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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, χ″(q,ω), 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 χ″(q,ω) 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.

A spatially modulated superconducting state, known as pair density wave (PDW), is a tantalizing state of matter with unique properties. Recent scanning tunneling microscopy (STM) studies revealed that spin-triplet superconductor UTe 2 hosts an unprecedented spin-triplet, multi-component PDW whose three wavevectors are indistinguishable from a preceding charge-density wave (CDW) order that survives to temperatures well above the superconducting critical temperature, T c . Whether the PDW is the mother or a subordinate order remains unsettled. Here, based on a systematic search for bulk charge order above T c using resonant elastic X-ray scattering (REXS), we show that the structure factor of charge order previously identified by STM is absent in the bulk within the sensitivity of REXS. Our results invite two scenarios: either the density-wave orders condense simultaneously at T c in the bulk, in which case PDW order is likely the mother phase, or the charge modulations are restricted to the surface. Surface-sensitive scanning tunneling microscopy (STM) has previously found a charge density wave (CDW) up to 10 K in the normal state of the heavy-fermion superconductor UTe 2 . Here, using resonant elastic X-ray scattering (REXS) above the superconducting transition, the authors find no evidence for a bulk CDW, suggesting the normal state CDW observed by STM is a surface effect.

A theoretical and experimental study reveals the relation between charge density waves and orbital textures for different stackings in a two-dimensional layered material. Low-dimensional electron systems, as realized in layered materials, often tend to spontaneously break the symmetry of the underlying nuclear lattice by forming so-called density waves 1 ; a state of matter that at present attracts enormous attention 2 , 3 , 4 , 5 , 6 . Here we reveal a remarkable and surprising feature of charge density waves, namely their intimate relation to orbital order. For the prototypical material 1T-TaS 2 we not only show that the charge density wave within the two-dimensional TaS 2 layers involves previously unidentified orbital textures of great complexity. We also demonstrate that two metastable stackings of the orbitally ordered layers allow manipulation of salient features of the electronic structure. Indeed, these orbital effects provide a route to switch 1T-TaS 2 nanostructures from metallic to semiconducting with technologically pertinent gaps of the order of 200 meV. This new type of orbitronics is especially relevant for the ongoing development of novel, miniaturized and ultrafast devices based on layered transition metal dichalcogenides 7 , 8 .

Competition between magnetism and the kinetic energy of mobile carriers (typically holes) in doped antiferromagnets may lead to ‘stripe’ phases 1 , 2 , 3 , 4 , which are charged rivers separating regions of oppositely phased antiferromagnetism. In copper oxides the main experimental evidence for such coexisting static spin and charge order comes from neutron scattering in La 1.48 Nd 0.4 Sr 0.12 CuO 4 (LNSCO; ref.  5 ) and La 1.875 Ba 0.125 CuO 4 (LBCO; ref.  6 ). However, as a neutron is neutral, it does not detect charge but rather its associated lattice distortion 7 , so it is not known whether the stripes involve ordering of the doped holes. Here we present a study of the charge order in LBCO with resonant soft X-ray scattering (RSXS). We observe giant resonances near the Fermi level as well as near the correlated gap 8 , 9 , demonstrating significant modulation in both the doped-hole density and the ‘Mottness’, or the degree to which the system resembles a Mott insulator 10 . The peak-to-trough amplitude of the valence modulation is estimated to be 0.063 holes, which suggests 11 an integrated area of 0.59 holes under a single stripe, close to the expected 0.5 for half-filled stripes.

When the charge density wave state in TiSe 2 is suppressed by hydrostatic pressure or chemical doping, superconductivity appears. This suggests the presence of a quantum critical point. Yet a high pressure X-ray study unexpectedly finds that the quantum critical point is nowhere near the superconducting dome. Superconductivity in so-called unconventional superconductors is nearly always found in the vicinity of another ordered state, such as antiferromagnetism, charge density wave (CDW), or stripe order. This suggests a fundamental connection between superconductivity and fluctuations in some other order parameter. To better understand this connection, we used high-pressure X-ray scattering to directly study the CDW order in the layered dichalcogenide TiSe 2 , which was previously shown to exhibit superconductivity when the CDW is suppressed by pressure 1 or intercalation of Cu atoms 2 . We succeeded in suppressing the CDW fully to zero temperature, establishing for the first time the existence of a quantum critical point (QCP) at P c  =  5.1   ±  0.2 GPa, which is more than 1 GPa beyond the end of the superconducting region. Unexpectedly, at P  = 3 GPa we observed a reentrant, weakly first order, incommensurate phase, indicating the presence of a Lifshitz tricritical point somewhere above the superconducting dome. Our study suggests that superconductivity in TiSe 2 may not be connected to the QCP itself, but to the formation of CDW domain walls.

Determining the nature of the electronic phases that compete with superconductivity in high-transition-temperature (high- T c ) superconductors is one of the deepest problems in condensed matter physics. One candidate is the ‘stripe’ phase 1 , 2 , 3 , in which the charge carriers (holes) condense into rivers of charge that separate regions of antiferromagnetism. A related but lesser known system is the ‘spin ladder’, which consists of two coupled chains of magnetic ions forming an array of rungs. A doped ladder can be thought of as a high- T c material with lower dimensionality, and has been predicted to exhibit both superconductivity 4 , 5 , 6 and an insulating ‘hole crystal’ 4 , 7 , 8 phase in which the carriers are localized through many-body interactions. The competition between the two resembles that believed to operate between stripes and superconductivity in high- T c materials 9 . Here we report the existence of a hole crystal in the doped spin ladder of Sr 14 Cu 24 O 41 using a resonant X-ray scattering technique 10 . This phase exists without a detectable distortion in the structural lattice, indicating that it arises from many-body electronic effects. Our measurements confirm theoretical predictions 4 , 7 , 8 , and support the picture that proximity to charge ordered states is a general property of superconductivity in copper oxides.

An unresolved issue concerning cuprate superconductors is whether the distribution of carriers in the CuO2plane is uniform or inhomogeneous. Because the carriers comprise a small fraction of the total charge density and may be rapidly fluctuating, modulations are difficult to detect directly. We demonstrate that in anomalous x-ray scattering at the oxygen K edge of the cuprates, the contribution of carriers to the scattering amplitude is selectively magnified 82 times. This enhances diffraction from the doped holes by more than 103, permitting direct structural analysis of the superconducting ground state. Scattering from thin films of$La_{2}CuO_{4+\\delta}$(superconducting transition temperature = 39 K) at$temperature = 50 \\pm 5 kelvin$on the reciprocal space intervals$(0,0,0.21) \\rightarrow (0,0,1.21)$and$(0,0,0.6) \\rightarrow (0.3,0,0.6)$shows a rounding of the carrier density near the substrate suggestive of a depletion zone or similar effect. The structure factor for off-specular scattering was less than$3 \\times 10^{-7}$electrons, suggesting an absence of in-plane hole ordering in this material.

A spatially modulated superconducting state, known as pair density wave (PDW), is a tantalizing state of matter with unique properties. Recent scanning tunneling microscopy (STM) studies revealed that spin-triplet superconductor UTe hosts an unprecedented spin-triplet, multi-component PDW whose three wavevectors are indistinguishable from a preceding charge-density wave (CDW) order that survives to temperatures well above the superconducting critical temperature, T . Whether the PDW is the mother or a subordinate order remains unsettled. Here, based on a systematic search for bulk charge order above T using resonant elastic X-ray scattering (REXS), we show that the structure factor of charge order previously identified by STM is absent in the bulk within the sensitivity of REXS. Our results invite two scenarios: either the density-wave orders condense simultaneously at T in the bulk, in which case PDW order is likely the mother phase, or the charge modulations are restricted to the surface.

Superconductivity in so-called unconventional superconductors is nearly always found in the vicinity of another ordered state, such as antiferromagnetism, charge density wave (CDW), or stripe order. This suggests a fundamental connection between superconductivity and fluctuations in some other order parameter. To better understand this connection, we used high-pressure X-ray scattering to directly study the CDW order in the layered dichalcogenide TiSe sub(2), which was previously shown to exhibit superconductivity when the CDW is suppressed by pressure or intercalation of Cu atoms. We succeeded in suppressing the CDW fully to zero temperature, establishing for the first time the existence of a quantum critical point (QCP) at P sub(c) = 5.1 plus or minus 0.2 GPa, which is more than 1 GPa beyond the end of the superconducting region. Unexpectedly, at P = 3 GPa we observed a reentrant, weakly first order, incommensurate phase, indicating the presence of a Lifshitz tricritical point somewhere above the superconducting dome. Our study suggests that superconductivity in TiSe sub(2) may not be connected to the QCP itself, but to the formation of CDW domain walls.