The density fluctuation spectrum is a key experimental observable that
captures many of the fundamental properties of strange metals. Using
momentum-resolved electron energy-loss spectroscopy (M-EELS), we recently
showed that the density response of the strange metal
Bi2βSr2βCaCu2βO8+xβ (Bi-2212) at large momentum, q, exhibits a
constant-in-frequency continuum reminiscent of the marginal Fermi liquid
hypothesis of the late 1980s. However, reconciling this observation with
infrared optics experiments, which establish a well-defined plasmon excitation
at q=0, has been challenging. Here we report M-EELS measurements of Bi-2212
using 4Γ improved resolution, allowing us to reach the optical limit
where direct comparison with IR optics is possible. We find that the M-EELS
data are consistent with a well-defined plasmon for q<0.04 r.l.u.. At
q>0.04 r.l.u., the spectra become incoherent with an MFL-like,
constant-in-frequency form. We speculate that, at finite frequency, Ο,
and nonzero q, some attribute of this Planckian metal randomizes the probe
electron in a way that causes it to lose information about its own momentum.Comment: 6 pages, 4 figure