Reexamining the strange metal charge response with transmission inelastic electron scattering

TL;DR

This study reexamines the finite-$q$ dynamic charge response of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi-2212) using high-resolution transmission EELS with $ΔE$ ≈ 30–39 meV and $Δq$ ≈ 0.01–0.014 Å$^{-1}$. Ten measurements on five Bi-2212 flakes, benchmarked against an aluminum reference, reveal a broad, highly damped excitation near ~1 eV for $q<0.15$ Å$^{-1}$ and no dispersive plasmon at larger $q$, instead transitioning into an incoherent continuum. These results do not support the RPA-like plasmon dispersion reported in some early studies and align with recent M-EELS and RIXS findings that Bi-based cuprates are incoherent metals with strongly damped charge excitations. The work underscores the need to reconcile different experimental geometries and emphasizes that the strange metal charge response at finite momentum deviates markedly from conventional metallic behavior, informing theories of Planckian dissipation in high-$T_c$ cuprates.

Abstract

The strange metal remains one of the great unsolved problems for 21st century science. Since the early development of the marginal Fermi liquid phenomenology, it has been clear that progress requires detailed knowledge of the momentum- and frequency-dependent charge susceptibility, $χ(\mathbf{q},ω)$, particularly at large momenta. Electron energy-loss spectroscopy (EELS), performed in either reflection or transmission geometry, provides the most direct probe of $χ(\mathbf{q},ω)$. However, measurements over the past four decades have yielded conflicting results, with some studies reporting a dispersing RPA-like plasmon and others observing a strongly overdamped, incoherent response. Here we report a transmission EELS study of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi-2212) that simultaneously achieves high energy resolution ($ΔE \approx 30$ meV) and high momentum resolution ($Δq \approx 0.01$ Å$^{-1}$). To address issues of reproducibility, measurements were repeated ten times on five different Bi-2212 flakes, benchmarked against aluminum, a well-characterized Fermi liquid, and quantitatively compared with prior studies spanning four decades. At momenta $q < 0.15$ Å$^{-1}$, we observe a highly damped plasmon whose linewidth is comparable to its energy. At larger momenta, $q > 0.15$ Å$^{-1}$, this excitation does not disperse but instead evolves into an incoherent continuum, with no evidence for the RPA-like dispersion reported in some earlier works. Comparison with recent RIXS measurements on Bi-based cuprates supports the view that Bi-2212 is an incoherent metal with strongly damped charge excitations.

Figures (4)

• Figure 1: (a) Loss function of Bi-2212 at various momenta, measured with momentum-resolved T-EELS as reported in Ref. Nucker1989 (blue line), Ref. Wang1990 (orange line), Ref. Nucker1991 (purple line), compared to our current study (black line). (b) Low-energy loss function of Bi-2212 measured with momentum-integrated T-EELS from Ref. Terauchi1999 (blue line) compared to our current study (black line).(c) Same comparison as (b) but using the data from Ref. Terauchi1995. (d) Loss function of Bi-2212 at $q=0$ extracted from several representative IR optics studies Bozovic1990Humlicek1990Shimada1992Quijada1999Levallois2016.
• Figure 2: (a) Schematic representation of a T-EELS experiment. The momentum selection is made with a slot aperture in the diffraction plane, after which the beam is dispersed in the spectrometer. (b) The loss function $\mathrm{Im}(-1/\epsilon(\omega))$ at $q=0.1$ Å$^{-1}$, measured with EELS as previously published in Refs. Nucker1989Wang1990, and as measured in this study. The legend lists the energy resolution in each experiment, as given by the FWHM of the quasielastic line.
• Figure 3: (a) T-EELS intensity $I(q,\omega)$ measured from aluminum, a classic Lindhard metal, as a function of $q$ and $\omega$, with the energy axis scaled to the plasma frequency, $\omega_P$=15 eV. Both the bulk and surface plasmon modes are visible, in agreement with many past studies. (b) T-EELS intensity $I(q,\omega)$ measured under the same conditions from the strange metal Bi-2212, this time scaled to $\omega_P$=1 eV. No similarly well-defined excitation is visible. This panel shows the sum of datasets F and G, as labeled in Table \ref{['table:samples']}.
• Figure 4: Line plots of the T-EELS intensity of Bi-2212 measured at momenta between 0.01 and 0.25 Å$^{-1}$. Blue and orange curves denote measurements taken perpendicular and parallel to the supermodulation direction, respectively. (a) Data from two experiments (A and B; see Table \ref{['table:samples']}) measured over an energy range up to 10.5 eV. (b) T-EELS spectra in the 0-1.7 eV range (shaded region in panel (a)) for ten different measurements. Variations at small momentum transfer ($q = 0.05$ Å$^{-1}$) are primarily due to differences in momentum resolution, while the large anisotropy at $q = 0.25$ Å$^{-1}$ arises from a supermodulation Bragg peak at $q = 0.24$ Å$^{-1}$.