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Short-range orthorhombic correlations in LSCO and Tl2201. (a) Crystal structures of LSCO and Tl2201. Both compounds crystallize in a body-centered tetragonal structure at high temperatures. The LTO distortion corresponds to tilts of the CuO6 octahedra, leading to a doubling of the unit cell volume. (b,c) Diffuse X-ray scattering for (b) LSCO (x = 0.24) and (c) slightly overdoped Tl2201. In both cases, the average structure is tetragonal at all temperatures. The HK9 planes are shown, and clear diffuse peaks are observed at reciprocal space positions corresponding to the LTO superlattice (white circles). Black regions are detector artefacts that have been masked. Additional diffuse scattering of a different origin is present, including around forbidden integer Bragg positions. The sharp Bragg peaks correspond to the average tetragonal structure and demonstrate the high quality of the crystals. The scattering in the LSCO sample is shown at 150 K, well above the superconducting transition at Tc = 15 K. For Tl2201, we show data at the experimental base temperature of 30 K, far below Tc = 89 K. See also Supplementary Fig. S1 for additional reciprocal space data.
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The interplay between structural and electronic degrees of freedom in complex materials is the subject of extensive debate in physics and materials science. Particularly interesting questions pertain to the nature and extent of pre-transitional short-range order in diverse systems ranging from shape-memory alloys to unconventional superconductors,...
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Citations
... Scale-free structural inhomogeneity and the formation of clusters with distinct local environments have been observed in one cuprate family [23]. Finally, studies of superconducting [24][25][26][27] and structural [28] fluctuations have uncovered an unusual scaling regime that seems to be caused by underlying, doping-and compound-independent inhomogeneity. It was recently proposed that such inherent inhomogeneity in conjunction with a universal transport scattering rate can explain the unconventional normalstate charge transport and superfluid density behavior [29,30]. ...
... In most other cuprates, specific structural characteristics complicate the analysis of local structure and make it difficult to extract underlying universal features. Examples include structural phase transitions and associated fluctuations in La-and Tl-based cuprates [2,28,33,34], complex superstructure in Bi-based systems [35], and oxygen ordering in YBa 2 Cu 3 O 7−δ and related compounds [36][37][38]. In contrast, Hg1201 exhibits a very simple (tetragonal) high-symmetry average structure without structural phase transitions. ...
... Recent work has uncovered doping-and compoundindependent features in the superconducting fluctuation regime [24][25][26][27], with similar universal behavior also found for fluctuations associated with the structural transition in La-and Tl-based cuprates that involves a staggered tilting of the CuO 6 octahedra [28]. The observed unusual exponential temperature dependences were related to the formation and proliferation of locally ordered regions, precipitated by the presence of underlying inhomogeneity. ...
Understanding the extent and role of inhomogeneity is a pivotal challenge in the physics of cuprate superconductors. While it is known that structural and electronic inhomogeneity is prevalent in the cuprates, it has proven difficult to disentangle compound-specific features from universally relevant effects. We combine advanced neutron and x-ray diffuse scattering with numerical modeling, which enables us to obtain insight into bulk structural correlations in HgBa$_2$CuO$_{4+\delta}$. This cuprate exhibits a high optimal transition temperature of nearly 100 K, pristine charge-transport behavior, and a simple average crystal structure without long-range structural instabilities, and is therefore uniquely suited for investigations of intrinsic inhomogeneity. We uncover diffuse reciprocal-space patterns that correspond to nanoscale correlations of atomic displacements predominant perpendicular to the CuO$_2$ planes. The real-space nature of the correlations is revealed through three-dimensional pair distribution function analysis and complementary numerical refinement. We find that relative displacements of ionic and CuO$_2$ layers play a crucial role, and that the structural inhomogeneity is not directly caused by the presence of conventional point defects. The observed correlations are therefore intrinsic to HgBa$_2$CuO$_{4+\delta}$, and thus likely important for the physics of cuprates more broadly. It is possible that the structural correlations are closely related to the unusual superconducting correlations and Mott-localization in these complex oxides. The experimental and analysis tools developed here for large volumes of diffuse scattering data can be expected to aid future investigations of a wide range of materials, especially as advances in scattering techniques present researchers with more comprehensive data to be analyzed.
... Similar exponents but with smaller precursor temperature intervals were previously observed in isostructural KMnF 3 and KMn x Ca 1−x F 3 [44,74,75] with values of κ ranging between −0.4 and −1. In PbSc 0.5 Ta 0.5 O 3 (PST), the exponent is ∼−0.5 [76] with a smaller precursor interval, while ∼−0.3 has recently been found for structural fluctuations in cuprate superconductors [77]. ...
Precursor elastic effects are investigated in a displacive anharmonic spring model and shown to extend greatly into the paraelastic phase. Weak precursor effects can be detected near 2T tr , where T tr is the ferroelastic transition temperature. The precursor effects become strong at T < 1.7T tr. Two effects were identified in our two-dimensional model: the symmetry-breaking strain e 3 (ε xy) leads to softening of the elastic modulus C 33 , while the nonsymmetry-breaking strain e 1 + e 2 (ε xx + ε yy) leads to hardening of C 11. The strain e 3 is proportional to the order parameter and scales as |e 1 + e 2 | ∼ e 2 3. The temperature evolutions of the elastic moduli are surprisingly well described by power laws and Vogel-Fulcher equations. The power-law exponents are ∼−0.5 for C 33 and ∼−1 for C 11 , (C 11 + C 12) and (C 11 − C 12). The Vogel-Fulcher temperatures are very similar, while the Vogel-Fulcher energies differ between the excess elastic moduli. The origin of the precursor effect is the evolution of short-range order in the paraelastic phase which gives rise to a characteristic local nanostructure. In the case of the symmetry-breaking strain, this microstructure resembles dynamical twinning patterns corresponding to the ferroelastic nanostructure, which weakens the material. In the case of the nonsymmetry-breaking strain, we find density fluctuations which make the material harder.
... Which, if any of these possibilities is essential in the cuprates is still open to debate. There is surely considerable evidence of significant inhomogeneity in the electronic structure revealed by local probes [53][54][55][56][57] , so much so that there are suggestions that the cuprates should be viewed as electronic glasses 15,[58][59][60][61][62][63] . In this light, it certainly is worth considering whether the materials might in some ways behave like granular superconductors. ...
We examine key aspects of the theory of the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover, focusing on the temperature dependence of the chemical potential, μ . We identify an accurate method of determining the change of μ in the cuprate high temperature superconductors from angle-resolved-photoemission data (along the ‘nodal’ direction), and show that μ varies by less than a few percent of the Fermi energy over a range of temperatures from far below to several times above the superconducting transition temperature, T c . This shows, unambiguously, that not only are these materials always on the BCS side of the crossover (which is a phase transition in the d -wave case), but are nowhere near the point of the crossover (where the chemical potential approaches the band bottom).
... They were found by molecular dynamics simulations and diffractions experiments [39][40][41][42]. Similar effects were postulated by Pelc et al. [43] for high-temperature superconductors. ...
... Simultaneously, we observe that the precursor temperature interval is smallest for SrTiO 3 , while it remains extremely large for Ba-rich materials with significant softening at least up to 800 K. Similar exponents, but smaller precursor temperature intervals, were previously observed in isostructural KMnF 3 and KMn x Ca 1−x F 3 [29,69,70] with values of κ ranging between 0.4 and 1. In PbSc 0.5 Ta 0.5 O 3 (PST) the exponent is near 0.5 [71] with a smaller precursor interval, while ∼1/3 has recently been found for structural fluctuations in cuprate superconductors [43]. ...
Elastic softening in the paraelastic phases of Ba 1−x Sr x TiO 3 is largest near the transition temperatures and decreases on heating smoothly over extended temperature ranges. Softening extends to the highest measured temperature (850 K) for Ba-rich compounds. The temperature evolution of the excess compliance of the precursor softening follows a power law δS ∝ |T − T C | −κ with a characteristic exponent κ ranging between 1.5 in SrTiO 3 and 0.2 in BaTiO 3. The latter value is below the estimated lower bounds of displacive systems with three orthogonal soft phonon branches (0.5). An alternative Vogel-Fulcher analysis shows that the softening is described by extremely low Vogel-Fulcher energies E a , which increase from SrTiO 3 to BaTiO 3 indicating a change from a displacive to a weakly order-disorder character of the elastic precursor. Mixed crystals of Ba x Sr 1−x TiO 3 possess intermediate behavior. The amplitude of the precursor elastic softening increases continuously from SrTiO 3 to BaTiO 3. Using power-law fittings reveals that the elastic softening is still 33% of the unsoftened Young's modulus at temperatures as high as 750 K in BaTiO 3 with κ 0.2. This proves that the high-temperature elastic properties of these materials are drastically affected by precursor softening.
... Strong electron-lattice interaction, in particular hot spots in the k-space has been observed also in pressurized sulfur hydrides [56]. This confirms the universal scenario of two-component superconductivity in systems with strong unconventional electron-lattice interaction and ubiquitous unconventional short-range structural fluctuations and percolation, as has been confirmed recently in cuprates [57,58]. Recently, static CDW, long-range CDW, short-range CDW, and dynamic charge fluctuations have been observed by resonant X-ray scattering in cuprates pervading the full phase diagram [59][60][61][62][63][64][65][66][67][68][69][70][71] of cuprates and nickelates [72]. ...
Fast and local probes, such as X-ray spectroscopy, X-ray diffraction (XRD), and X-ray microscopy, have provided direct evidence for nanoscale phase separation in high temperature perovskite superconductors composed of (i) free particles coexisting with (ii) Jahn Teller polarons (i.e., charges associated with local lattice distortions) not detected by slow experimental methods probing only delocalized states. Moreover, these experimental probes have shown the formation of a superstripes phase in the pseudogap regime below T* in cuprates. Here, we focus on the anomalous temperature dependence of short range X-ray diffraction CDW reflection satellites with high momentum transfer, probing both charge and lattice fluctuations in superconducting HgBa2CuO4+y (Hg1201) in the pseudogap regime below T* and above Tc. We report compelling evidence of the anomalous anticorrelation of the coherence volume with the peak maximum amplitude of the CDW XRD satellite by cooling below T*. This anomalous temperature trend of the short-range striped Jahn Teller polaronic CDW puddles is in agreement with predictions of the Q-ball theory of the quark gluon plasma extended to cuprates, providing compelling evidence for non topological soliton puddles of striped condensate of pairs in the pseudogap phase.
... They were found by molecular dynamics simulations and diffractions experiments [39][40][41][42]. Similar effects were postulated by Pelc et al. [43] for high temperature superconductors. ...
... Simultaneously we observe that the precursor temperature interval is smallest for SrTiO 3 while it remains extremely large for Ba-rich materials with significant softening at least up to 800 K. Similar exponents, but smaller precursor temperature intervals, were previously observed in isostructural KMnF 3 and KMn x Ca 1−x F 3 [29,68,69] with values of κ ranging between 0.4 and 1. In PbSc 0.5 Ta 0.5 O 3 (PST) the exponent is near 0.5 [70] with a smaller precursor interval, while ∼ 1/3 has recently been found for structural fluctuations in cuprate superconductors [43]. ...
Elastic softening in the paraelastic phases of Ba$_{1-x}$Sr$_{x}$TiO$_{3}$ is largest near the transition temperatures and decreases on heating smoothly over extended temperature ranges. Softening extends to the highest measured temperature(850~K) for Ba-rich compounds. The temperature evolution of the excess compliance of the precursor softening follows a power law $\delta S\propto |T-T_{\mathrm{C}}|^{-\kappa }$\ with a characteristic exponent $\kappa $\ ranging between 1.5 in SrTiO$_{3}$\ and 0.2 in BaTiO$_{3}$. The latter value is below the estimated lower bounds of displacive systems with three orthogonal soft phonon branches (0.5). An alternative Vogel-Fulcher analysis shows that the softening is described by extremely low Vogel-Fulcher energies $E_{a}$, which increase from SrTiO$_{3}$% \ to BaTiO$_{3}$\ indicating a change from a displacive to a weakly order/disorder character of the elastic precursor. Mixed crystals of Ba$_{x}$% Sr$_{1-x}$TiO$_{3}$ possess intermediate behaviour. The amplitudes of the precursor elastic softening increases continuously from SrTiO$_{3}$ to BaTiO$% _{3}$. Using power law fittings reveals that the elastic softening is still $% 33\%$ of the unsoftened Young's modulus at temperatures as high as 750 K in BaTiO$_{3}$ with $\kappa \simeq $ 0.2. This proves that the high temperature elastic properties of these materials are drastically affected by elastic precursor softening.
... Which, if any of these possibilities is essential in the cuprates is still open to debate. There is surely considerable evidence of significant inhomogeneity in the electronic structure revealed by local probes [68][69][70][71][72], so much so that there are suggestions that the cuprates should be viewed as electronic glasses [15,[73][74][75][76][77][78]. In this light, it certainly is worth considering whether the materials might in some ways behave like granular superconductors. ...
We examine key aspects of the theory of the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover, focusing on the temperature dependence of the chemical potential, $\mu$. We identify an accurate method of determining the change of $\mu$ in the cuprate high temperature superconductors from angle-resolved-photoemission data (along the "nodal'' direction), and show that $\mu$ varies by less than a few percent of the Fermi energy over a range of temperatures from far below to several times above the superconducting transition temperature, $T_c$. This shows, unambiguously, that not only are these materials always on the BCS side of the crossover (which is a phase transition in the $d$-wave case), but are nowhere near the point of the crossover (where the chemical potential approaches the band bottom).
... Notably, the value of the charge transfer gap is well defined in the parent compound, while the doped material shows a broad gap distribution (Fig. 4). Depending on the overall crystal structure as a result of negotiation/competition of the three involved subsystems (two electronic and lattice) either short-range HTT/LTT/LTO disorder will be present (e.g., Tl2201 [108], or nematicity will appear (e.g., Y123 [109] or BSCCO [110]) or in some cases stripes (e.g., LSCO [111]) which correspond to two different conformations of the CuO 6 octahedra assigned to two types of stripes with different (LTO-like or HTT-like) lattices [112]. Finally, it should be mentioned that the currently much-discussed CDW correlations seem not to be related to the localized charge, but that they should be primarily associated with the itinerant subsystem. ...
A review of the phenomenology and microscopy of cuprate superconductors is presented, with particular attention to universal conductance features, which reveal the existence of two electronic subsystems. The overall electronic system consists of 1+p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+p$$\end{document} charges, where p is the doping. At low dopings, exactly one hole is localized per planar copper–oxygen unit, while upon increasing doping and temperature, the hole is gradually delocalized and becomes itinerant. Remarkably, the itinerant holes exhibit identical Fermi liquid character across the cuprate phase diagram. This universality enables a simple count of carrier density and yields comprehensive understanding of the key features in the normal and superconducting state. A possible superconducting mechanism is presented, compatible with the key experimental facts. The base of this mechanism is the interaction of fast Fermi liquid carriers with localized holes. A change in the microscopic nature of chemical bonding in the copper oxide planes, from ionic to covalent, is invoked to explain the phase diagram of these fascinating compounds.
The layered metamagnet CrSBr offers a rich interplay between magnetic, optical, and electrical properties that can be extended down to the two‐dimensional (2D) limit. Despite the extensive research regarding the long‐range magnetic order in magnetic van der Waals materials, short‐range correlations have been loosely investigated. By using small‐angle neutron scattering (SANS) the formation of short‐range magnetic regions in CrSBr with correlation lengths that increase upon cooling up to ≈3 nm at the antiferromagnetic ordering temperature (T N ≈ 140 K) is shown. Interestingly, these ferromagnetic correlations start developing below 200 K, i.e., well above T N. Below T N, these correlations rapidly decrease and are negligible at low‐temperatures. The experimental results are well‐reproduced by an effective spin Hamiltonian, which pinpoints that the short‐range correlations in CrSBr are intrinsic to the monolayer limit, and discard the appearance of any frustrated phase in CrSBr at low‐temperatures within the experimental window between 2 and 200 nm. Overall, the obtained results are compatible with a spin freezing scenario of the magnetic fluctuations in CrSBr and highlight SANS as a powerful technique for characterizing the rich physical phenomenology beyond the long‐range order paradigm offered by van der Waals magnets.
Empirical A-site cation substitution has advanced the stability and efficiency of hybrid organic-inorganic lead halide perovskites solar cells and the functionality of X-ray detectors. Yet, the fundamental mechanisms underpinning their unique performance remain elusive. This multi-modal study unveils the link between nanoscale structural dynamics and macroscopic optoelectronic properties in these materials by utilising X-ray diffuse scattering, inelastic neutron spectroscopy and optical microscopy complemented by state-of-the-art machine learning-assisted molecular dynamics simulations. Our approach uncovers the presence of dynamic, lower-symmetry local nanodomains embedded within the higher-symmetry average phase in various perovskite compositions. The properties of these nanodomains are tunable via the A-site cation selection: methylammonium induces a high density of anisotropic, planar nanodomains of out-of-phase octahedral tilts, while formamidinium favours sparsely distributed isotropic, spherical nanodomains with in-phase tilting, even when crystallography reveals cubic symmetry on average. The observed variations in the properties of dynamic nanodomains are in agreement with our simulations and are directly linked to the differing macroscopic optoelectronic and ferroelastic behaviours of these compositions. By demonstrating the influence of A-site cation on local nanodomains and consequently, on macroscopic properties, we propose leveraging this relationship to engineer the optoelectronic response of these materials , propelling further advancements in perovskite-based photovoltaics, optoelectronics, and X-ray imaging.
