In-plane optical features of the underdoped La₂CuO₄ based compounds: theoretical multiband analysis

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The three-component ab-plane optical conductivity of the high-Tc cuprates is derived using the gauge invariant response theory, and compared to the data previously obtained from the optical reflectivity measurements in the La₂CuO₄ based families. The valence electrons are described by the Emery three-band model with the antiferromagnetic correlations represented by an effective single-particle potential. In the 0 < delta < 0.3 doping range, it is shown that the total spectral weight of the three-band model is shared between the intra- and interband channels nearly in equal proportions. At optimum doping, the low-frequency conductivity has a (non-Drude) nearly single-component form, which transforms with decreasing doping into a two-component structure. The mid-infrared spectral weight is found to be extremely sensitive to the symmetry of the effective single-particle potential, as well as to the doping level. The gauge invariant form of the static and elastic Raman vertices is determined, allowing explicit verification of the effective mass theorem and the related conductivity sum rules.