Abstract
How Cooper pairs form and condense has been the main challenge in the physics of copper-oxide high-temperature superconductors. Great efforts have been made in the ‘underdoped’ region of the phase diagram, through doping a Mott insulator or cooling a strange metal. However, there is still no consensus on how superconductivity emerges when electron-electron correlations dominate and the Fermi surface is missing. To address this issue, here we carry out high-resolution resonant inelastic X-ray scattering and scanning tunneling microscopy studies on prototype cuprates Bi2Sr2Ca0.6Dy0.4Cu2O8+δ near the onset of superconductivity, combining bulk and surface, momentum- and real-space information. We show that an incipient charge order exists in the antiferromagnetic regime down to 0.04 holes per CuO2 unit, entangled with a particle-hole asymmetric pseudogap. The charge order induces an intensity anomaly in the bond-buckling phonon branch, which exhibits an abrupt increase once the system enters the superconducting dome. Our results suggest that the Cooper pairs grow out of a charge-ordered insulating state, and then condense accompanied by an enhanced interplay between charge excitations and electron-phonon coupling.
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Introduction
High-Tc superconductivity (SC) is closely proximal to a charge order (CO) electronic state in the cuprate phase diagram1, which exhibits an incommensurate wavevector QCO that varies with hole concentration (Fig. 1a and ref. 2). While there is growing evidence suggesting that CO competes with SC since its amplitude is weakened below Tc3,4,5,6, it might actually be the first emerged phase during the doping of a Mott insulator1, acting as a precursor to SC. Conforming to this scenario, scanning tunneling microscopy (STM) studies on Bi2Sr2−xLaxCuO6+δ (La-Bi2201)7 and Ca2−xNaxCuO2Cl2 (Na-CCOC)8 reveal that a surface-form CO has already become manifest even in the antiferromagnetic regime, with only a small amount of holes (p = 0.07~0.08) introduced into the parent compounds. However, whether the CO exists in insulating cuprates has not been confirmed by bulk-sensitive probes such as resonant inelastic X-ray scattering (RIXS). Thus, it remains unclear whether the CO has a bulk nature in the non-superconducting regime or exists only in a surface form, and whether it extends to even lower doping levels. Furthermore, it is important to determine whether the CO wavevector QCO is commensurate, as reported in refs. 7,8, to understand its relation with the underlying lattice. Answering these questions is critical in delineating a clear story about the relationship between unconventional SC and CO in cuprates.
One more piece of the puzzle that remains elusive is the origin of CO. This CO is typically observed at relatively high doping levels and is intertwined with pseudogap (PG) and SC through a truncated Fermi surface. For example, angle-resolved photoemission spectroscopy (ARPES) experiments have found discontinuous segments known as Fermi arcs9, and momentum-space nesting mechanism has been suggested as a possible explanation for the origin4,10. On a different front, quantum oscillations11 and magnetoresistance12 measurements suggest that the CO is closely connected with a reconstructed Fermi pocket. However, all these previous pictures fail to explain the above-mentioned charge-ordered insulating phase, where the Fermi surface is absent13,14. To address these issues, we have designed a comprehensive set of temperature paths (Fig. 1b) to explore the property, universality, and extension of the CO, and how the SC emerges in the vicinity of its onset doping level.
We choose lightly doped Bi2Sr2Ca1−xDyxCu2O8+δ (Dy-Bi2212, x = 0.4) to study utilizing the state-of-art RIXS and STM techniques. Dy-Bi2212 has proved to be a feasible system for our purposes that can achieve hole concentration as low as the Mott insulating limit15. Importantly, its crystal structure (Fig. 1a inset) allows an atomically flat cleavage that is ideal for both STM and RIXS. A recent RIXS study on underdoped Dy-Bi2212 (p ≈ 0.09) has identified dispersive excitations associated with the CO, which is proposed to induce a peak of electron-phonon coupling (EPC) strength at the in-plane bond-stretching (BS) phonon branch16. This EPC peak grows once the system enters the SC dome6, providing intriguing connections between SC, CO, and EPC. However, the implications of these findings remain contentious among different cuprate compounds when the inelastic spectral weight is solely attributed to the BS phonon mode16,17,18. Moreover, the extension of the EPC “anomaly" to lower doping levels, especially to the insulating phase diagram, remains largely unexplored. In this work, we investigate this lightly doped region with p = 0.04 and p = 0.06 (Methods and Supplementary Fig. S1) across the edge of the superconducting dome (p = 0.05), where the Fermi surface is found missing in both samples from ARPES studies13.
Results
RIXS and STM measurements
Figure 1 c shows a series of high-resolution RIXS spectra (ΔE = 36 meV, ΔQ = 0.006 r.l.u., see Methods)19 taken in the insulating sample (p = 0.04) at 17 K. The incident X-ray was tuned to the Cu-L3 edge, corresponding to resonant absorption and emission between Cu 2p and Cu 3d orbitals (Fig. 1c inset and Supplementary Fig. 1), which provides energy- and momentum-resolved information of elementary excitations, such as the paramagnons and phonons. The same sample was cleaved at an ultra-high vacuum and immediately loaded into the STM stage. As displayed in Fig. 1d, we succeeded in performing single-particle spectroscopic and atomically-resolved topographic measurements in Dy-Bi2212 with p = 0.04, by exploiting the reliable methodology we have previously developed (Methods). As the sample is spatially inhomogeneous, the spectra evolve from a charge-transfer gap (black curve) to a PG lineshape (red curve), similar to that exhibited in superconducting samples20.
Observation of charge order
We now focus on the lower-energy range of our high-resolution RIXS and STM data, which is most relevant to CO, PG, EPC, and SC. Intriguingly, in this insulating Dy-Bi2212 we observe an evident bulk CO through careful examination of the energy-momentum RIXS intensity maps (Fig. 2a–c), which has never been reported before. It is directly visualized that at the quasi-elastic region a broad peak along the (H, 0) direction (i.e., Cu-O bond direction) associated with CO has already formed at 273 K and gradually becomes stronger as the temperature decreases (along path #1 of Fig. 1b). The CO intensity profile can be well-fitted by a Gaussian peak (blue shaded) plus a Lorentzian background (Methods), which is centered at an incommensurate QCO = 0.31 r.l.u. at 17 K. The elastic intensity peak is absent along the diagonal (H, H) direction (gray squares in Fig. 2c), consistent with CO characteristics in other cuprate materials2. Previous studies have only proposed CO down to p = 0.07 using surface-specific STM7,8,21, while a bulk-form CO was only identified in superconducting Bi2212 down to p = 0.09 (Tc = 45 K)16. Our findings substantially extend the lower doping limit of CO to p = 0.04 in the insulating regime, suggesting that CO in insulating cuprates is incommensurate with the underlying lattice, contrary to some previous reports7,8.
From a real-space perspective, the checkerboard CO feature is particularly weak at a high temperature of 77 K as revealed by the dI/dV map (see Methods) in Fig. 2d. At this temperature, only a small portion of space with large local density-of-states (bright) holds charge ‘puddles’ that are poorly connected along the Cu-O bond directions (white arrows). This observation aligns with the broad full-width at half-maximum (FWHM) of the CO peak revealed by RIXS (e.g., 0.072 r.l.u. at 90 K, corresponding to a very short correlation length ξ ≈ 4.4 a0). A closer examination in Fig. 2e reveals that the dark region, where no CO develops, is characterized by a full charge-transfer gap. In contrast, the CO is accompanied by a density-of-states modulation, especially near the energy scale of the ‘V-shaped’ PG. Figure 2f, g are the low-temperature (T = 5 K) real-space patterns of the CO and PG magnitude (Methods) in the same area. It becomes immediately apparent that the CO is spatially correlated with smaller, or more precisely, sharper PG regions. The spectral linecut in Fig. 2h illustrates a smooth transition from the charge-transfer gap (which has been subtracted and shown as the red curve) in CO-poor locations to PG (CO-rich). Interestingly, the PG size is asymmetric at positive and negative bias, distinct from SC. This asymmetry is not unexpected, as a broken translational-symmetry phase, such as the CO here or the PG itself20,22, generally breaks particle-hole symmetry. Our result has, for the first time, demonstrated such asymmetry in both the occupied and unoccupied states.
To comprehend the evolution of a charge-ordered insulator into a high-temperature superconductor (along path #2 of Fig. 1b), we next move to the p = 0.06 sample with Tc = 20 K. The dI/dV map at 5 K (Fig. 3a) shows that the CO pattern is stronger than that in the insulator (Fig. 2f), which is also visualized by comparing the CO peak intensity and area from the RIXS data (Figs. 3c and 2c). This observation appears inconsistent with the notion that CO competes with SC, but rather plays a reinforced role. Remarkably, both STM (Fig. 3b) and RIXS (Fig. 3c) provide virtually identical QCO = 0.30 r.l.u. (≈3.3 a0 periodicity) along the (H, 0) directions, reconciling the charge modulations at the surface and in the bulk. The QCO of Bi2212 extended to p = 0.04 and p = 0.06 follows the extrapolated trend shown in Fig. 1a, in agreement with the behavior observed in most cuprates2.
Interplay between CO and phonons
Regarding the SC, it has been proposed that EPC plays a significant role in realizing high Tc, irrespective of the exact pairing mechanism23,24. However, the phonon modes are inaccessible by STM in the strongly underdoped regime, since the prominent PG prevents the extraction process, such as a strong-coupling Eliashberg approach25. In contrast, the RIXS cross-section offers the capability to simultaneously map the dispersion and EPC strength for specific phonon branches26, which also have an intricate interplay with CO16. Consequently, we conduct a more in-depth investigation to explore the potential connection between CO, EPC, and SC, utilizing the inelastic spectral weight of RIXS.
A previous study on antiferromagnetic NBCO demonstrated that Cu L3-edge RIXS can simultaneously detect the Cu-O bond stretching (BS) mode at approximately 70 meV and the out-of-plane A1g bond buckling (BB) phonon at about 35 meV27. When there is no charge order, the electron coupling to the BS phonon follows a sin2(πH) trend, while the BB phonon follows a cos2(πH) trend27, consistent with the model calculations of momentum-dependent EPC26. Figure 3d, e shows a raw RIXS spectrum and the inelastic parts after subtracting a resolution-limited elastic peak, respectively. The highly asymmetric lineshapes in the spectra indicate the necessity of considering two phonons in data fitting. With improved energy resolution and superb momentum accuracy in our experiment, we use two Gaussian functions (Methods) to extract the BS mode (shown in black) and the BB mode (in red). Our analyses show that both modes are nearly dispersionless within the energy resolution, which is distinct from previous one-phonon fitting models that presented a BS mode “softening”16,17,18. However, it is important to note that our present study is insufficient to rule out the softening behavior of lower-energy phonons. As energy resolution is further improved, softened phonons have been revealed by IXS on YBCO28 and higher-resolution RIXS in LSCO29.
Figure 4 a, b compare the decomposed CO (lower panels), BB phonon (middle panels), and BS phonon (upper panels) in the insulating and superconducting Dy-Bi2212 samples (Methods and Supplementary Fig. 8). The corresponding energy-integrated intensity profiles are shown in Fig. 4c. Intriguingly, the BB phonon exhibits a broad peak centered around 0.32 r.l.u., which is likely due to an interaction between the phonon and the dispersive CO excitation16. Both the CO and BB phonon intensities are higher in the superconducting sample (see also Fig. 4d). In contrast, the momentum-dependent EPC of the BS phonon lacks a peak structure and is well captured by a sin2(πH) profile within a non-interacting model27. Therefore, our new analysis suggests that the intensity anomaly observed in previous studies should be attributed to the BB phonon mode, which varies with material, doping, and temperature.
Doping- and T-dependence of CO and EPC
To gain more insights into what happens when the system enters the superconducting phase, we consider both the doping and systematic temperature evolutions following the three paths depicted in Fig. 1b. The short-range charge correlation already exists at 273 K (Fig. 5a), which is accompanied by a very broad BB phonon intensity peak (Fig. 5b). Therefore, the weak CO and its interplay with EPC set the stage for the formation and condensation of Cooper pairs. Upon cooling along paths #1 and #3, both CO and BB phonon gradually gain more weight, but they follow very different trends (see Fig. 5c,d): the CO intensity grows faster in the superconducting sample than in the insulating one. In contrast, the BB phonon displays a concurrent and smooth increase, except for an abrupt jump (paths #2 and #3) when the SC appears. These results agree with previous reports on the separation of CO intensity and excitations6,17. The intensity profile of the BS phonon, on the other hand, maintains a sinusoidal trend at different dopings, temperatures (Fig. 5e), and materials (refs. 26,27), indicating a negligible correlation with CO excitations and SC.
Figure 6 delineates our idea of how the SC emerges below Tc. Our findings reveal that while the SC emerges from the CO phase (along paths #2 and #3 in Fig. 1b), the CO wavevector QCO continuously changes with doping, irrespective of the SC (Fig. 6a). In concert with this observation, previous studies have noted that the CO intensity could respond differently to SC3,30,31. It is the BB phonon intensity anomaly, or the dispersive CO excitations6 triggered by the underlying CO, that induces an abrupt enhancement in the SC state (Fig. 6b). The enhanced EPC strength of the BB phonon may drive or accompany the condensation of Cooper pairs, as evidenced by the coherent superconducting gap everywhere (Fig. 6c). Therefore, the CO and EPC play distinct roles but work together in establishing the macroscopic SC.
Discussion
The combined RIXS and STM results here touch on the important issues regarding the relations between PG, CO, EPC, and SC, all of which are at play in the present study. While a short-range CO has been found pervading the hole-doped phase diagram, where SC acts as the ground state, its extension to the insulating regime remains elusive, with only two STM works (refs. 7 and 8) reporting surface CO. Our work, for the first time, has not only provided concrete evidence of CO in an insulating cuprate through a combined bulk and surface study but also substantially extended the lower doping limit of CO to p = 0.04 with a broad temperature range. Our observations reveal an incommensurate CO wave vector surrounding ~ 0.31 r.l.u. However, our RIXS results and traditional Fourier-transformed dI/dV (proportional to the local density-of-states) channel cannot differentiate between truly incommensurate charge order and discommensurations within a locally commensurate phase resulting from disorder or topological defects29,32,33. Therefore, the true nature of the CO, whether it is genuinely incommensurate or merely appears to be incommensurate due to certain factors, remains a topic of controversy.
Another hotly debated issue pertains to the origin of CO. In a weak coupling k-space Fermi-surface nesting scenario, the CO wave vector would continuously decrease with increased doping4,10. Alternatively, in a strong coupling r-space scenario, the charge order would be commensurate with the underlying lattice. While we have noted a continuous decrease in QCO with doping, the nesting scenario is not applicable in the heavily underdoped regime where the Fermi surface is entirely gapped13. However, our findings can be reconciled through discommensuration in the r-space strong correlation scenario, where smaller random commensurate domains can cause a larger mismatch of commensurate wave vectors at low doping, as proposed by phase-resolved STM studies32. One may also suspect if this incipient CO is caused by antiferromagnetic excitations in the insulating regime, as suggested in other hole-doped cuprates34,35. However, our RIXS results reveal a smooth paramagnon dispersion and damping across QCO (Fig. 1c and Supplementary Fig. 11), showing an absence of intertwining between spin excitations and CO.
We move forward to the initial question of how the unconventional SC emerges. In the lightly doped cuprates, we are close to a non-Fermi-liquid Bose-Einstein condensate regime. Although our experiments do not give direct evidence on incoherent Cooper pairs, we do suggest that CO is indispensable for their formation. Signatures of “pre-formed” Cooper pairs have been widely observed by STM36,37, ARPES38, and transport measurements39,40. The coexistence of pre-formed Cooper pairs and CO outside the superconducting dome suggests that the charge-ordered electronic state is energetically favorable for the formation of Cooper pairs, akin to the description provided by the stripe model41. This agrees with the observation that two holes are distributed on the peak of the checkerboard plaquette, as visualized by a periodical superconducting coherence peak modulation atop the CO37,42.
In cuprates, another intriguing correspondence is between the short-range nature of CO and nanoscale electronic inhomogeneity43, indicative of the weakly-overlapped Cooper pairs in a real-space picture. The CO, though still short-ranged, gains more amplitude with cooling (along paths #1 and #3) or doping (along path #2). Working in conjunction with the CO, it is the enhanced EPC strength that accompanies the eventual condensation of Cooper pairs (Fig. 6b, c). Remarkably, the BS phonon is invariable against temperature and doping (Fig. 5e), agreeing well with the model calculations26, RIXS measurements in Nd1+xBa2−xCu3O7−δ27, and ARPES measurements in Bi221244. In contrast, the coupling to the BB phonon is a more relevant process, which has been proposed to promote the magnitude of Tc when the long-range Coulomb interaction is plausible24. Similar observations sensitive to the Cooper pairs condensation include the antinodal kink of the buckling B1g phonon observed by ARPES45, and the spin resonance mode observed by inelastic neutron scattering46. Whether these are the driving forces or natural consequences of the itinerant Cooper pairs remains an open question.
Methods
Sample growth and characterizations
High-quality Bi2Sr2Ca0.6Dy0.4Cu2O8+δ single crystals were grown by the traveling solvent floating zone method. The high Dy concentration was intentionally introduced during the growth to achieve the highly underdoped regime. The as-grown sample displays a superconducting transition with \({T}_{{{\rm{c}}}}^{{{\rm{onset}}}}\) = 40 K as revealed by the magnetic susceptibility curve, corresponding to a hole doping level of p = 0.067 (0.067 ± 0.008). The doping and error bar were estimated using the empirical formula from ref. 47, where the \({T}_{{{\rm{c}}}}^{\max }\) was set to 96 K for the Bi2212 system. One as-grown sample was divided into two crystals, which were used in the present study after different post-annealing processes in a vacuum atmosphere. Notably, the STM measurements were carried out in the very same samples after the RIXS experiments. The first annealing condition (Ann1) was T = 350 ∘C for 2 days, which yields a superconducting transition with Tc ~ 20 K and p = 0.062 (0.062 ± 0.006). The second one (Ann2) was T = 450 ∘C for 3 days, which completely suppressed SC showing no evidence of the Meissner effect. We estimate the doping level of Ann2 to be p ~ 0.04 (0.04 ± 0.01) for two reasons: (i) It is below the onset doping of the superconducting dome (p ~ 0.05) and is highly insulating as revealed by the resistivity measurement, and (ii) Previous reports have proposed that it is impossible to carry out liquid-helium-temperature STM measurements on cuprates at or below p = 0.037, even with our delicate methodology (see below). Therefore, the sample prepared by Ann2 is located somewhere below but in the vicinity of the SC onset. The magnetization and resistivity curves are shown in Supplementary Fig. 1.
RIXS measurements
The RIXS experiments were performed at the I21 RIXS beamline of the Diamond Light Source19. The momentum resolution is estimated to be 0.01 Å−1 based on the scattering geometry employed in our study19. For Bi2212, the lattice parameters are a = b = 3.83 Å, corresponding to ΔQ ~ 0.006 r.l.u., which is sufficient for the CO analysis. The Dy-Bi2212 samples were cleaved to expose a fresh surface and then immediately transferred into the ultrahigh vacuum (UHV) chamber. Before the RIXS measurements, we did careful alignments for our samples utilizing the (002) Bragg peak and the (1-10) superstructure peak, which are critical for an accurate determination of the scattering vector q. All RIXS spectra in our study were collected with the incident photon energy tuned to the Cu L3 resonant edge (see Supplementary Fig. 1), where we can achieve an ultra-high energy resolution ΔE ~ 36 meV. To enhance the charge-related excitations, such as CO and phonon branches, all data, except for those shown in Supplementary Fig. 9, were taken with the vertical (σ) polarization of the incident X-ray. To maximize the in-plane momentum-transfer H along the (H, 0) direction, a large scattering angle 2θ = 154° was chosen.
STM measurements
The STM experiments were performed on the same crystals immediately after their return from the RIXS measurements at the Diamond Light Source. We used a commercial (CreaTec) STM system working at low-temperature and UHV environments. Each Dy-Bi2212 single crystal was cleaved in situ at T = 77 K and then immediately transferred into the STM stage stabilized at 77 K or 5 K.
To carry out STM measurements in insulators and to obtain high-quality tunneling spectra over a large bias range (e.g. Fig. 1d), it is crucial to have a stable metallic tip. In our experiment, an electrochemically etched tungsten tip was transferred into the UHV chamber and was then electron-beam bombarded for 15 min to remove the oxides. Before the measurements, the tip was carefully treated and calibrated on an Au(111) single crystal. The basic requirements include: (i) an atomically sharp apex, (ii) metallic DOS which reveals a well-defined surface state and quasi-particle interference pattern of the Au(111), and (iii) stable enough under a point-contact current as high as 10 uA between the tip and Au(111). The tip was then slowly approached onto the cleaved Dy-Bi2212 sample surface with a large magnitude of negative bias voltage, since the occupied state has a much larger DOS due to the tunneling asymmetry seen in CT gap and PG (e.g. Fig. 1d). More details of this methodology can be found in our previous paper48.
Set-point conditions for Fig. 1: tunneling current I = 30 pA, bias voltage V0 = − 1.0 V, ac − modulation Vm = 30 meV. To mitigate the effect of V0 on the low-energy density-of-states, which is known as the set-point effect, a higher V0 is utilized to reveal the CO signal. In our experiment, set-point conditions for Fig. 2 (the p = 0.04 sample): I = 100 pA, V = − 0.5 V, Vm = 6 mV. Set-point conditions for Fig. 3 and Fig. 5 (the p = 0.06 sample): I = 150 pA, V = − 0.3 V, Vm = 4 mV.
RIXS Data analysis
We first determined the zero-energy-loss of each RIXS spectrum by comparing it with that recorded on a nearby carbon tape with the same scattering geometry. After that, the data were normalized to the incident beamline flux and then corrected for the self-absorption effect using the procedures described in ref. 49. The data in Supplementary Fig. 8 were normalized to the areas of the dd-excitations.
The quasi-elastic CO peak profiles shown in Figs. 2a–c, 3c, and 5a were fitted to a Gaussian peak with a Lorentzian background centered at H = 0. From this analysis, the CO wavevector (e.g., Fig. 6a) and amplitude (e.g., Fig. 5c) were respectively characterized by the position and area of the Gaussian component.
The inelastic phonon branches were extracted through a fitting model to each RIXS spectrum, as exemplified in Fig. 3d. It involves resolution-restricted Gaussians for the quasi-elastic, BB phonon, and BS phonon peaks, and a higher-energy background of an anti-symmetric Lorentzian convoluted with the energy resolution. From this analysis, we decomposed the raw data to CO, BB phonon, and BS phonon intensity maps shown in Fig. 4 and Supplementary Fig. 8, which further generate Fig. 5a,b. The adequacy of our model and the comparison with other one-phonon fitting models are demonstrated in Supplementary Fig. 7 and discussed in the accompanying text.
STM data analysis
For characterizing the bi-directional checkerboard CO, the dI/dV map is widely employed for STM analysis4,7,8,10,21,37, which provides a direct comparison with the resonant X-ray scattering signal4,10. From the STM point of view, the defining feature of the CO is an in-phase density-of-states distribution between the particle (-E) and hole (+E) state, distinguishing it from other electronic modulations that are studied by the “Z-map"20,32,36,50,51. In practice, the “Z-map" has been effective in mitigating the CO signal for QPI and uni-directional modulation studies.
The PG map ΔPG(r) shown in Fig. 2g was obtained by fitting the tunneling spectrum at each pixel dI/dV(r, E). The fit was done on the positive-E side (unoccupied state) with an evident peak, where a s-wave Dynes formula works pretty well for the broad feature in this highly underdoped regime50. We note that the density-of-states, or tunneling rate, asymmetry seen in the PG lineshape is generic for cuprates20, which is due to the inequivalence between electron injection and extraction and reflects, thereby, the strong electron-electron correlation effect52.
The STM momentum resolution is estimated to be ΔQ = 2π/23.8 nm = 0.026 Å−1 ~ 0.016 r.l.u. (where 23.8 nm represents the real-space size of Fig. 3a), which is sufficient for the CO analysis. To directly compare the QCO between Fourier-transformed STM and RIXS (Fig. 3), we have corrected the thermal and piezoelectric drifts of the p = 0.06 dataset. The methodology used for this correction, Lawler-Fujita’s algorithm, has been well documented in ref. 51.
Data availability
The data used to support the findings of this work are available from the corresponding author upon request. Source data are provided with this paper.
References
Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).
Comin, R. & Damascelli, A. Resonant X-ray scattering studies of charge order in cuprates. Annu. Rev. Condens. Matter Phys. 7, 369–405 (2016).
Ghiringhelli, G. et al. Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O6+x. Science 337, 821–825 (2012).
Neto, E. H. D. S. et al. Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates. Science 343, 393–396 (2014).
Boschini, F. et al. Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane. Nat. Commun. 12, 1–8 (2021).
Lee, W. S. et al. Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate. Nat. Phys. 17, 53–57 (2021).
Cai, P. et al. Visualizing the evolution from the Mott insulator to a charge-ordered insulator in lightly doped cuprates. Nat. Phys. 12, 1047–1051 (2016).
Hanaguri, T. et al. A ‘checkerboard’ electronic crystal state in lightly hole-doped Ca2−xNaxCuO2Cl2. Nature 430, 1001–1005 (2004).
Damascelli, A., Hussain, Z. & Shen, Z.-X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473–541 (2003).
Comin, R. et al. Charge order driven by fermi-arc instability in Bi2Sr2−xLaxCuO6+δ. Science 343, 390–392 (2014).
Doiron-Leyraud, N. et al. Quantum oscillations and the fermi surface in an underdoped high-Tc superconductor. Nature 447, 565–568 (2007).
Fang, Y. et al. Fermi surface transformation at the pseudogap critical point of a cuprate superconductor. Nat. Phys. https://doi.org/10.1038/s41567-022-01514-1 (2022).
Vishik, I. et al. Phase competition in trisected superconducting dome. Proc. Natl. Acad. Sci. USA 109, 18332–18337 (2012).
Peng, Y. et al. Disappearance of nodal gap across the insulator-superconductor transition in a copper-oxide superconductor. Nat. Commun. 4, 2459 (2013).
Ruan, W. et al. Relationship between the parent charge transfer gap and maximum transition temperature in cuprates. Sci. Bull. 61, 1826–1832 (2016).
Chaix, L. et al. Dispersive charge density wave excitations in Bi2Sr2CaCu2O8+δ. Nat. Phys. 13, 952–956 (2017).
Wang, Q. et al. Charge order lock-in by electron-phonon coupling in La1.675Eu0.2Sr0.125CuO4. Sci. Adv. 7, 27 (2021).
Lin, J. Q. et al. Strongly correlated charge density wave in La2−xSrxCuO4 evidenced by doping-dependent phonon anomaly. Phys. Rev. Lett. 124, 207005 (2020).
Zhou, K. J. et al. I21: an advanced high-resolution resonant inelastic X-ray scattering beamline at Diamond Light Source. J. Synchrotron Radiat. 29, 563–580 (2022).
Kohsaka, Y. et al. An intrinsic bond-centered electronic glass with unidirectional domains in underdoped cuprates. Science 315, 1380–1385 (2007).
Yu, Y., Ma, L., Cai, P., Zhong, R. & Zhang, Y. High-temperature superconductivity in monolayer Bi2Sr2CaCu2O8+δ. Nature 575, 156–163 (2019).
Hashimoto, M. et al. Particle-hole symmetry breaking in the pseudogap state of Bi2201. Nat. Phys. 6, 414–418 (2010).
Sakai, T., Poilblanc, D. & Scalapino, D. J. Hole pairing and phonon dynamics in generalized two-dimensional t-J Holstein models. Phys. Rev. B 55, 8445–8451 (1997).
Johnston, S. et al. Systematic study of electron-phonon coupling to oxygen modes across the cuprates. Phys. Rev. B 82, 064513 (2010).
Levy de Castro, G., Berthod, C., Piriou, A., Giannini, E. & Fischer, O. Preeminent role of the van Hove singularity in the strong-coupling analysis of scanning tunneling spectroscopy for two-dimensional cuprate superconductors. Phys. Rev. Lett. 101, 267004 (2008).
Devereaux, T. P. et al. Directly characterizing the relative strength and momentum dependence of electron-phonon coupling using resonant inelastic X-ray scattering. Phys. Rev. X 6, 041019 (2016).
Braicovich, L. et al. Determining the electron-phonon coupling in superconducting cuprates by resonant inelastic x-ray scattering: Methods and results on Nd1+xBa2−xCu3O7−δ. Phys. Rev. Res. 2, 023231 (2020).
Tacon, M. L., Bosak, A., Souliou, S. M., Dellea, G. & Keimer, B. Inelastic X-ray scattering in YBa2Cu3O6.6 reveals giant phonon anomalies and elastic central peak due to charge-density-wave formation. Nat. Phys. 10, 52–58 (2013).
Huang, H. Y. et al. Quantum fluctuations of charge order induce phonon softening in a superconducting cuprate. Phys. Rev. X 11, 041038 (2021).
Miao, H. et al. Formation of incommensurate charge density waves in cuprates. Phys. Rev. X 9, 031042 (2019).
Wen, J. J., Huang, H., Lee, S. J., Jang, H. & Lee, J. S. Observation of two types of charge-density-wave orders in superconducting La2−xSrxCuO4. Nat. Commun. 10, 3269 (2019).
Mesaros, A. et al. Commensurate 4a0-period charge density modulations throughout the Bi2Sr2CaCu2O8+x pseudogap regime. Proc. Natl. Acad. Sci. USA 113, 12661–12666 (2016).
Vinograd, I., Zhou, R., Hirata, M., Wu, T. & Julien, M. H. Locally commensurate charge-density wave with three-unit-cell periodicity in YBa2Cu3Oy. Nat. Commun. 12 (2021).
Miao, H. et al. High-temperature charge density wave correlations in La1.875Ba0.125CuO4 without spin-charge locking. Proc. Natl. Acad. Sci. USA 114, 12430–12435 (2017).
Peng, Y. Y. et al. Magnetic excitations and phonons simultaneously studied by resonant inelastic x-ray scattering in optimally doped Bi1.5Pb0.55Sr1.6La0.4CuO6+δ. Phys. Rev. B 92, 064517 (2015).
Lee, J. et al. Spectroscopic fingerprint of phase-incoherent superconductivity in the underdoped Bi2Sr2CaCu2O8+δ. Science 325, 1099–1103 (2009).
Ye, S. et al. The emergence of global phase coherence from local pairing in underdoped cuprates. Nat. Phys. https://doi.org/10.1038/s41567-023-02100-9 (2023).
He, Y. et al. Superconducting fluctuations in overdoped Bi2Sr2CaCu2O8+δ. Phys. Rev. X 11, 031068 (2021).
Wang, Y. et al. Field-enhanced diamagnetism in the pseudogap state of the cuprate Bi2Sr2CaCu2O8+δ superconductor in an intense magnetic field. Phys. Rev. Lett. 95, 247002 (2005).
Tallon, J. L., Storey, J. G. & Loram, J. W. Fluctuations and critical temperature reduction in cuprate superconductors. Phys. Rev. B 83, 092502 (2011).
Tranquada, J. M., Dean, M. P. M. & Li, Q. Superconductivity from charge order in cuprates. J. Phys. Soc. Jpn. 90, 111002 (2021).
Ruan, W. et al. Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor. Nat. Phys. 14, 1178–1182 (2018).
Zeljkovic, I. et al. Imaging the impact of single oxygen atoms on superconducting Bi2+ySr2−yCaCu2O8+x. Science 337, 320–323 (2012).
Lanzara, A. et al. Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors. Nature 412, 510–514 (2001).
Cuk, T. et al. Coupling of the B1g Phonon to the antinodal electronic states of Bi2Sr2Ca0.92Y0.08Cu2O8+δ. Phys. Rev. Lett. 93, 117003 (2004).
Liu, D. Z., Zha, Y. & Levin, K. Theory of neutron scattering in the normal and superconducting states of YBa2Cu3O6+x. Phys. Rev. Lett. 75, 4130–4133 (1995).
Presland, M., Tallon, J., Buckley, R., Liu, R. & Flower, N. General trends in oxygen stoichiometry effects on Tc in Bi and Tl superconductors. Phys. C 176, 95–105 (1991).
Ye, C. et al. Visualizing the atomic-scale electronic structure of the Ca2CuO2Cl2 Mott insulator. Nat. Commun. 4, 1365 (2013).
Minola, M. et al. Collective nature of spin excitations in superconducting cuprates probed by resonant inelastic X-Ray scattering. Phys. Rev. Lett. 114, 217003 (2015).
Kohsaka, Y. et al. Visualizing the emergence of the pseudogap state and the evolution to superconductivity in a lightly hole-doped mott insulator. Nat. Phys. 8, 604–10 (2012).
Lawler, M. J. et al. Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states. Nature 466, 347–351 (2010).
Anderson, P. & Ong, N. Theory of asymmetric tunneling in the cuprate superconductors. J. Phys. Chem. Solids 67, 1–5 (2006).
Lu, H. et al. Identification of a characteristic doping for charge order phenomena in Bi-2212 cuprates via RIXS. Phys. Rev. B 106, 155109 (2022).
Du, Z. et al. Periodic atomic displacements and visualization of the electron-lattice interaction in the cuprate. Phys. Rev. X 13, 021025 (2023).
Acknowledgements
We thank J. Wang, Y. Li, Z. Y. Wang, S. Johnston and Z. Y. Weng for their helpful discussions. Y. Peng is grateful for the financial support from the Ministry of Science and Technology of China (Grants No. 2021YFA1401903 and No. 2019YFA0308401), the Beijing Natural Science Foundation (Grant No. JQ24001), and the National Natural Science Foundation of China (Grants No. 12374143 and 11974029). Y. Wang acknowledges the support by the MOST of China grant No. 2017YFA0302900. C. Zou benefits from the Project funded by China Postdoctoral Science Foundation (Grant No. BX2021019). X. J. Z. is supported by the National Natural Science Foundation of China (Grant No. 11888101). We acknowledge Diamond Light Source for providing the beamtime at the I21-RIXS beamline under Proposal MM28855.
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C.Z. and Y.P. proposed and designed the research. C.Z., J.C., K.J.Z. and Y.P. carried out the RIXS experiments with the help of Q.L., M.G.F., S.A., Q.Q., X.C., and Q.X., C.Z., S.Y. and Y.W. carried out the STM experiments. C.Z. and Q.L. analyzed the data. C.Y. and X.Z. provided the Dy-Bi2212 single crystals. C.Z. performed the vacuum annealing. C.Z. and S.Y. characterized the samples. C.Z. and Y.P. prepared the manuscript. All authors have read and approved the final version of the manuscript.
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Zou, C., Choi, J., Li, Q. et al. Evolution from a charge-ordered insulator to a high-temperature superconductor in Bi2Sr2(Ca,Dy)Cu2O8+δ. Nat Commun 15, 7739 (2024). https://doi.org/10.1038/s41467-024-52124-9
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DOI: https://doi.org/10.1038/s41467-024-52124-9
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