Many body effects on c- axis properties: out of plane coherence and bilayer splitting

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The out-of-plane hopping in layered metals with strong electronic correlation is analyzed theoretically. By studying the effects of in-plane interactions on the interlayer tunnelling we investigate one of the oldest unresolved problems of high-Tc cuprates, the so-called bilayer splitting. The strong electron-electron interactions within each layer reduce the quasiparticle weight, and modify the hopping between layers. We analyze the effect of the in-plane correlations on the interlayer hopping using a Renormalization Group scheme already applied to the problem of interlayer coherence. The bilayer band splitting acquires a significant temperature and doping dependence, and can be completely suppressed when the Fermi energy coincides with a Van Hove singularity.