Characterization of collective phenomena in cuprate superconductors by momentum-resolved electron energy loss spectroscopy

There exists a wide variety of strongly correlated electronic materials, including high temperature superconductors, exotic topological insulators, and charge density wave materials, that exhibit emergent behavior that cannot be understood through current theories of metals and insulators. These materials are classified by the low temperature ordered phases these materials take on, and there may be several ordered phases interacting over the various regions of phase space. High temperature superconductors, for example, may also exhibit Mott insulator, charge density wave, spin glass, and pseudogap phases in their phase diagram. The current consensus in describing most strongly correlated electron systems is, at best, qualitative, and understanding these ordered phases, the mechanisms that drive them, and their relation to related emergent phenomena is necessary for developing a microscopic understanding of this class of materials. The electron-electron interactions that drive the collective electronic state can be described by the dynamic charge susceptibility, χ(q,ω). This quantity encodes information about the propagation of density fluctuations in a system—the collective "sloshing" of electrons—as mediated by bosonic excitations. In order to measure this quantity, we have developed a new experimental technique, momentum-resolved electron energy loss spectroscopy (M-EELS). As a part of this development, we derived the theoretical framework for describing the scattering cross section in terms of the imaginary part of the dynamic susceptibility, χ''(q,ω), and implemented the software and hardware stack necessary to perform this measurement. Using this technique, we are able to measure finite momentum charge dynamics at 2 meV energy scales. We used M-EELS to investigate materials in the Bi2Sr2CaCu2O8+δ (Bi2212) family of cuprate high temperature superconductors. In studying optimally doped crystals, we have performed a full energy and momentum characterization of the low-energy dynamic susceptibility. Our measurement identifies known phonon modes, as previously seen in Raman scattering, infrared spectroscopy, and HR-EELS. Using a one-loop correction model, we have identified these modes as giving rise to the kinks in the electron spectral function as seen in ARPES, suggesting that these modes are related to the emergent phenomena exhibited in these materials. Furthermore, we observe a background in the optimally doped spectra that extends out to ∼1 eV, consistent with a marginal Fermi liquid description of these materials. In addition, from our measurements of the static component of the charge susceptibility, we have discovered diffuse, short-range charge order in optimally doped Bi2212. Proximity to the charge order state is suspected to be important in unconventional superconductivity, and has previously been seen in many families of high temperature superconductors, including underdoped Bi2212. At underdoping, we observe sharp elastic peaks consistent with previous charge order observations. At optimal doping, we observe diffuse scattering at low temperatures that exhibits a quasielastic broadening. This is a signature of the emergence of fluctuating order on a time scale of 180 fs