Towards a global theory for the high T_c cuprates: Explanation of the puzzling optical properties

Abstract

A theory has been worked out for the cuprates, which is based on the major features of their first-principles-derived electronic structure, including the contribution of a large-U band. Within this theory the puzzling physics of the cuprates is shown to be a behavior specific of their structure, within the regime of a Mott transition. The translational symmetry within the CuO_2 planes is disturbed by dynamical stripe-like inhomogeneities, which provide quasi-one-dimensional segments where the large-U scenario of separation between spin and charge is materialized. However, these charge carriers gain itineracy only due to the coupling with electrons in the regions where spin and charge are inseparable. Consequently a two-component scenario is obtained of heavy and light charge carriers, which are coupled through spin carriers. The theory could explain all the anomalous properties of the cuprates that were studied by it, including those observed in transport, tunneling, ARPES, and neutron-scattering results, the pairing mechanism and its symmetry, the observed phase diagram, and the occurrence of intrinsic nanoscale heterogeneity. Here this theory is applied to study a variety of puzzling optical properties of the cuprates, and again provides a natural explanation, for each property tested. This includes "violations" of the f-sum rule, Tanner's law, Homes' law, Uemura's law, the behavior of the n/m^* ratio with doping, the behavior in the heavily underdoped and overdoped regimes, states within the gap and on its edge, the drop in the ab-plane scattering rate below T^* and T_c, the gap-like behavior of the c-direction optical conductivity below T^*, and c-direction collective modes.