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High resolution laser-based angle-resolved photoemission measurements werecarried out on an overdoped $Bi_2Sr_2CaCu_2O_{8+\delta}$ superconductor with aTc of 75 K. Two Fermi surface sheets caused by bilayer splitting are clearlyidentified with rather different doping levels: the bonding sheet correspondsto a doping level of 0.14 which is slightly underdoped while the antibondingsheet has a doping of 0.27 that is heavily overdoped, giving an overall dopinglevel of 0.20 for the sample. Different superconducting gap sizes on the twoFermi surface sheets are revealed for the first time. The superconducting gapon the antibonding Fermi surface sheet follows a standard d-wave form while itdeviates from the standard d-wave form for the bonding Fermi surface sheet. Themaximum gap difference between the two Fermi surface sheets near the antinodalregion is $\sim$2 meV. These observations provide important information forstudying the relationship between the Fermi surface topology andsuperconductivity, and the layer-dependent superconductivity in hightemperature cuprate superconductors.

Distinct Superconducting Gap on Two Bilayer-Split Fermi Surface Sheets in $Bi_2Sr_2CaCu_2O_{8+\delta}$ Superconductor