Absence of static phase separation in the high T(c) cuprate YBa(2)Cu(3)O(6+y)

Charge ordering in superconducting copper oxides

Charge order has recently been identified as a leading competitor of high-temperature superconductivity in moderately doped cuprates. We provide a survey of universal and materials-specific aspects of this phenomenon, with emphasis on results obtained by scattering methods. In particular, we discuss the structure, periodicity, and stability range of the charge-ordered state, its response to various external perturbations, the influence of disorder, the coexistence and competition with superconductivity, as well as collective charge dynamics. In the context of this journal issue which honors Roger Cowley's legacy, we also discuss the connection of charge ordering with lattice vibrations and the central-peak phenomenon. We end the review with an outlook on research opportunities offered by new synthesis methods and experimental platforms, including cuprate thin films and superlattices.

Unusual behavior of cuprates explained by heterogeneous charge localization

The discovery of high-temperature superconductivity in cuprates ranks among the major scientific milestones of the past half century, yet pivotal questions regarding the complex phase diagram of these materials remain unanswered. Generally thought of as doped charge-transfer insulators, these complex oxides exhibit pseudogap, strange-metal, superconducting, and Fermi liquid behavior with increasing hole-dopant concentration. Motivated by recent experimental observations, here we introduce a phenomenological model wherein exactly one hole per planar copper-oxygen unit is delocalized with increasing doping and temperature. The model is percolative in nature, with parameters that are highly consistent with experiments. It comprehensively captures key unconventional experimental results, including the temperature and the doping dependence of the pseudogap phenomenon, the strange-metal linear temperature dependence of the planar resistivity, and the doping dependence of the superfluid density. The success and simplicity of the model greatly demystify the cuprate phase diagram and point to a local superconducting pairing mechanism.

Emergence of superconductivity in the cuprates via a universal percolation process

A pivotal step toward understanding unconventional superconductors would be to decipher how superconductivity emerges from the unusual normal state. In the cuprates, traces of superconducting pairing appear above the macroscopic transition temperature Tc, yet extensive investigation has led to disparate conclusions. The main difficulty has been to separate superconducting contributions from complex normal-state behaviour. Here we avoid this problem by measuring nonlinear conductivity, an observable that is zero in the normal state. We uncover for several representative cuprates that the nonlinear conductivity vanishes exponentially above Tc, both with temperature and magnetic field, and exhibits temperature-scaling characterized by a universal scale Ξ0. Attempts to model the response with standard Ginzburg-Landau theory are systematically unsuccessful. Instead, our findings are captured by a simple percolation model that also explains other properties of the cuprates. We thus resolve a long-standing conundrum by showing that the superconducting precursor in the cuprates is strongly affected by intrinsic inhomogeneity.

Defect-dependent colossal negative thermal expansion in UiO-66(Hf) metal-organic framework

Thermally-densified hafnium terephthalate UiO-66(Hf) is shown to exhibit the strongest isotropic negative thermal expansion (NTE) effect yet reported for a metal-organic framework (MOF). Incorporation of correlated vacancy defects within the framework affects both the extent of thermal densification and the magnitude of NTE observed in the densified product. We thus demonstrate that defect inclusion can be used to tune systematically the physical behaviour of a MOF.

Electrostatic control of the evolution from a superconducting phase to an insulating phase in ultrathin YBa₂Cu₃O(7-x) films

The electrical transport properties of ultrathin YBa₂Cu₃O(7-x) films have been modified using an electric double layer transistor configuration employing an ionic liquid. A clear evolution from superconductor to insulator was observed in nominally 7 unit-cell-thick films. Using a finite size scaling analysis, curves of resistance versus temperature, R(T), over the temperature range from 6 to 22 K were found to collapse onto a single scaling function, which suggests the presence of a quantum critical point. However, the scaling fails at the lowest temperatures indicating the possible presence of an additional phase between the superconducting and insulating regimes.

Incommensurate magnetic order and dynamics induced by spinless impurities in YBa(2)Cu(3)O(6.6)

We report an inelastic-neutron-scattering and muon-spin-relaxation study of the effect of 2% spinless (Zn) impurities on the magnetic order and dynamics of YBa(2)Cu(3)O(6.6), an underdoped high-temperature superconductor that exhibits a prominent spin pseudogap in its normal state. Zn substitution induces static magnetic order at low temperatures and triggers a large-scale spectral-weight redistribution from the magnetic resonant mode at 38 meV into uniaxial, incommensurate spin excitations with energies well below the spin pseudogap. These observations indicate a competition between incommensurate magnetic order and superconductivity close to a quantum critical point. Comparison to prior data on La(2-x)Sr(x)CuO(4) suggests that this behavior is universal for the layered copper oxides and analogous to impurity-induced magnetic order in one-dimensional quantum magnets.

High-field μSR studies of superconducting and magnetic correlations in cuprates above T(c)

The advent of high transverse field muon spin rotation (TF-μSR) has led to recent μSR investigations of the magnetic field response of cuprates above the superconducting transition temperature T(c). Here the results of such experiments on hole-doped cuprates are reviewed. Although these investigations are currently ongoing, it is clear that the effects of high field on the internal magnetic field distribution of these materials is dependent upon competition between superconductivity and magnetism. In La(2 - x)Sr(x)CuO(4) the response to the external field above T(c) is dominated by heterogeneous spin magnetism. However, the magnetism that dominates the observed inhomogeneous line broadening below x ∼ 0.19 is overwhelmed by the emergence of a completely different kind of magnetism in the heavily overdoped regime. The origin of the magnetism above x ∼ 0.19 is probably related to intrinsic disorder, but the systematic evolution of the magnetism with doping changes in the doping range beyond the superconducting 'dome'. In contrast, the width of the internal field distribution of underdoped Y Ba(2)Cu(3)O(y) above T(c) is observed to track T(c) and the density of superconducting carriers. This observation suggests that the magnetic response above T(c) is not dominated by electronic moments, but rather inhomogeneous fluctuating superconductivity. The spatially inhomogeneous response of Y Ba(2)Cu(3)O(y) to the applied field may be a means of minimizing energy, rather than being caused by intrinsic disorder.

Disorder-induced static antiferromagnetism in cuprate superconductors

Using model calculations of a disordered d-wave superconductor with on-site Hubbard repulsion, we show how dopant disorder can stabilize novel states with antiferromagnetic order. We find that the critical strength of correlations or impurity potential necessary to create an ordered magnetic state in the presence of finite disorder is reduced compared to that required to create a single isolated magnetic droplet. This may explain why, in cuprates such as La2-xSrxCuO4, low-energy probes have identified a static magnetic component which persists well into the superconducting state, whereas, in cleaner systems such as YBa(2)Cu(3)O(6+delta), it is absent or minimal.

Nernst effect and disorder in the normal state of high-T(c) cuprates

We have studied the influence of disorder induced by electron irradiation on the Nernst effect in optimally and underdoped YBa2Cu3O(7-delta) single crystals. The fluctuation regime above T(c) expands significantly with disorder, indicating that the T(c) decrease is partly due to the induced loss of phase coherence. In pure crystals the temperature extension of the Nernst signal is found to be narrow whatever the hole doping, contrary to data reported in the low-T(c) cuprate families. Our results show that the presence of intrinsic disorder can explain the enhanced range of the Nernst signal found in the pseudogap phase of the latter compounds.

Atomic-Scale Sources and Mechanism of Nanoscale Electronic Disorder in Bi2Sr2CaCu2O8+

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+delta, 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.