  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.
