2 If a fluid of bosons is cooled to sufficiently low temperature, a significant fraction will condense into the lowest quantum state, forming a Bose condensate. Bose condensation is a consequence of the even symmetry of the many-body wave function of bosons under particle interchange, and allows for the manifestation of macroscopic quantum phenomena, the most striking being superfluidity.Traditionally, Bose condensates are said to come in two types. Bose-Einstein condensates (BECs) occur in systems of stable bosons, such as dilute atomic gases or liquid Excitons are bosons that are bound states between an electron and hole in a solid, and were predicted long ago to Bose condense (2,3,4). Because of their light mass and high binding energy, exciton condensates should be stable at higher temperature than traditional BEC or BCS phases (5,6).Different theories predict that a Bose condensate of excitons could be a superfluid (5) or innately insulating (7), so there is tremendous need for experimental input. Identifying an exciton condensate in nature could have a profound impact on future understanding of macroscopic quantum phenomena, as well the classic problem of the metal-insulator transition in band solids, in which exciton condensation has long been believed to play a fundamental role (2,3,4).Condensed phases of photogenerated excitons have been realized in semiconductor quantum wells in resonance with a Fabry-Perot cavity which, although not fully thermally equilibrated, have exhibited evidence for transient superfluidity (8). Excitonic phases have also been realized in quantumHall bilayers in a perpendicular magnetic field (9). Although the order in these two-dimensional structures is not strictly long-ranged, and the order parameter cannot be measured directly, compelling evidence for excitonic correlations has been observed in Coulomb drag experiments (9). Despite these 3 achievements, there is a great need to identify an exciton condensate in a fully thermalized, threedimensional system in which the order is long-ranged.An ideal approach would be to identify a material in which an exciton condensate forms "naturally." Long ago, a BCS condensate of excitons was predicted to arise spontaneously in semimetals in which an indirect band gap is tuned close to zero ( Fig. 1) (2,3,4). This condensate is expected to break a spatial symmetry, rather than the U(1) symmetry broken by a superconductor, and in the absence of pinning should exhibit perfect conductivity without a Meissner effect (10). This phase can be thought of as a solid crystal of excitons, which early authors dubbed "excitonium" (4), and is the two-band analogue of the Wigner crystal instability of an interacting electron gas (10). This condensate is closely related to that in bilayer quantum wells (9), the coherence developing between electrons and holes in different bands ( Fig. 1) rather than in different layers. If found, this exciton condensate would be threedimensional, guaranteed to reside in thermodynamic equilibrium, and could potentially...

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 BiSrCaCuO ( = 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 behavior at low energy and/ behavior at high energy. Measurements of an overdoped crystal ( = 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.

One of the most fundamental properties of an interacting electron system is its frequency-and wave-vector-dependent density response function, χ(q, ω). The imaginary part, χ (q, ω), defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. χ quantifies the electronic compressibility of a material, its response to external fields, its ability to screen charge, and its tendency to form charge density waves. Unfortunately, there has never been a fully momentum-resolved means to measure χ(q, ω) at the meV energy scale relevant to modern electronic materials. Here, we demonstrate a way to measure χ with quantitative momentum resolution by applying alignment techniques from x-ray and neutron scattering to surface high-resolution electron energy-loss spectroscopy (HR-EELS). This approach, which we refer to here as "M-EELS", allows direct measurement of χ (q, ω) with meV resolution while controlling the momentum with an accuracy better than a percent of a typical Brillouin zone. We apply this technique to finite-q excitations in the optimally-doped high temperature superconductor, Bi 2 Sr 2 CaCu 2 O 8+x (Bi2212), which exhibits several phonons potentially relevant to dispersion anomalies observed in ARPES and STM experiments. Our study defines a path to studying the long-sought collective charge modes in quantum materials at the meV scale and with full momentum control.

A normal metal exhibits a valence plasmon, which is a sound wave in its conduction electron density. The mysterious strange metal is characterized by non-Boltzmann transport and violates most fundamental Fermi liquid scaling laws. A fundamental question is: Do strange metals have plasmons? Using momentum-resolved inelastic electron scattering (M-EELS) we recently showed that, rather than a plasmon, optimally-doped Bi2.1Sr1.9Ca1.0Cu2.0O8+x (Bi-2212) exhibits a featureless, temperature-independent continuum with a power-law form over most energy and momentum scales [M. Mitrano, PNAS 115, 5392-5396 (2018)]. Here, we show that this continuum is present throughout the fan-shaped, strange metal region of the phase diagram. Outside this region, dramatic changes in spectral weight are observed: In underdoped samples, spectral weight up to 0.5 eV is enhanced at low temperature, biasing the system towards a charge order instability. The situation is reversed in the overdoped case, where spectral weight is strongly suppressed at low temperature, increasing quasiparticle coherence in this regime. Optimal doping corresponds to the boundary between these two opposite behaviors at which the response is temperature-independent. Our study suggests that plasmons do not exist as well-defined excitations in Bi-2212, and that a featureless continuum is a defining property of the strange metal, which is connected to a peculiar crossover where the spectral weight change undergoes a sign reversal. arXiv:1903.04038v2 [cond-mat.str-el]

These authors contributed equally to this work 2The single-layered ruthenate Sr2RuO4 has attracted a great deal of interest as a spin-triplet superconductor with an order parameter that may potentially break time reversal invariance and host half-quantized vortices with Majorana zero modes. While the actual nature of the superconducting state is still a matter of controversy, it has long been believed that it condenses from a metallic state that is well described by a conventional Fermi liquid. In this work we use a combination of Fourier transform scanning tunneling spectroscopy (FT-STS) and momentum resolved electron energy loss spectroscopy (M-EELS) to probe interaction effects in the normal state of Sr2RuO4. Our high-resolution FT-STS data show signatures of the β-band with a distinctly quasi-one-dimensional (1D) character. The band dispersion reveals surprisingly strong interaction effects that dramatically renormalize the Fermi velocity, suggesting that the normal state of Sr2RuO4 is that of a `correlated metal' where correlations are strengthened by the quasi 1D nature of the bands. In addition, kinks at energies of approximately 10meV, 38meV and 70meV are observed. By comparing STM and M-EELS data we show that the two higher energy features arise from coupling with collective modes. The strong correlation effects and the kinks in the quasi 1D bands may provide important information for understanding the superconducting state. This work opens up a unique approach to revealing the superconducting order parameter in this compound.

The characteristic excitation of a metal is its plasmon, which is a quantized collective oscillation of its electron density. In 1956, David Pines predicted that a distinct type of plasmon, dubbed a ‘demon’, could exist in three-dimensional (3D) metals containing more than one species of charge carrier1. Consisting of out-of-phase movement of electrons in different bands, demons are acoustic, electrically neutral and do not couple to light, so have never been detected in an equilibrium, 3D metal. Nevertheless, demons are believed to be critical for diverse phenomena including phase transitions in mixed-valence semimetals2, optical properties of metal nanoparticles3, soundarons in Weyl semimetals4 and high-temperature superconductivity in, for example, metal hydrides3,5–7. Here, we present evidence for a demon in Sr2RuO4 from momentum-resolved electron energy-loss spectroscopy. Formed of electrons in the β and γ bands, the demon is gapless with critical momentum qc = 0.08 reciprocal lattice units and room-temperature velocity v = (1.065 ± 0.12) × 105 m s−1 that undergoes a 31% renormalization upon cooling to 30 K because of coupling to the particle–hole continuum. The momentum dependence of the intensity of the demon confirms its neutral character. Our study confirms a 67-year old prediction and indicates that demons may be a pervasive feature of multiband metals.

A crowning achievement of twentieth-century condensed matter physics is the Fermi Liquid paradigm, which reduces the incredibly complicated problem of >10 23 interacting electrons to a simple singleelectron picture. However, a growing class of materials has been found which dramatically violate Fermi Liquid theory, requiring quantum interactions to be carefully accounted for and thus earning the name "quantum materials" [1]. Quantum materials exhibit powerful and exotic phases, including superconductivity, multiferroicity, metal-insulator transitions, topological phases, etc., and understanding their driving mechanisms is a holy grail of modern physics [1,2].