Reexamining the strange metal charge response with transmission inelastic electron scattering

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, $\chi(\mathbf{q},\omega)$, particularly at large momenta. Electron energy-loss spectroscopy (EELS), performed in either reflection or transmission geometry, provides the most direct probe of $\chi(\mathbf{q},\omega)$. 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 ($\Delta E \approx 30$ meV) and high momentum resolution ($\Delta q \approx 0.01$ \r{A}$^{-1}$). 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 $q<0.15$ \r{A}$^{-1}$, we observe a highly damped plasmon whose linewidth is comparable to its energy. At larger momenta, $q>0.15$ \r{A}$^{-1}$, 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.