  In high temperature cuprate superconductors, it was found that the
superconducting transition temperature Tc depends on the number of CuO2 planes
(n) in the structural unit and the maximum Tc is realized in the trilayer
system (n=3). It was also found that the trilayer superconductors exhibit an
unusual phase diagram that Tc keeps nearly constant in the overdoped region
which is in strong contrast to the Tc decrease usually found in other cuprate
superconductors. The electronic origin of the Tc maximization in the trilayer
superconductors and its high Tc persistence in the overdoped region remains
unclear. By taking high resolution laser-based angle resolved photoemission
(ARPES) measurements, here we report our revelation of the microscopic origin
of the unusual superconducting properties in the trilayer superconductors. For
the first time we have observed the trilayer splitting in Bi2Sr2Ca2Cu3O10+d
(Bi2223) superconductor. The observed Fermi surface, band structures,
superconducting gap and the selective Bogoliubov band hybridizations can be
well described by a three-layer interaction model. Quantitative information of
the microscopic processes involving intra- and interlayer hoppings and pairings
are extracted. The electronic origin of the maximum Tc in Bi2223 and the
persistence of the high Tc in the overdoped region is revealed. These results
provide key insights in understanding high Tc superconductivity and pave a way
to further enhance Tc in the cuprate superconductors.
