Coexisting Fermi Liquid and Strange Metal Phenomena in Sr$_2$RuO$_4$

The strange metal is an enigmatic phase whose properties are irreconcilable with the established Fermi liquid theory of conductors. A fundamental question is whether a strange metal and a Fermi liquid are distinct phases of matter, or whether a material can be intermediate between or in a superposition of the two. We studied the collective density response of the correlated metal Sr$_2$RuO$_4$ by momentum-resolved electron energy-loss spectroscopy (M-EELS). We discovered that a broad continuum of non-propagating charge fluctuations (a characteristic of strange metals) and also a dispersing Fermi liquid-like collective mode at low energies and long wavelengths coexist in the same material at the same temperature. These features exhibit a spectral weight redistribution and velocity renormalization when we cool the material through the quasiparticle coherence temperature. Our results show not only that strange metal and Fermi liquid phenomena can coexist but also that Sr$_2$RuO$_4$ serves as an ideal test case for studying the interaction between the two.

Enhanced electron-phonon coupling for charge-density-wave formation in La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4+delta}$

Charge density wave (CDW) correlations are prevalent in all copper-oxide superconductors. While CDWs in conventional metals are driven by coupling between lattice vibrations and electrons, the role of the electron-phonon coupling (EPC) in cuprate CDWs is strongly debated. Using Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS), we study the CDW and Cu-O bond-stretching phonons in the stripe-ordered cuprate La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4+delta}$. We investigate the interplay between charge order and EPC as a function of doping and temperature, and find that the EPC is enhanced in a narrow momentum region around the CDW wave vector. By detuning the incident photon energy from the absorption resonance, we extract an EPC matrix element at the CDW wave vector of $Msimeq$ 0.36 eV, which decreases to $Msimeq$ 0.30 eV at high temperature in the absence of the CDW. Our results suggest a feedback mechanism in which the CDW enhances the EPC which, in turn, further stabilizes the CDW.

Crossover of Charge Fluctuations across the Strange Metal Phase Diagram

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 Bi$_{2.1}$Sr$_{1.9}$Ca$_{1.0}$Cu$_{2.0}$O$_{8+x}$ (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.

Anomalous density fluctuations in a strange metal

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, $chi(q,omega)$, would directly reveal the collective properties of the strange metal, but it has never been possible to measure this quantity with meV resolution. Here, we present the first measurement of $chi(q,omega)$ for a cuprate, optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ ($T_c=91$ 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 eV energy scale. This continuum displays a simple power law form, exhibiting $q^2$ behavior at low energy and $q^2/omega^2$ behavior at high energy. Measurements of an overdoped crystal ($T_c=50$ 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.