Optical model-solution to the competition between a pseudogap phase and a Mott-gap phase in high-temperature cuprate superconductors

We present a theoretical framework for a quantitative understanding of the full doping dependence of the optical spectra of the cuprates. In accord with experimental observations, the computed spectra show how the high-energy Mott features continue to persist in the overdoped regime even after the mid-infrared (MIR) peak originating from the pseudogap has collapsed in a quantum critical point. In this way, we reconcile the opposing tendencies of the MIR and Mott peaks to shift in opposite directions in the optical spectra with increasing doping. The competition between the pseudogap and the Mott gap also results in rapid loss of spectral weight in the high energy region with doping.