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.

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.

We present an investigation of the planar direct-current (dc) paraconductivity of the model cuprate material HgBa 2 CuO 4+δ in the underdoped part of the phase diagram. The simple quadratic temperature-dependence of the Fermi-liquid normal-state resistivity enables us to extract the paraconductivity above the macroscopic T c with great accuracy. The paraconductivity exhibits unusual exponential temperature dependence, with a characteristic temperature scale that is distinct from T c . In the entire temperature range where it is discernable, the paraconductivity is quantitatively explained by a simple superconducting percolation model, which implies that underlying gap disorder dominates the emergence of superconductivity.The nature of the metallic normal state and of the emergence of superconductivity in the cuprates belong to the most extensively debated problems in condensed matter physics [1]. At temperatures above the macroscopic superconducting transition temperature T c , there exists no long-range coherence, yet traces of superconductivity remain observable, and different experimental investigations have led to widely disparate conclusions [2][3][4][5][6][7][8][9][10][11][12][13][14]. In contrast to prevailing thought, it was recently proposed that the normal state of underdoped cuprates exhibits Fermi-liquid charge transport [15][16][17][18], and that superconductivity emerges from this state in a percolative manner [7]. Direct-current (dc) conductivity is a highly sensitive probe that can, in principle, provide a unique opportunity to test the consistency of these ideas. Furthermore, the effective-medium approximation required to model such a mixed regime is

The properties of quantum materials are commonly tuned using experimental variables such as pressure, magnetic field and doping. Here we explore a different approach: irreversible, plastic deformation of single crystals. We show for the archetypal unconventional superconductor SrTiO3 that compressive plastic deformation induces lowdimensional superconductivity significantly above the superconducting transition temperature (Tc) of undeformed samples. We furthermore present evidence for unusual normal-state transport behaviour that suggests superconducting correlations at temperatures two orders of magnitude above the bulk Tc. The superconductivity enhancement is correlated with the appearance of structural features related to selforganized dislocation structures, as revealed by diffuse neutron and X-ray scattering.These results suggest that deformed SrTiO3 is a potential high-temperature superconductor, and push the limits of superconductivity in this low-density electronic system. More broadly, we demonstrate the promise of plastic deformation and dislocation engineering as tools to manipulate electronic properties of quantum materials.

A pivotal challenge posed by unconventional superconductors is to unravel how superconductivity emerges upon cooling from the generally complex normal state. Here, we use nonlinear magnetic response, a probe that is uniquely sensitive to the superconducting precursor, to uncover remarkable universal behaviour in three distinct classes of oxide superconductors: strontium titanate, strontium ruthenate, and the cuprate high- T c materials. We find unusual exponential temperature dependence of the diamagnetic response above the transition temperature T c , with a characteristic temperature scale that strongly varies with T c . We correlate this scale with the sensitivity of T c to local stress and show that it is influenced by intentionally-induced structural disorder. The universal behaviour is therefore caused by intrinsic, self-organized structural inhomogeneity, inherent to the oxides’ perovskite-based structure. The prevalence of such inhomogeneity has far-reaching implications for the interpretation of electronic properties of perovskite-related oxides in general.

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Using a unique home-made cell for four-contact impedance spectroscopy of conductive liquid samples, we establish the existence of two low frequency conductivity relaxations in aqueous solutions of gelatin, in both liquid and gel states. A comparison with diffusion measurements using pulsed field gradient NMR, and circular dichroism spectroscopy, shows that the faster relaxation process is due to gelatin macromolecule self-diffusion. This single molecule diffusion is mostly insensitive to the macroscopic state of the sample, implying that we have a clear separation of gelatin molecules into a free and network-bound phase. Scaling relationships for the self-diffusion indicate that the gelation process is not a percolative phenomenon, but is caused by aggregation of triple helices into a system-spanning fibre network.

The phase diagram of the cuprate superconductors has posed a formidable scientific challenge for more than three decades. This challenge is perhaps best exemplified by the need to understand the normal-state charge transport as the system evolves from Mott insulator to Fermi-liquid metal with doping. Here we report a detailed analysis of the temperature (T) and doping (p) dependence of the planar resistivity of simple-tetragonal HgBa2CuO4+δ (Hg1201), the single-CuO2-layer cuprate with the highest optimal superconducting transition temperature, Tc. The data allow us to test a recently proposed phenomenological model for the cuprate phase diagram that combines a universal transport scattering rate with spatially inhomogeneous (de)localization of the Mott-localized hole. We find that the model provides an excellent description of the data. We then extend this analysis to prior transport results for several other cuprates, including the Hall number in the overdoped part of the phase diagram, and find little compound-to-compound variation in (de)localization gap scale. The results point to a robust, universal structural origin of the inherent gap inhomogeneity that is unrelated to doping-related disorder. They are inconsistent with the notion that much of the phase diagram is controlled by a quantum critical point, and instead indicate that the unusual electronic properties exhibited by the cuprates are fundamentally related to strong nonlinearities associated with subtle nanoscale inhomogeneity.