Nonadiabatic coupling of the dynamical structure to the superconductivity in YSr2Cu2.75Mo0.25O7.54 and Sr2CuO3.3

A crucial issue in cuprates is the extent and mechanism of the coupling of the lattice to the electrons and the superconductivity. Here we report Cu K edge extended X-ray absorption fine structure measurements elucidating the internal quantum tunneling polaron (iqtp) component of the dynamical structure in two heavily overdoped superconducting cuprate compounds, tetragonal YSr₂Cu_2.75Mo_0.25O_7.54 with superconducting critical temperature, T_c = 84 K and hole density p = 0.3 to 0.5 per planar Cu, and the tetragonal phase of Sr₂CuO_3.3 with T_c = 95 K and p = 0.6. In YSr₂Cu_2.75Mo_0.25O_7.54 changes in the Cu-apical O two-site distribution reflect a sequential renormalization of the double-well potential of this site beginning at T_c, with the energy difference between the two minima increasing by ∼6 meV between T_c and 52 K. Sr₂CuO_3.3 undergoes a radically larger transformation at T_c, >1-Å displacements of the apical O atoms. The principal feature of the dynamical structure underlying these transformations is the strongly anharmonic oscillation of the apical O atoms in a double-well potential that results in the observation of two distinct O sites whose Cu–O distances indicate different bonding modes and valence-charge distributions. The coupling of the superconductivity to the iqtp that originates in this nonadiabatic coupling between the electrons and lattice demonstrates an important role for the dynamical structure whereby pairing occurs even in a system where displacements of the atoms that are part of the transition are sufficiently large to alter the Fermi surface. The synchronization and dynamic coherence of the iqtps resulting from the strong interactions within a crystal would be expected to influence this process.

More than 30 y after the discovery of unconventional superconductivity in cuprates (1) and subsequently in analogous materials its underlying mechanism and in particular the role of the lattice are still under debate. Proposed microscopic theories range from purely electronic Mott–Hubbard and t-J approaches at one extreme to Bose–Einstein condensates of bipolarons at the other (2–4). Experimentally, however, anomalous isotope effects (5), resonant ultrasound (6), angle-resolved photoemission spectroscopy (7–9), femtosecond optical pump terahertz (10)/megaelectron-volt transmission electron microscopy probe (11), infrared pump (12), and so on have demonstrated that specific phonons not only couple to the superconductivity but correlate directly with the gap energy and may even transiently induce it well above the superconducting critical temperature, T_c. Cuprates also exhibit a plethora of superstructures indicative of strong electron–lattice coupling, stripes that have been proposed to stabilize the superconductivity (13), and charge-density waves (14, 15) and the pseudogap (PG) (16) that compete with it. Another possibility is mechanisms that boost T_c from a low value expected within a conventional Bardeen-Cooper-Schrieffer (BCS) scheme. That this question remains unanswered suggests considering more unconventional approaches (4). One candidate is the dynamical structures of cuprates, S(Q, E) or experimentally S(Q, t = 0), specifically their internal quantum tunneling polarons (iqtp). An iqtp is a set of atoms oscillating between two structures that possess different geometries, energy levels, and charge distributions (17–19). A chemist would describe these endpoints as separate species, adapting this term that applies more intuitively to solutions to the atoms in crystalline solids. Neutron scattering and X-ray absorption fine structure (XAFS) measurements identified O-centered iqtps and their correlation with the superconductivity 30 y ago (17–25). We now present Cu K edge extended XAFS (EXAFS) results from “overdoped” YSr₂Cu_2.75Mo_0.25O_7.54 (YSCO-Mo) that is isostructural with YBa₂Cu₃O₇ (Fig. 1A and SI Appendix, Fig. S1), T_c = 84 K (26) and hole doping p (excess charge on the planar Cu2 site) = 0.3 to 0.5 (27) and Sr₂CuO_3.3 (SCO) that is structurally analogous to La₂CuO₄ (Fig. 1B and SI Appendix, Fig. S1), T_c = 95 K (28, 29), and p = 0.6, both synthesized via high-pressure oxygenation (HPO) (30, 31). In YSCO-Mo the Cu2-apical O (Oap) double-well potential is degenerate in the normal state but renormalizes below T_c with the energy difference between its two minima increasing with decreasing temperature by ∼6 meV. SCO is already unique among cuprates in not having intact CuO₂ planes (32, 33). Its Cu EXAFS demonstrate that it is unique among superconductors in that its Oap shift by >1 Å at its superconducting transition, challenging our conception of superconductivity as an electronic transition that is incompatible with structural transformations.Open in a separate windowFig. 1.Structures and modulus and real components of the Fourier transforms of the EXAFS spectra, χ(R), of YSCO-Mo and SCO across temperature ranges bracketing their superconducting transitions. (A) Structure representation of YSCO-Mo. The CuO₂ planes are turqoise (Cu2) and magenta (Opl), Cu-O chains are blue (Cu1) and gold (Och), Oap is red, and Sr is green. In the actual structure one-fourth of Cu1 are substituted by Mo. The orientation is shown underneath. (B) The same as A for SCO, except a significant number of Oap and half of the O sites in the a direction in the CuO₂ planes are vacant. The CuO₂ planes are blue (Cu) and gold (O). For the χ(R) spectra the blue traces denote the lowest temperatures, then green to yellow, purple, and red-orange to brown at the highest ones. (C) YSCO-Mo spectra for E of the X-ray probe beam in the aa plane, with the modulus peaks labeled with their principal sources. The first temperature above T_c is red. (D) YSCO-Mo spectra for E||c, with the Cu1- and Cu2-Oap contributions overlapping at R = 1.6 Å. The peaks at higher R are a combination of direct, two-leg path contributions from more distant neighbor atom shells and ordered multiple scattering paths. (E) SCO spectra for E||H used for the orientation that is assigned to the a direction of the orthorhombic O sublattice. T_c is red and double width. (F–I) SCO over the designated temperature ranges for E⊥H spectra that will be the contributions in the bc plane defined by the orthorhombic O sublattice. (F) The extent of the change in the spectra, and by inference in their originating structures, across the superconducting transition. The features appearing at R = 2 to 2.5 Å below T_c result from the ∼2 Å shift of the O depicted in Fig. 3 B–D. In G the first temperature above T_c is orange and double width.We have recently shown that HPO cuprates are described by their own phase diagram (34). The principal feature of the well-known one for non-HPO cuprates is the superconducting “dome” that begins at p ∼0.06, peaks at p ∼ 0.16, and ends at p ∼ 0.27. Subsequent augmentations with the microstrain in the planes (35) and hole density on the O atoms (36) explain some of the material specificity but do not modify this overall pattern. For HPO compounds the superconductivity may begin at p < 0.06 and continues to increase beyond p = 0.27 with possible flattening but no reduction in T_c. Although we have found that the excess O in YSCO-Mo is mostly taken up by domains enriched in octahedral Mo(VI) substituting in the Cu(1) chains, much of the extra charge resides in the CuO₂ planes (27) and some of the carriers constitute a normal Fermi liquid that coexists with the superconductivity (26). The inherent inhomogeneity (37) in YSCO-Mo and SCO was probed by EXAFS, which is arguably the most incisive experimental method for characterizing short-range order and is especially sensitive to its changes. Diffraction patterns originate in the long-range average structure of a material and provide precise information on the symmetry and symmetry-constrained locations of the atoms that dominate the Bragg peaks. In contrast, EXAFS—and pair distribution function (pdf) analysis—are sensitive to local order separate from the crystallographic symmetry. The element selectivity of EXAFS provides further advantages by separating the atom pairs comprising the distribution function. Especially important for this study, EXAFS measures the instantaneous structure factor, S(Q, t = 0), that incorporates the dynamic structure components, S(Q, E), observed with inelastic scattering. EXAFS therefore accesses time and energy scales corresponding to collective dynamical phenomena (25, 38, 39). Dynamical structures such as the iqtp are demonstrated when S(Q, E/t = 0) gives locations for atoms that differ from those (19, 38) obtained from diffraction and elastic scattering measurements (20–22, 40). This complementarity was the basis for the original identification of the Cu-Oap two-site distribution (41) and its assignment to the double-well potential of the iqtp (17, 19, 42).