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A central mystery in high-temperature superconductivity is the origin of the so-called strange metal (i.e., the anomalous conductor from which superconductivity emerges at low temperature). Measuring the dynamic charge response of the copper oxides, [Formula: see text], would directly reveal the collective properties of the strange metal, but it has never been possible to measure this quantity with millielectronvolt resolution. Here, we present a measurement of [Formula: see text] for a cuprate, optimally doped Bi2.1Sr1.9CaCu2O8+x (Tc = 91 K), using momentum-resolved inelastic electron scattering. In the medium energy range 0.1-2 eV relevant to the strange metal, the spectra are dominated by a featureless, temperature- and momentum-independent continuum persisting to the electronvolt energy scale. This continuum displays a simple power-law form, exhibiting q2 behavior at low energy and q2/ω2 behavior at high energy. Measurements of an overdoped crystal (Tc = 50 K) showed the emergence of a gap-like feature at low temperature, indicating deviation from power law form outside the strange-metal regime. Our study suggests the strange metal exhibits a new type of charge dynamics in which excitations are local to such a degree that space and time axes are decoupled.

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.

The absorption of light by materials proceeds through the formation of excitons, which are states in which an excited electron is bound to the valence hole it vacated. Understanding the structure and dynamics of excitons is important, for example, for developing technologies for light-emitting diodes or solar energy conversion. However, there has never been an experimental means to study the time-dependent structure of excitons directly. Here, we use causality-inverted inelastic x-ray scattering (IXS) to image the charge-transfer exciton in the prototype insulator LiF, with resolutions Delta t = 20.67 as (2.067 x 10(-17) s) in time and Delta x = 0.533 A (5.33 x 10(-11) m) in space. Our results show that the exciton has a modulated internal structure and is coherently delocalized over two unit cells of the LiF crystal (approximately 8 A). This structure changes only modestly during the course of its life, which establishes it unambiguously as a Frenkel exciton and thus amenable to a simplified theoretical description. Our results resolve an old controversy about excitons in the alkali halides and demonstrate the utility of IXS for imaging attosecond electron dynamics in condensed matter.