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We report on results of our theoretical study of the c-axis infraredconductivity of bilayer high-Tc cuprate superconductors using a microscopicmodel involving the bilayer-split (bonding and antibonding) bands. An emphasisis on the gauge-invariance of the theory, which turns out to be essential forthe physical understanding of the electrodynamics of these compounds. Thedescription of the optical response involves local (intra-bilayer andinter-bilayer) current densities and local conductivities. The localconductivities are obtained using a microscopic theory, where thequasiparticles of the two bands are coupled to spin fluctuations. The couplingleads to superconductivity and is described at the level of generalizedEliashberg theory. Also addressed is the simpler case of quasiparticles coupledby a separable and nonretarded interaction. The gauge invariance of the theoryis achieved by including a suitable class of vertex corrections. The resultingresponse of the model is studied in detail and an interpretation of twosuperconductivity-induced peaks in the experimental data of the real part ofthe c-axis conductivity is proposed. The peak around 400/cm is attributed to acollective mode of the intra-bilayer regions, that is an analogue of theBogolyubov-Anderson mode playing a crucial role in the theory of thelongitudinal response of superconductors. For small values of the bilayersplitting, its nature is similar to that of the transverse plasmon of thephenomenological Josephson superlattice model. The peak around 1000/cm isinterpreted as a pair breaking-feature that is related to the electroniccoupling through the spacing layers separating the bilayers.

physical review. b, condensed matter and materials physics

Microscopic gauge-invariant theory of the c-axis infrared response of  bilayer cuprate superconductors and the origin of the superconductivity  induced absorption bands