Rapid suppression of the superconducting gap in overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$

Angle-resolved photoemission experiments have been performed on overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$. With a modest $T_c$ reduction of about 10%, the size of the superconducting gap decreases by about 35%. The rapid suppression of the superconducting gap is correlated with an almost complete collapse of the normal-state excitation gap and a dramatic evolution of the electronic structure near ($\pi , 0$) with doping.