  High resolution laser-based angle-resolved photoemission measurements were
carried out on an overdoped $Bi_2Sr_2CaCu_2O_{8+\delta}$ superconductor with a
Tc of 75 K. Two Fermi surface sheets caused by bilayer splitting are clearly
identified with rather different doping levels: the bonding sheet corresponds
to a doping level of 0.14 which is slightly underdoped while the antibonding
sheet has a doping of 0.27 that is heavily overdoped, giving an overall doping
level of 0.20 for the sample. Different superconducting gap sizes on the two
Fermi surface sheets are revealed for the first time. The superconducting gap
on the antibonding Fermi surface sheet follows a standard d-wave form while it
deviates from the standard d-wave form for the bonding Fermi surface sheet. The
maximum gap difference between the two Fermi surface sheets near the antinodal
region is $\sim$2 meV. These observations provide important information for
studying the relationship between the Fermi surface topology and
superconductivity, and the layer-dependent superconductivity in high
temperature cuprate superconductors.

Superconductivity;Materials Science;Strongly Correlated Electrons