Incoherent transport across the strange-metal regime of overdoped cuprates.

Strange metals possess highly unconventional electrical properties, such as a linear-in-temperature resistivity1-6, an inverse Hall angle that varies as temperature squared7-9 and a linear-in-field magnetoresistance10-13. Identifying the origin of these collective anomalies has proved fundamentally challenging, even in materials such as the hole-doped cuprates that possess a simple bandstructure. The prevailing consensus is that strange metallicity in the cuprates is tied to a quantum critical point at a doping p* inside the superconducting dome14,15. Here we study the high-field in-plane magnetoresistance of two superconducting cuprate families at doping levels beyond p*. At all dopings, the magnetoresistance exhibits quadrature scaling and becomes linear at high values of the ratio of the field and the temperature, indicating that the strange-metal regime extends well beyond p*. Moreover, the magnitude of the magnetoresistance is found to be much larger than predicted by conventional theory and is insensitive to both impurity scattering and magnetic field orientation. These observations, coupled with analysis of the zero-field and Hall resistivities, suggest that despite having a single band, the cuprate strange-metal region hosts two charge sectors, one containing coherent quasiparticles, the other scale-invariant 'Planckian' dissipators.

Magnetic excitations in infinite-layer nickelates.

The discovery of superconductivity in infinite-layer nickelates brings us tantalizingly close to a material class that mirrors the cuprate superconductors. We measured the magnetic excitations in these nickelates using resonant inelastic x-ray scattering at the Ni L 3-edge. Undoped NdNiO2 possesses a branch of dispersive excitations with a bandwidth of approximately 200 milli-electron volts, which is reminiscent of the spin wave of strongly coupled, antiferromagnetically aligned spins on a square lattice. The substantial damping of these modes indicates the importance of coupling to rare-earth itinerant electrons. Upon doping, the spectral weight and energy decrease slightly, whereas the modes become overdamped. Our results highlight the role of Mottness in infinite-layer nickelates.

Propagation of shear stress in strongly interacting metallic Fermi liquids enhances transmission of terahertz radiation.

A highlight of Fermi-liquid phenomenology, as explored in neutral [Formula: see text]He, is the observation that in the collisionless regime shear stress propagates as if one is dealing with the transverse phonon of a solid. The existence of this "transverse zero sound" requires that the quasiparticle mass enhancement exceeds a critical value. Could such a propagating shear stress also exist in strongly correlated electron systems? Despite some noticeable differences with the neutral case in the Galilean continuum, we arrive at the verdict that transverse zero sound should be generic for mass enhancement higher than 3. We present an experimental setup that should be exquisitely sensitive in this regard: the transmission of terahertz radiation through a thin slab of heavy-fermion material will be strongly enhanced at low temperature and accompanied by giant oscillations, which reflect the interference between light itself and the "material photon" being the actual manifestation of transverse zero sound in the charged Fermi liquid.

Publisher Correction: Electronic structure of the parent compound of superconducting infinite-layer nickelates.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Electronic structure of the parent compound of superconducting infinite-layer nickelates.

The search continues for nickel oxide-based materials with electronic properties similar to cuprate high-temperature superconductors1-10. The recent discovery of superconductivity in the doped infinite-layer nickelate NdNiO2 (refs. 11,12) has strengthened these efforts. Here, we use X-ray spectroscopy and density functional theory to show that the electronic structure of LaNiO2 and NdNiO2, while similar to the cuprates, includes significant distinctions. Unlike cuprates, the rare-earth spacer layer in the infinite-layer nickelate supports a weakly interacting three-dimensional 5d metallic state, which hybridizes with a quasi-two-dimensional, strongly correlated state with [Formula: see text] symmetry in the NiO2 layers. Thus, the infinite-layer nickelate can be regarded as a sibling of the rare-earth intermetallics13-15, which are well known for heavy fermion behaviour, where the NiO2 correlated layers play an analogous role to the 4f states in rare-earth heavy fermion compounds. This Kondo- or Anderson-lattice-like 'oxide-intermetallic' replaces the Mott insulator as the reference state from which superconductivity emerges upon doping.

Rapid change of superconductivity and electron-phonon coupling through critical doping in Bi-2212.

Electron-boson coupling plays a key role in superconductivity for many systems. However, in copper-based high-critical temperature (T c) superconductors, its relation to superconductivity remains controversial despite strong spectroscopic fingerprints. In this study, we used angle-resolved photoemission spectroscopy to find a pronounced correlation between the superconducting gap and the bosonic coupling strength near the Brillouin zone boundary in Bi2Sr2CaCu2O8+δ The bosonic coupling strength rapidly increases from the overdoped Fermi liquid regime to the optimally doped strange metal, concomitant with the quadrupled superconducting gap and the doubled gap-to-T c ratio across the pseudogap boundary. This synchronized lattice and electronic response suggests that the effects of electronic interaction and the electron-phonon coupling (EPC) reinforce each other in a positive-feedback loop upon entering the strange-metal regime, which in turn drives a stronger superconductivity.

From quantum matter to high-temperature superconductivity in copper oxides.

The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.

Topological defects coupling smectic modulations to intra-unit-cell nematicity in cuprates.

We study the coexisting smectic modulations and intra-unit-cell nematicity in the pseudogap states of underdoped Bi(2)Sr(2)CaCu(2)O(8+δ). By visualizing their spatial components separately, we identified 2π topological defects throughout the phase-fluctuating smectic states. Imaging the locations of large numbers of these topological defects simultaneously with the fluctuations in the intra-unit-cell nematicity revealed strong empirical evidence for a coupling between them. From these observations, we propose a Ginzburg-Landau functional describing this coupling and demonstrate how it can explain the coexistence of the smectic and intra-unit-cell broken symmetries and also correctly predict their interplay at the atomic scale. This theoretical perspective can lead to unraveling the complexities of the phase diagram of cuprate high-critical-temperature superconductors.

Mottness collapse and statistical quantum criticality.

We put forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness, as advocated by Phillips and supported by recent dynamical cluster approximation results on the Hubbard model, sets the necessary microscopic conditions. The crucial insight is due to Weng, who demonstrated that, in the presence of Mottness, the fundamental workings of quantum statistics change, and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing it further using numerical methods. The pseudo-gap physics of the underdoped regime appears as a consequence of the altered statistics and the profound question is how to connect this by a continuous quantum phase transition to the overdoped regime ruled by normal Fermi-Dirac statistics. Proof of principle follows from Ceperley's constrained path integral formalism, in which states can be explicitly constructed showing a merger of Fermi-Dirac sign structure and scale invariance of the quantum dynamics.

Proximity of the superconducting dome and the quantum critical point in the two-dimensional Hubbard model.

We use the dynamical cluster approximation to understand the proximity of the superconducting dome to the quantum critical point in the two-dimensional Hubbard model. In a BCS formalism, T(c) may be enhanced through an increase in the d-wave pairing interaction (V(d)) or the bare pairing susceptibility (χ(0d)). At optimal doping, where V(d) is revealed to be featureless, we find a power-law behavior of χ(0d)(ω=0), replacing the BCS log, and strongly enhanced T(c). We suggest experiments to verify our predictions.

Charge dynamics of doped holes in high Tc cuprate superconductors: a clue from optical conductivity.

The charge dynamics in weakly hole doped high temperature superconductors is studied in terms of the accurate numerical solution to a model of a single hole interacting with a quantum lattice in an antiferromagnetic background, and accurate far-infrared ellipsometry measurements. The experimentally observed two electronic bands in the infrared spectrum can be identified in terms of the interplay between the electron correlation and electron-phonon interaction resolving the long standing mystery of the midinfrared band.

Quantum critical electron systems: the uncharted sign worlds.

Phases of classical matter, such as solids and liquids, are ruled by emergence principles that are well understood. Although the same principles govern forms of quantum matter that have no secrets for physicists, such as the superfluids, having to deal with fermions and the associated Fermi sign problem shatters this analogy. This Perspective addresses the Fermion sign problem and describes experiments on metals undergoing quantum phase transitions exhibiting scale-invariant electronic behavior, a description of which is at odds with established quantum theory.

Quantum smectic as a dislocation Higgs phase.

The theory describing quantum smectics in 2+1 dimensions, based on topological quantum melting is presented. This is governed by a dislocation condensate characterized by an ordering of Burger's vector and this "dual shear superconductor" manifests itself in the form of a novel spectrum of phononlike modes.

Doping dependence of the coupling of electrons to bosonic modes in the single-layer high-temperature Bi2Sr2CuO6 superconductor.

A recent highlight in the study of high-T(c) superconductors is the observation of band renormalization or self-energy effects on the quasiparticles. This is seen in the form of kinks in the quasiparticle dispersions as measured by photoemission and interpreted as signatures of collective bosonic modes coupling to the electrons. Here we compare for the first time the self-energies in an optimally doped and strongly overdoped, nonsuperconducting single-layer Bi-cuprate (Bi2Sr2CuO6). In addition to the appearance of a strong overall weakening, we also find that the weight of the self-energy in the overdoped system shifts to higher energies. We present evidence that this is related to a change in the coupling to c-axis phonons due to the rapid change of the c-axis screening in this doping range.

Nodal quasiparticle in pseudogapped colossal magnetoresistive manganites.

A characteristic feature of the copper oxide high-temperature superconductors is the dichotomy between the electronic excitations along the nodal (diagonal) and antinodal (parallel to the Cu-O bonds) directions in momentum space, generally assumed to be linked to the 'd-wave' symmetry of the superconducting state. Angle-resolved photoemission measurements in the superconducting state have revealed a quasiparticle spectrum with a d-wave gap structure that exhibits a maximum along the antinodal direction and vanishes along the nodal direction. Subsequent measurements have shown that, at low doping levels, this gap structure persists even in the high-temperature metallic state, although the nodal points of the superconducting state spread out in finite 'Fermi arcs'. This is the so-called pseudogap phase, and it has been assumed that it is closely linked to the superconducting state, either by assigning it to fluctuating superconductivity or by invoking orders which are natural competitors of d-wave superconductors. Here we report experimental evidence that a very similar pseudogap state with a nodal-antinodal dichotomous character exists in a system that is markedly different from a superconductor: the ferromagnetic metallic groundstate of the colossal magnetoresistive bilayer manganite La1.2Sr1.8Mn2O7. Our findings therefore cast doubt on the assumption that the pseudogap state in the copper oxides and the nodal-antinodal dichotomy are hallmarks of the superconductivity state.

NMR evidence for a two-step phase separation in Nd1.85Ce0.15CuO4-delta.

By Cu NMR we studied the spin and charge structure in Nd(2-x)Ce(x)CuO(4-delta). For x=0.15, starting from a superconducting sample, the low temperature magnetic order in the sample reoxygenated under 1 bar oxygen at 900 degrees C reveals a peculiar modulation of the internal field, indicative of a phase characterized by large charge droplets ("blob" phase). By prolonged reoxygenation at 4 bars the blobs break up and the spin structure changes to that of an ordered antiferromagnet. We conclude that the superconductivity in the n-type systems competes with a genuine type I Mott-insulating state.

Quantum critical behaviour in a high-T(c) superconductor.

Quantum criticality is associated with a system composed of a nearly infinite number of interacting quantum degrees of freedom at zero temperature, and it implies that the system looks on average the same regardless of the time- and length scale on which it is observed. Electrons on the atomic scale do not exhibit such symmetry, which can only be generated as a collective phenomenon through the interactions between a large number of electrons. In materials with strong electron correlations a quantum phase transition at zero temperature can occur, and a quantum critical state has been predicted, which manifests itself through universal power-law behaviours of the response functions. Candidates have been found both in heavy-fermion systems and in the high-transition temperature (high-T(c)) copper oxide superconductors, but the reality and the physical nature of such a phase transition are still debated. Here we report a universal behaviour that is characteristic of the quantum critical region. We demonstrate that the experimentally measured phase angle agrees precisely with the exponent of the optical conductivity. This points towards a quantum phase transition of an unconventional kind in the high-T(c) superconductors.

Impurity states and interlayer tunneling in high temperature superconductors.

We argue that the scanning tunneling microscope (STM) images of resonant states generated by doping Zn or Ni impurities into Cu-O planes of BSCCO are the result of quantum interference of the impurity signal coming from several distinct paths. The impurity image seen on the surface is greatly affected by interlayer tunneling matrix elements. We find that the optimal tunneling path between the STM tip and the metal (Cu, Zn, or Ni) d(x(2)-y(2)) orbitals in the Cu-O plane involves intermediate excited states. This tunneling path leads to the fourfold nonlocal filter of the impurity state in Cu-O plane that explains the experimental impurity spectra. Applications of the tunneling filter to the Cu vacancy defects and "direct" tunneling into Cu-O planes are also discussed.

First time determination of the microscopic structure of a stripe phase: low temperature NMR in La(2)NiO(4.17).

The experimental observations of stripes in superconducting cuprates and insulating nickelates clearly show the modulation in charge and spin density. However, these have proven to be rather insensitive to the harmonic structure and (site or bond) ordering. Using (139)La NMR in La(2)NiO(4+delta) with delta = 0.17, we show that in the 1/3 hole doped nickelate below the freezing temperature the stripes are strongly solitonic and site ordered with Ni(3+) ions carrying S = 1/2 in the domain walls and Ni(2+) ions with S = 1 in the domains.

Order out of disorder in a gas of elastic quantum strings in 2+1 dimensions.

A limiting case of a dynamical stripe state which is of potential significance to cuprate superconductors is considered: a gas of elastic quantum strings in 2+1 dimensions, interacting merely via a hard-core condition. It is demonstrated that this gas always solidifies, by a mechanism which is the quantum analog of the entropic interactions known from soft condensed matter physics.