Mapping of the formation of the pairing gap in Bi₂ Sr₂ Ca₂ CuO_{8 + δ}

High-resolution scanning tunneling microscopy has been used to study the formation of Cooper pairs in the cuprate superconductor Bi₂ Sr₂ CaCu₂ O_{8 + δ}. We measured the evolution of the tunneling gap as function of temperature (from 20 to 180 K) and doping (x = 0.12 - 0.22). Real space mapping of the density of states establish that the tunneling gap observed below the transition temperature (T_c) vanish inhomogenously in space, leading to the formation of a unique intermediate state, where nanoscale regions of pairing are present. Despite the inhomogeneity, we find that locally the gap spectrum evolves smoothly across T_c and, over a wide range of doping (x ≥ 0.16), the energy gap Δ vanishes at a temperature T_p, following a local criterion 2 Δ / k_B T_p = 7.9 ± 0.5. Our observations suggest that at least in optimally doped and overdoped samples, all our measurements can be described with one single energy scale and that the gap measured above and below T_c must have the same origin. In the underdoped regime, this simple description fails to capture the temperature evolution of the local electronic states, indicating the presence of an additional phenomenon.