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We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-t′-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative t′ values (t′/t = ±0.2) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The t′ < 0 (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find t′ < 0 strongly suppresses superconductivity. The t′ > 0 (electron-doped) region shows the expected circular Fermi pocket of holes around the (π, π) point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector (π, π) induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with t′ > 0 is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near x = 0.08 for t′ ∼ −0.2, we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.

Although all superconducting cuprates display charge-ordering tendencies, their low-temperature properties are distinct, impeding efforts to understand the phenomena within a single conceptual framework. While some systems exhibit stripes of charge and spin, with a locked periodicity, others host charge density waves (CDWs) without any obviously related spin order. Here we use resonant inelastic X-ray scattering to follow the evolution of charge correlations in the canonical stripe-ordered cuprate La1.875Ba0.125CuO₄ across its ordering transition. We find that high-temperature charge correlations are unlocked from the wavevector of the spin correlations, signaling analogies to CDW phases in various other cuprates. This indicates that stripe order at low temperatures is stabilized by the coupling of otherwise independent charge and spin density waves, with important implications for the relation between charge and spin correlations in the cuprates.

Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition can be complicated by coupling between distinct order parameters. We show how measurement of the divergent nematic susceptibility of the iron pnictide superconductor Ba(Fe 1−x Co x ) 2 As 2 distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also indicate an electronic nematic quantum phase transition near the composition with optimal superconducting transition temperature.

Charge-density waves (CDWs) are ubiquitous in underdoped cuprate superconductors. As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3d and O-2p orbital character owing to the strong hybridization of these orbitals near the Fermi level. Here, we investigate underdoped Bi₂Sr1.4La0.6CuO6+δ using resonant inelastic X-ray scattering (RIXS) and find that a shortrange CDW exists at both Cu and O sublattices in the copper-oxide (CuO₂) planes with a comparable periodicity and correlation length. Furthermore, we uncover bond-stretching and bond-buckling phonon anomalies concomitant to the CDWs. Comparing to slightly overdoped Bi₂Sr1.8La0.2CuO6+δ, where neither CDWs nor phonon anomalies appear, we highlight that a sharp intensity anomaly is induced in the proximity of the CDW wavevector (QCDW) for the bond-buckling phonon, in concert with the diffused intensity enhancement of the bond-stretching phonon at wavevectors much greater than QCDW. Our results provide a comprehensive picture of the quasistatic CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates.

Charge density waves (CDWs) have been observed in nearly all families of copper-oxide superconductors. But the behavior of these phases across different families has been perplexing. In La-based cuprates, the CDW wavevector is an increasing function of doping, exhibiting the so-called Yamada behavior, while in Y- and Bi-based materials the behavior is the opposite. Here, we report a combined resonant soft X-ray scattering (RSXS) and neutron scattering study of charge and spin density waves in isotopically enriched La1.8–xEu0.2SrₓCuO₄ over a range of doping 0.07 ≤ x ≤ 0.20. We find that the CDW amplitude is temperature independent and develops well above experimentally accessible temperatures. Further, the CDW wavevector shows a nonmonotonic temperature dependence, exhibiting Yamada behavior at low temperature with a sudden change occurring near the spin ordering temperature. We describe these observations using a Landau–Ginzburg theory for an incommensurate CDW in a metallic system with a finite charge compressibility and spin-CDW coupling. Extrapolating to high temperature, where the CDW amplitude is small and spin order is absent, our analysis predicts a decreasing wavevector with doping, similar to Y and Bi cuprates. Our study suggests that CDW order in all families of cuprates forms by a common mechanism.

Charge density modulations have been observed in all families of high–critical temperature (Tc ) superconducting cuprates. Although they are consistently found in the underdoped region of the phase diagram and at relatively low temperatures, it is still unclear to what extent they influence the unusual properties of these systems. Using resonant x-ray scattering, we carefully determined the temperature dependence of charge density modulations in YBa₂Cu₃O7–δ and Nd1+xBa2–xCu₃O7–δ for several doping levels. We isolated short-range dynamical charge density fluctuations in addition to the previously known quasi-critical charge density waves. They persist up to well above the pseudogap temperature T*, are characterized by energies of a few milli–electron volts, and pervade a large area of the phase diagram.

Although high-transition-temperature (high- T c ) superconductivity in cuprates has been known for more than three decades, the underlying mechanism remains unknown 1 – 4 . Cuprates are the only unconventional superconductors that exhibit bulk superconductivity with T c above the liquid-nitrogen boiling temperature of 77 K. Here we observe that high-pressure resistance and mutual inductive magnetic susceptibility measurements showed signatures of superconductivity in single crystals of La 3 Ni 2 O 7 with maximum T c of 80 K at pressures between 14.0 GPa and 43.5 GPa. The superconducting phase under high pressure has an orthorhombic structure of Fmmm space group with the 3 d x 2 − y 2 and 3 d z 2 orbitals of Ni cations strongly mixing with oxygen 2 p orbitals. Our density functional theory calculations indicate that the superconductivity emerges coincidently with the metallization of the σ-bonding bands under the Fermi level, consisting of the 3 d z 2 orbitals with the apical oxygen ions connecting the Ni–O bilayers. Thus, our discoveries provide not only important clues for the high- T c superconductivity in this Ruddlesden–Popper double-layered perovskite nickelates but also a previously unknown family of compounds to investigate the high- T c superconductivity mechanism. Signatures of superconductivity in single crystals of La 3 Ni 2 O 7 were observed at a maximum transition temperature of 80  K at pressures between 14.0  GPa and 43.5  GPa.

Experiments have shown that the families of cuprate superconductors that have the largest transition temperature at optimal doping also have the largest oxygen hole content at that doping [D. Rybicki et al., Nat. Commun. 7, 1–6 (2016)]. They have also shown that a large charge-transfer gap [W. Ruan et al., Sci. Bull. (Beijing) 61, 1826–1832 (2016)], a quantity accessible in the normal state, is detrimental to superconductivity. We solve the three-band Hubbard model with cellular dynamical mean-field theory and show that both of these observations follow from the model. Cuprates play a special role among doped charge-transfer insulators of transition metal oxides because copper has the largest covalent bonding with oxygen. Experiments [L. Wang et al., arXiv [Preprint] (2020). https://arxiv.org/abs/2011.05029 (Accessed 10 November 2020)] also suggest that superexchange is at the origin of superconductivity in cuprates. Our results reveal the consistency of these experiments with the above two experimental findings. Indeed, we show that covalency and a charge-transfer gap lead to an effective short-range superexchange interaction between copper spins that ultimately explains pairing and superconductivity in the three-band Hubbard model of cuprates.

The randomness of dopant atom distributions in cuprate high-critical temperature superconductors has long been suspected to cause nanoscale electronic disorder. In the superconductor Bi₂Sr₂CaCu₂O₈₊δ, we identified populations of atomic-scale impurity states whose spatial densities follow closely those of the oxygen dopant atoms. We found that the impurity-state locations are strongly correlated with all manifestations of the nanoscale electronic disorder. This disorder occurs via an unanticipated mechanism exhibiting high-energy spectral weight shifts, with associated strong superconducting coherence peak suppression but very weak scattering of low-energy quasi-particles.

To investigate proposed ferromagnetic fluctuations in the so-called single-layer Bi-2201 and La-214 high-Tc cuprates, we performed magnetization and electrical resistivity measurements using single-layer Tl-2201 cuprates Tl2Ba2CuO6+δ and La-214 La2−xSrxCuO4 in the heavily overdoped regime. Magnetization of Tl2Ba2CuO6+δ and La2−xSrxCuO4 exhibited the tendency to be saturated in high magnetic fields at low temperatures, suggesting the precursor behavior toward the formation of a ferromagnetic order. It was found that the power of temperature n obtained from the temperature dependence of the electrical resistivity is ~4/3 and ~5/3 for Bi-2201 and La2−xSrxCuO4, respectively, and is ~4/3 at high temperatures and ~5/3 at low temperatures in Tl2Ba2CuO6+δ. These results suggest that two- and three-dimensional ferromagnetic fluctuations exist in Bi-2201 and La2−xSrxCuO4, respectively. In Tl2Ba2CuO6+δ, it is suggested that the dimension of ferromagnetic fluctuations is two at high temperatures and three at low temperatures, respectively. The dimensionality of ferromagnetic fluctuations is understood in terms of the dimensionality of the crystal structure and the bonding of atoms in the blocking layer.