Distinct Superconducting Gap on Two Bilayer-Split Fermi Surface Sheets in Bi_2Sr_2CaCu_2O_8+\delta Superconductor

High resolution laser-based angle-resolved photoemission measurements are carried out on an overdoped superconductor Bi_2Sr_2CaCu_2O_8+\delta with a T_\rm c 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. 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 \sim2 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.