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Understanding the physical properties of unconventional superconductors as
well as of other correlated materials presents a formidable challenge. Their
unusual evolution with doping, frequency, and temperature has frequently led to
non-Fermi-liquid (non-FL) interpretations. Optical conductivity is a major
challenge in this context. Here, the optical spectra of two archetypal
cuprates, underdoped HgBa$_2$CuO$_{4+\delta }$ and optimally-doped
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta }$, are interpreted based on the standard
Fermi liquid (FL) paradigm. At both dopings, perfect frequency-temperature FL
scaling is found to be modified by the presence of a second, gapped electronic
subsystem. This non-FL component emerges as a well-defined mid-infrared
spectral feature after the FL contribution -- determined independently by
transport -- is subtracted. Temperature, frequency, and doping evolution of the
MIR feature identify a gapped rather than dissipative response. In contrast,
the dissipative response is found to be relevant for pnictides and ruthenates.
Such an unbiased FL/non-FL separation is extended across the cuprate phase
diagram, capturing all the key features of the normal state and providing a
natural explanation why the superfluid density is attenuated on the overdoped
side. Thus, we obtain a unified interpretation of optical responses and
transport measurements in all analyzed physical regimes and all analyzed
compounds.
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