Consistency between reflection momentum-resolved electron energy loss spectroscopy and optical spectroscopy measurements of the long-wavelength density response of Bi₂Sr₂CaCu₂O_8+x

The density fluctuation spectrum captures many fundamental properties of strange metals. Using momentumresolved electron energy loss spectroscopy (M-EELS), we recently showed that the density response of the strange metal Bi2Sr2CaCu2O8+x (Bi-2212) at large momentum, q, exhibits a constant-in-frequency continuum (2019)] reminiscent of the marginal Fermi liquid (MFL) hypothesis of the late 1980s [C. M. Varma et al., Phys. Rev. Lett. 63, 1996 (1989)]. However, reconciling this observation with infrared (IR) optics experiments, which show a well-defined plasmon excitation at q similar to 0, has been challenging. Here we report M-EELS measurements of Bi-2212 using 4x improved momentum resolution, allowing us to reach the optical limit. For momenta q < 0.04 reciprocal lattice unites (r.l.u.), the M-EELS data show a plasmon feature that is quantitatively consistent with IR optics. For q > 0.04 r.l.u., the spectra become incoherent with an MFL-like, constant-in-frequency form. We speculate that, at finite frequency, omega, and nonzero q, some attribute of this Planckian metal randomizes the probe electron, causing it to lose information about its own momentum.