Electronic States and Superconductivity in Multi-layer High-Tc Cuprates

We study electronic states of multilayer cuprates in the normal phases as functions of the number of CuO_2 planes and the doping rate. The resonating valence bond wave function and the Gutzwiller approximation are used for a two-dimensional multilayer t-t'-t''-J model. We calculate the electron-removal spectral functions at (\pi,0) in the CuO_2 plane next to the surface to understand the angle-resolved photoemission spectroscopy (ARPES) spectra. We find that the trilayer spectrum is narrower than the bilayer spectrum but is wider than the monolayer spectrum. In the tri- and tetralayer systems, the outer CuO_2 plane has different superconducting amplitude from the inner CuO_2 plane, while each layer in the bilayer systems has same amplitude. The recent ARPES and NMR experiments are discussed in the light of the present theory.