One of the most fundamental properties of an interacting electron system is its frequency- and wave-vector-dependent density response function, \chi({\bf q},\omega). The imaginary part, \chi''({\bf q},\omega), defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. \chiχ 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 \chi({\bf q},\omega) at the meV energy scale relevant to modern electronic materials. Here, we demonstrate a way to measure \chiχ 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 \chi''({\bf q},\omega) 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_22Sr_22CaCu_22O_{8+x}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.

Bose condensation has shaped our understanding of macroscopic quantum phenomena, having been realized in superconductors, atomic gases, and liquid helium. Excitons are bosons that have been predicted to condense into either a superfluid or an insulating electronic crystal. Using the recently developed technique of momentum-resolved electron energy-loss spectroscopy (M-EELS), we studied electronic collective modes in the transition metal dichalcogenide semimetal 1T-TiSe2 Near the phase-transition temperature (190 kelvin), the energy of the electronic mode fell to zero at nonzero momentum, indicating dynamical slowing of plasma fluctuations and crystallization of the valence electrons into an exciton condensate. Our study provides compelling evidence for exciton condensation in a three-dimensional solid and establishes M-EELS as a versatile technique sensitive to valence band excitations in quantum materials.

Identifying what broken symmetries are present in the cuprates has become a major area of research. Many authors have reported evidence for so-called "Q ∼ 0"order that involves broken inversion, mirror, chiral, or time-reversal symmetry that is uniform in space. Not all these observations are well understood and new experimental probes are needed. Here we use resonant soft x-ray scattering (RSXS) to search for Q ∼ 0 order in Bi2.1Sr1.9CaCu2O8+x (Bi-2212) by measuring the region of a forbidden Bragg peak, 0; 0; 3 , which is normally extinguished by symmetry but may become allowed on resonance if valence band order is present. Using circularly polarized light, we found that this reflection becomes allowed on the Cu L3 resonance for temperatures Tc < T < T+, though remains absent in linear polarization and at other temperatures. This observation suggests the existence of spatially uniform valence band order near the pseudogap temperature. In addition, we observed periodic oscillations in the specular reflectivity from the sample surface that resemble thin film interference fringes, though no known film is present. These fringes are highly resonant, appear in all polarizations, and exhibit a period that depends on the location where the beam strikes the sample surface. We speculate that these fringes arise from interaction between some intrinsic valence band instability and extrinsic structural surface morphologies of the material. Our study supports the existence of some kind of Q ∼ 0 broken symmetry state in Bi-2212 at intermediate temperatures. Further studies using a microfocused beam, which could disentangle microscopic effects from macroscopic heterogeneities, are needed to ascertain the universality of the effect.

The single-layered ruthenate Sr$_2$RuO$_4$ 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 Sr$_2$RuO$_4$. Our high-resolution FT-STS data show signatures of the \beta-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 Sr$_2$RuO$_4$ 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.