Electronic states and superconductivity in multilayer high-Tccuprates

We study electronic states of multilayer cuprates in the normal phases as functions of the number of ${\mathrm{CuO}}_2$ planes and the doping rate. The resonating valence bond wave function and the Gutzwiller approximation are used for a two-dimensional multilayer $t-t^{\prime }-t^{″}-J$ model. We calculate the electron-removal spectral functions at $(\pi ,0)$ in the ${\mathrm{CuO}}_2$ 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 ${\mathrm{CuO}}_2$ plane has different superconducting amplitude from the inner ${\mathrm{CuO}}_2$ 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.