable. Rather than rely solely on curve-fit results, the location of the O vacancies is addressed by directly comparing the isolated Cu-O-Cu and Cu-O EXAFS waves against appropriate standards, in this case the same waves from, respectively, the Ejjbc-oriented spectra and the Ejja spectra from YBa 2 are around half filled (Fig. 4A). This half filling corresponds to the Cu(II):(III) ratio. Since ordering of the O vacancies in the b-oriented -Cu-Ochains would be observed in the diffraction, these are likely located aperiodically. However, within the constraints of an aperiodic distribution it is still possible that the O atoms in these -Cu-Ochains cluster. At one extreme there is no cooperativity between them, these O atoms are located randomly, and their overall distribution is homogeneous on a scale sufficiently large to overcome small deviations (Fig. 4A). This random distribution results in Cu ions with two, three, and four O neighbors within the aa Cu plane whose Cu-O distances would be close to half of the 3.79-Å distance between the pairs of Cu atoms that they bridge as in La 2 CuO 4 (Fig. 4D). At the other extreme these O atoms may cluster into domains with the ordered CuO 2 plane structure (Fig. 4 C and E) whose only restriction is that their size must be below the diffraction limit, which becomes larger if these domains are aperiodically distributed in the material. This distribution results in a heterogeneous, nanophase separated structure. Intermediate distributions that would be inhomogeneous (Fig. 4B) are not antithetical to any of these considerations. However, that Q:10 which occurs does have consequences. If these O atoms are fully clustered then it is easily understood that the superconductivity resides in the CuO 2 domains, enabled by the short pair-correlation lengths, and would be very similar to conventional cuprates except it would percolate between the domains instead of flowing unobstructed. In contrast, in the homogeneous distribution

Q:11
, the superconductivity would be quenched at either the vacancy or occupied sites and therefore filamentary. For YSr 2 Cu 2.75 Mo 0.25 O 7.54 , the Mo served as a probe for its own organization ( 6), but there is no comparable probe for the O atoms within SCO. However, our unpublished EXAFS spectra over a range of temperatures are more consistent with the random, homogeneous type of structure.

The remaining issue for the structure is local, the disposition of the O neighbors with Cu-O distances greater than 2 Å and the possibility of Sr at ∼2.8 Å. Assigning formal charges or valence, the Cu with four O neighbors therefore already has the preferred Cu 2+ square planar geometry if Oap are missing or at longer distances that may be tilted from the c axis. Similarly, if the Oap are at their Sr 2 CuO 3 positions the Cu ions with two a-chain O vacancies will have the same Cu(II) assignment with the axial positions on the a chain vacant. This scenario implies that the Cu ions with three O neighbors from the plane would be Cu(III) that accommodates a wider range of geometries that would include their Oap neighbors. Consistent with the added charge, each adventitious O therefore results in ∼2 Cu(III) and a similar number of O in a-oriented -Cu-O-chains, with the second coming from a 2) from the fits followed by Fourier back-transformation over the width of the spectral feature from the Cu. These are the original waves; converting to relative numbers of atoms from the amplitude ratios requires the polarization correction described in the text. displacement of an Oap into the bridging position in the chain. The varying Cu geometries will give the range of Cu-Oap distances, with disorder reducing the EXAFS amplitudes. Further insight is gained by tracking the evolution of the structure from Sr 2 CuO 3 to T-La 2 CuO 4 at the Sr site. The Sr in Sr 2 CuO 3 has seven O nearest neighbors with Sr-O distances in a narrow range around 2.5 Å (Fig. 5A), whereas La 2 CuO 4 has eight La-O from 2.6 to 2.8 Å and a ninth very short one to the apical O at 2.36 Å (Fig. 5B). Sr 2 CuO 3 is presumably stable because of its high local symmetry and uniform Cu(II). In SCO this symmetry is destroyed by the half-filled b-oriented Cu-O-chains, apical O vacancies, and the mixed Cu valence. The noninteger bulk stoichiometry will also result in unit cells with different compositions and structures whose distribution lacks translational symmetry. The removal of the apical O opens an extremely large space for the Sr (Fig. 5C). Displacements of the Sr in combination with the Cu(II, III) mixture would cause collective displacements and highly unusual Sr and Cu geometries. One such possibility, a rotation of a CuO 2 moiety, is depicted (Fig. 5C). The longer Cu-O pairs could thus be Cu-Oap expanded because of the displaced Sr. The very short ∼2.8-Å Cu-Sr distance that gives the best fits of the Cu EXAFS at some temperatures would thus be somewhat analogous to the 2.7-Å Cu-Cu distances in the alkali metal MCuO 2 compounds, here caused by bent, double-O bridges.

The question of the whether the O vacancies are located in the apical positions or in highly disrupted CuO 2 planes is therefore moot; they are located in both positions. The vacancies will result in substantial displacements of the O ions to give

Q:12
Cu and Sr geometries compatible with the Cu(II, III) combination. Collective and cooperative effects could be expected to result in preferred configurations of sets of atoms, but these would be positioned aperiodically throughout the crystal. Solving the structure in the tetragonal space group would give the average position of their projections onto the axes through the nearest Cu. In contrast, EXAFS gives a more complete depiction of this system because of its sensitivity to local order. The unpaired electron density along the a-oriented Cu-O chains resides in a different orbital than in other cuprates, and the a-b anisotropy rotates the magnetization. Superconductivity in the disrupted CuO 1.5 planes has been described: percolation of the short coherence length superconductivity that resides in domains with the conventional CuO 2 structure, or filamentary superconductivity through continuous Cu-O networks. If ordered, 2D Q:13 structures with Cu and O atoms are required there is an alternative: planes in the c direction with Sr that still have a square sublattice of Cu but with a Q:14 type of Cu-Sr-O unit that will have different Cu energy levels and occupations. These unique attributes of the composition, structure, magnetism, and other properties of SCO demonstrate the existence of a Q:15 class of exotic superconductors. This class of materials would have the secondhighest transition temperature after conventional cuprates. Under certain conditions, superconductivity can occur just as effectively via more structurally complex alternatives to the ubiquitous CuO 2 planes.

Materials and Methods

Single-phase SCO with T c = 95 K (SI Appendix, Fig. S1) and 19% superconducting volume fraction was prepared by annealing Sr 2 CuO 3 and KClO 4 in amounts giving a nominal composition of Sr 2 CuO 3.3 at around 7 GPa and 1,050 °C for 30 min [START_REF] Liang | Growth of Sr 2 CuO 3+delta superconductor single crystals at high pressure[END_REF][START_REF] Liu | A new modulated structure in Sr 2 CuO 3+delta superconductor synthesized under high pressure[END_REF]. The XAFS samples were prepared by having a mixture of the Sr 2 CuO 3.3 in epoxy set in the bore of a 16-T magnet. X-ray diffraction analysis of these samples showed only the Sr 2 CuO 3.3 pattern (SI Appendix, Fig. S2). XAFS was measured in the continuous transmission mode on beamline 2-2 at the Stanford Synchrotron Radiation Lightsource. XAFS spectra were analyzed by standard methods [START_REF] Conradson | Nanoscale heterogeneity, premartensitic nucleation, and a new plutonium structure in metastable delta fcc Pu-Ga alloys[END_REF] with curve fits using amplitudes and phases calculated by the feff9 code [START_REF] Rehr | Parameter-free calculations of X-ray spectra with FEFF9[END_REF]. A more detailed description is found in SI Appendix. Original data are available from S.D.C. on request (st3v3n.c0nrads0n@icloud.com).

Fig. 1 . 27 .

 127 Fig. 1. March and Dollase probability factors (39) for sample orientation in magnetic field. The result for the YBa 2 Cu 3 O 7 jjH sample that was prepared in the same mold as the SCOjjH sample is included for reference to show the 90°rotation of the (001) axis (c axis) of the two compounds Q:27

  Cu 2.75 Mo 0.25 O 7.54 that we have shown has fully ordered CuO 2 planes and CuO 3 -type chains. This comparison not only gives the relative numbers of Cu-O-Cu pairs and bridging O in the EjjHjja spectrum by direct comparison of their magnitudes but also tests the extent to which their originating structures are identical via the similarity of their phases and amplitude envelopes. The Cu-O-Cu waves in χ(k) from the two orientations (Fig. 3A) are almost identical, verifying this assignment and the presumption that uncorrelated thermal motion makes the contributions of any unbridged Cu-Cu pairs negligible. Deriving the relative numbers of Cu atoms requires correcting the spectral amplitudes by the polarization geometry factors of 3 for the EjjHjja spectrum and 3/2 for the E⊥Hjjbc (43). The essentially identical amplitudes therefore demonstrate that the numbers of Cu-O-Cu neighbors and therefore bridging O in the a direction are only close to half that for b. The a-oriented, partial -Cu-O-chains and presumably the mixed Cu(II, III) valence resulting from the added charge from the excess O account for the conversion of the rectangular arrangement of the Cu and Sr atoms of Sr 2 CuO 3 to their square geometry in SCO, even while the O atoms separate into different arrangements along the a and b directions so that their sublattice has orthorhombic symmetry (40). This same parameter is obtained independently by comparing the Cu-O wave from the EjjHjja spectrum with the one from, e.g., YSr 2 Cu 2.75 Mo 0.25 O 7.54 (Fig. 3B) with its known structure (6). The amplitude ratio is 0.6-0.7. After the same factor of 2 polarization correction, the corrected amplitude of 0.35 times the average 3-1/3 O/Cu neighbors in YSr 2 Cu 2.75 Mo 0.25 O 7.54 gives ∼1.1 O atoms in the a direction for SCO. The numbers of O and Cu neighbors therefore show that the b⊥H -Cu-Ochains are essentially intact from Sr 2 CuO 3 and the ajjH -Cu-O-chains

Fig. 2 .

 2 Fig. 2. EXAFS [Fourier transform or χ(R) representation] of SCO (A) along the same direction as the magnetic field and (B) perpendicular to the magnetic field. The main figures show the data and fit in real space, the Upper Right Insets the same in k, and the Lower Right Insets show the Fourier transform moduli of the data, fits, and differences in their upper halves and the contributions of the individual neighbor shells, inverted for clarity, in their lower halves Q:28. The vertical chartreuse lines trace the position of the spectral features for, from low to high, the O neighbor at 1.92 Å, the O neighbor at 2.6 Å, the Sr neighbors, and the Cu neighbors with a bridging O ion between them. The relative numbers of atoms are reflected by the peak amplitudes, reduced by 1/R 2 .

Fig. 3 .

 3 Fig. 3. EXAFS waves and amplitudes for direct comparison of relative atom numbers. (A) The Cu-Cu EXAFS from the two orientations of SCO. (B) The nearest-neighbor Cu-O waves and amplitudes from the a orientation of SCO and the ab orientation of YSr 2 Cu 2.75 Mo 0.25 O 7.54 and the ratio of the amplitudes ×5. The Cu-O-Cu and Cu-O EXAFS from the spectra were separated by subtracting all of the other components (Fig.2) from the fits followed by Fourier back-transformation over the width of the spectral feature from the Cu. These are the original waves; converting to relative numbers of atoms from the amplitude ratios requires the polarization correction described in the text.

Fig. 4 .

 4 Fig. 4. Conceptual depictions of O vacancies in Sr 2 CuO 3.3 . The a-oriented -Cu-Ochain occupancy distribution for: (A) a random, homogeneous distribution caused by no cooperation between the O atoms; (B) a moderate tendency for clustering resulting in an inhomogeneous distribution; (C) a strong tendency for clustering causing nanophase separation and a heterogeneous structure composed of domains below the diffraction limit in size consisting of either CuO 2 planes or -Cu-O-chains. (D) The corresponding structure of A. (E) The corresponding structure of C.

Fig. 5 .

 5 Fig. 5. Conceptual depictions of possible displacements in Sr 2 CuO 3.3 . (A) Sr 2 CuO 3 with the Cu-O chains at the bottom, (B) the T structure of La 2 CuO 4 with the CuO 2 planes derived from the Cu-O chains by the insertion of O bridges between the Cu pairs on the b axis of Sr 2 CuO 3 at the bottom, and (C) Sr 2 CuO 3.3 with the Cu atoms in the ab planes at the bottom and Oap and one of the bridging O atoms removed. The structure in C with Sr is produced from B with La by removing the central apical and a b-oriented Cu-O-chain O atoms and displacing the central Sr atom and two of its O neighbors in the directions of the arrows in B, with expanded Sr-O bonds magenta and pink, expanded Cu-O bonds turquoise. The Oap vacancy in SCO creates a large volume for the Sr atom that the chain O vacancy renders asymmetric. The O excess results in comparable amounts of Cu(II) and (III). The displacement of the Sr atom accompanied by a rotation of the O-Cu-O moiety around the b axis is a possible mechanism for giving the longer Cu-O distances found by the EXAFS. These motions would be facilitated by cooperative action of the atoms in neighboring unit cell in which the inverse motions are synchronized so that this extended set of atoms oscillate between this structure and its mirror image coherently as a tunneling polaron.

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ACKNOWLEDGMENTS. The authors acknowledge the financial support from the Slovenian Research Agency (Research Core Funding P1-0040). Work at Washington State University is partially supported by the US National Science Foundation (NSF) DMR EAGER Grant 1928874. Work at IOPCAS Q:16 was supported by MOST and NSF of China through Research Projects 2018YFA03057001, 2017YFA0302901, 11820101003, 2016YFA0300301, 2015CB921000, and 112111KYS820150017. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract DE-AC02-76SF00515. Work at Stanford and SLAC is supported by the Stanford Institute for Materials and Energy Science, SLAC National Accelerator Laboratory, under Department of Energy, Office of Basic Energy Sciences Contract DEAC02-76SF00515.